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... Excellence in manufacturing is just the admission fee for being a player in the larger game of SC competition. In the supply chain context, there are three kinds of competitions: a) competition among the firms of one tier of a specific supply chain, b) competition among the firms of different tiers of a specific supply chain, and c) competition between rival supply chains [3][4][5][6][7][8]. There is a limited analytic research with focus on the multi-product competitive supply chain interactions [8][9][10][11] and particularly, supply chain versus supply chain competition and design. ...

... There are many research papers investigating the SCND problem, but unfortunately, there are few that talk about competitive SCND between two SCs [3][4][5][6][7][15][16][17], and also none of them represent the multi-product competitive SCND between two SCs. On the other hand, there are few researches around multi-product competition between supply chains without designing concerns [8][9][10][11]. ...

... The price and service level were competition criteria and strategic decisions were made for the upper-level model. Rezapour et al. [5] proposed a bi-level model in order to represent the competition between two single-product SCs with probabilistic demand and distance as competition criterions. They solve the bi-level model using Nash equilibrium and an exact meta-heuristic algorithm. ...

According to the recent studies, competition between supply chains (SCs) will play a noticeable part of competition in the future's market. This study considers a SC vs. SC multi-product competition in the duopolistic markets. Pricing, location, transportation and production decisions are taken in a Stackelbrg game formulated as bi-level model. These supply chains (called leader and follower) are three-stage, multi-product, multi-source, and single-period SCs. Karush-Kuhn-Tucker (KKT) conditions are applied in order to transform the presented bi-level model into a single-level mixed integer nonlinear programming (MINLP). Due to computational complexity of the problem, an efficient Hybrid Genetic Algorithm (HGA) is proposed to solve the large size problems. In order to obtain more robust solutions, Taguchi method is applied to calibrate hybrid meta-heuristic parameters. The efficiency of the proposed HGA is investigated through the comparisons with optimal solutions and also with GA. Managerial insights are proposed alongside with the Sensitivity Analysis for important parameters.

... [13], Rezapour ve Farahani [23], Rezapour vd. [24], Rezapour vd. [25] önceden var olan rekabetçi bir tedarik zinciri varlığında piyasaya giren bir tedarik zinciri tasarlamak için tedarik zincirleri arasında dinamik rekabeti varsayan iki seviyeli bir model geliştirmişlerdir. ...

... Değişken fiyatlar ve hizmet seviyelerini öngörülü talebin esnek olduğu Rezapour ve Farahani [23], ve talebin fiyat ve mesafeye göre esnek olduğu Rezapour vd. [24] çalışmaları çözüm için kesin ve metasezgisel algoritmalar önermişlerdir. Talebin deterministik ve fiyata bağlı olduğu Rezapour vd. ...

Limited natural resources and unconscious consumption have led to a substantial increase in the rate of processing waste material instead of raw materials in recent years and changed the dynamics of Supply Chain Management (SCM) by making the industrial environment more competitive. The interest in Closed Loop Supply Chain (CLSC) design and optimization is increased with great care being taken to reverse logistics in order to respond to customer pressures as well as environmental concerns associated with the increasing number of end-of-life products. CLSC has extensive literature and many models have been developed to optimize supply chain costs. Most of the literature deals with single supply chains and ignores existing competing supply chains. However, in today's competitive markets, supply chains are integrated with each other by several competitive companies and work together to gain more market share. In such an environment, there are different forms of competition within and between supply chains. In this context, the paper addresses the problem of design and optimization of distribution networks in multi-level competitive CLSC management consisting of two producers, a collection & recycling center and customers trying to improve sustainable consumption by increasing the willingness to return used products with some incentives for product recovery. In order to reach a consensus solution for decision makers who have a different purpose in CLSC management, four different Interactive Fuzzy Programming (IFP) approaches are used and the results are analyzed.

... After the outer part of the model determined the network structure, it predicted the market variable priceand service-level competition under the elastic demand of random price and service level. Rezapour et al. [16] proposed a bilevel model for a Stackelberg game, describing the competition between two single-product SCs in which demand was elastic in terms of retail price and distance. Fallah et al. [17] studied single-product competition between two closed-loop supply chains with stochastic demand in simultaneous and Stackelberg competition, respectively. ...

... Constraints (15) and (19) show the capacity constraints of manufacturers and retailers, respectively. Constraints (16) and (17) are the inventory constraints of products in manufacturers. Constraints (20) and (21) are the inventory constraints of products in retailers. ...

This paper studies a supply chain network design model with price competition. The supply chain provides multiple products for a market area in multiple periods. The model considers the location of manufacturers and retailers and assumes a probabilistic customer behavior based on an attraction function depending on both the location and the quality of the retailers. We aim to design the supply chain under the capacity constraint and maximize the supply chain profit in the competitive environment. The problem is formulated as a mixed integer nonlinear programming model. To solve the problem, we propose two heuristic algorithms—Simulated Annealing Search (SA) and Particle Swarm Optimization (PSO)—and numerically demonstrate the effectiveness of the proposed algorithms. Through the sensitivity analysis, we give some management insights.

... Concerns on environmental degradation, resource depletion, resilience, and competitiveness of economy are shaping the current view in many industrial sectors, including forestry [3,4], which employs and provides goods and services for many around the world [5,6]. Dependence of human society on wood consumption is undeniable [7,8] and substantial improvements are expected in all the supply chain so as to ensure its sustainability [9][10][11]. In this context, providing updated information to support planning and decision making is of crucial importance for the forestry economic sector. ...

Forest policies aiming for a greener future and decarbonization require scientific support to help in decision making on resource economy and sustainability of forest operations. Timber skidding is one of the most prevalent options in wood extraction around the world. While its operational and environmental performance is affected by several factors, of which the extraction distance, removal intensity, and machine capabilities are of first importance, there are few studies on the subject in low-access and low-intensity removals. Based on a time study which accounted for production and fuel consumption, this work modeled and quantified productivity and fuel consumption for such operational conditions. Dependence of fuel and time consumption on relevant operational factors was modeled by least square stepwise ordinary regression techniques. Then, the developed models and summary statistics were used to simulate productivity and fuel consumption for a wide range of extraction distances. The main results indicate that, for removal intensities in the range of 7 to 15 m 3 /ha, productivity of skidding operations in mature broadleaved forests depended heavily on the extraction distance. Taking as a reference an extraction distance of 200 m, productivity halved at 800 m, and decreased to one fourth at 2000 m. For the same conditions, fuel consumption increased linearly, being doubled at 800 m and four times higher at 2000 m. Although the unit fuel consumption increased linearly as a function of extraction distance, its magnitude of increment was much lower. The results of this study indicate that shortening the extraction distances may be the best option in increasing the operational and environmental performance of skidding operations. This may be achieved by developing further the forest road network, which, in addition to the benefits for harvesting operations, could support a more sustainable forest management.

... The modern global economy has developed interconnected and complex supply chains which are largely due to the benefits companies have found in sophisticated trends and strategies, such as global outsourcing, supply base rationalisation, just-in-time deliveries, and lean practices (Hasani & Khosrojerdi, 2016;Rezapour, Farahani, Dullaert, & De Borger, 2014). Although these practices have led to lower costs, higher quality, and enhanced business agility for many supply chains, they are not without risk (Tang, 2006). ...

The modern global economy has developed interconnected and complex supply chains largely due to the benefits companies have found in sophisticated trends and strategies; however, these practices are not without risk. In the wake of disruptions caused by COVID-19, natural disasters, Brexit, and the US–China trade war, supply chain resilience has become more important than ever. This study aims to provide a comprehensive review of recent literature on resilient supply chain network design (RSCND). The focus was on studies that used a quantitative approach. This study utilised a systematic literature review methodology to evaluate the body of literature on RSCND. The main contributions of this paper are as follows: (1) exploring and analysing existing literature on RSCND, particularly focusing on different types of resilience measures used from an analytical modelling perspective; (2) presenting a new way to classify the quantitative resilience measures used for RSCND and clarifying the implications of incorporating it in terms of costs and benefits; and (3) identifying the gaps and limitations of existing literature and proposing a list of potential issues for future research directions. An analysis of the literature shows that existing resilience measures mainly focus on the resilience of the nodes. The benefits of incorporating resilience measures in the RSCND are illustrated quantitatively in terms of monetary value, lost sales, and demand fulfilment. This study is the first attempt to combine studies on the RSCND using quantitative resilience measures. This study can serve as a starting point for understanding the different resilience measures discussed in the literature, how to incorporate them in designing new or redesigning existing supply chain networks, and the benefits associated with their implementation. Although only 21 studies were found in the analysis, we believe that this topic has a huge scope for future research.

... However, this view is not universally accepted in the literature as a new opportunity for the logistics supplier, with some arguing that 3DP technologies might not need any distribution infrastructure. Rezapour, Farahani, Dullaert and Borger (2014) argue that organisations can adopt 3DP technologies by piggybacking on the existing efficient market-based infrastructure to shorten the delivery between sites. Researchers, therefore, have argued that 3DP might be a game-changer for the logistics suppliers and transfer to become a 3DP-enabled logistics supplier (Arbabian & Wagner, 2020;Li, Li et al., 2016). ...

3-Dimensional Printing (3DP) has been widely used in the circular supply chain. Still, most of the literature focused on addressing only the manufacturer's adoption of 3DP and how it influences the supply chain. A growing number of non-manufacturer (e.g., logistic suppliers) have adopted 3DP, but its impact on manufacturers and customers is still underexplored. This paper uses a two-player single-period supply chain model, supported by an in-depth interview, to investigate how the logistics supplier's 3DP adoption impacts the circular supply chain in the spare parts aftersales market. The findings show that cost reduction of 3DP does not always benefit the logistics supplier. Still, this finding opens a new revenue stream for the logistics supplier and the integrated supply chain. Further, the manufacturer can financially benefit from such adoption only when the cost of 3DP production is relatively high. Interestingly, the logistics supplier can use 3DP adoption as a game-changer to become a new "green manufacturer", thereby posing a strategic threat that can influence the traditional manufacturer's decisions regarding financial benefits. Customers can also enjoy more surplus when logistics suppliers adopt low-cost 3DP. This study is one of the first to investigate how non-manufacturer 3DP adoption impacts the circular supply chain.

... Song et al. [20] studied the price competition and cooperation between two hub ports from the perspective of game theory. In addition, Rezapour et al. [21] studied the competition between the new supply chain and the existing supply chain. The research involved product pricing and distribution center and retailer location issues, and carried out small-scale and large-scale solutions at the same time. ...

With the rapid development of the logistics market, the construction of an efficient “channel + hub + network” logistics system, that is, a hub-and-spoke logistics network, is of great importance to enterprises. In particular, how to reduce costs and increase efficiency in both the construction of network facilities and actual operations, and to formulate reasonable prices for the logistics service needs in the entire market are crucial strategies and decisions for enterprises. Under such a background, this article starts from the perspective of duopoly logistics enterprises that jointly build networks and allow the transfer of surplus capacity and carbon credits, and studies the hub-and-spoke logistics network design that also considers the relationship between service pricing and co-opetition. Considering the corporate profit and difficulty of implementation as a whole, the co-opetition is a better choice than the complete competition and perfect cooperation. In addition, the remaining capacity of the company, the transfer of carbon credits, the joint construction and sharing of hubs, and strategic cooperation in the area of corporate common pricing under the price framework agreement are conducive to the realization of an increase in corporate operating profits, a better market share and more favorable pricing.

... They then examined the presented model for a real industrial case. In another study, Rezapour et al. (2014) proposed a novel bi-level competitive model for determining the strategic facility location along with flows decisions. The customers' demand was considered to be elastic with regard to price and distance. ...

This paper utilizes a Stackelberg game approach for designing resilient supply chains under price competition and facilities disruption. The impact of using resilience strategies, namely holding extra inventory at distribution centers and considering reliable distribution centers, was investigated on the supply chains competition. A two-phase bi-level mixed integer programming approach is utilized to model the assumed problem, and a decomposition-based approach is utilized to solve the resultant model. Then, the performance of the presented model and solution approach is examined through numerical experiments. Finally, some discussions are presented with a number of examples, and managerial insights are suggested for the conditions similar to the assumed problem. Our analysis focuses on exploring the advantages of considering resilience strategies in the competitive supply chain netwrok design problems.

... This assumption is valid in view of the practice of some online stores in Taobao.com. When customers buy the product in the physical store, they incur the travel cost, which we assume as c t (Rezapour et al., 2014;Wollenburg et al., 2018). ...

We consider a dual-channel supply chain consisting of a manufacturer, an online retailer, and a physical store, where the online order is fulfilled by either the conventional wholesale contract or the drop-shipping contract. We study the vertical and horizontal competitions among the three members via considering different power structures of the supply chain. To derive the contract choices of the online retailer and the manufacturer, we construct three game models to determine their optimal pricing decisions, investigate the corresponding applicable conditions and the most profitable power structure under each contract, then compare the profits between the two contracts. We find that: (i) The drop-shipping contract is the only option when the product's matching probability and the travel cost to the physical store are relatively low. (ii) No matter under which contract, the online retailer can benefit from the unbalanced bargaining power between the dual-channel retailers. But the manufacturer makes the most profit if the two retailers have the same bargaining power under the wholesale contract or if the online retailer is the first-mover under the drop-shipping contract. (iii) For the online retailer, the contract choice always depends on the profit-sharing ratio. For the manufacturer, the contract choice depends on the profit-sharing ratio if the product's matching probability and the travel cost to the physical store are moderate. Otherwise, either of the two contracts should be adopted under certain circumstances regardless of the profit-sharing ratio.

... For instance, Apple Company reuses the material of the old iPhone 6 in creating new products in order to decrease the need for raw material and through this approach, they kept 28.2 million pounds of its waste out of landfills in the year 2016. 1 The Xerox Company has succeeded in reducing landfill waste through recycling more than145 million pounds of waste over a period of time two decades. 2 Besides, from the manufacturers' perspective, paying attention to these issues derives advantages for them such as saving in costs, increasing customer willingness to return and larger market demand, and as a result company growth, enhanced profit and competitive advantages gained (Lee, Realff, and Ammons 2011;Golicic and Smith 2013;Rezapour et al. 2014;Eskandarpour et al. 2015;Gao et al. 2016). For example, Xerox Company saved more than 200 million dollars by remanufacturing during five years. ...

This paper addresses coordination and competition problem in two reverse supply chains each having its own exclusive retailer and manufacturer. The chains have various collecting channel structures so that one of them uses the advantages of dual channels, where the consumer can return their e-waste through direct or traditional channels, while its competitor collects obsolete products only through its traditional channel. The willingness to return in each channel is a function of self- and cross-discounts of the competitors. Four decision scenarios are investigated; the first and second chain respectively select, Decentralised-Decentralised, Centralised-Centralised, Centralised-Decentralised or Decentralised-Centralised scenario. The closed-form optimal solution of each channel is derived based on the Stackelberg game when the second chain acts as a leader. The most economical scenario is determined by using a Non-Zero-Sum game when each chain plays as a single player in the game. To coordinate the members’ decisions and to convince unsatisfied members, two coordination contracts are offered. Numerical investigations reveal that direct channel suggests more discount and obtains more share of market. The results show that Centralised-Centralised scenario is the best decision from the SCs’ perspective which proposing contracts are able to persuade members to change their strategy to a global decision.

... For example, an analytical multi-attribute decision making framework was constructed to evaluate the 4PL operating models for a logistics company that is willing to expand its operations [28]. In recent days, to identify the cost-effective ways of increasing the operational efficiency of logistics, a variety of interesting issues have been investigated, such as the routing problem [9,19,29,30] and the network design problem [2,[31][32][33]. The above models developed so far assumed that the 4PL could have full information during the decision-making process. ...

As a supply chain solution integrator, fourth party logistics (4PL) has become an important focus for improving the operational efficiency of the logistics industry in recent days. This paper addresses the mechanism design problem of the 4PL for selecting a third party logistics (3PL) provider who involves loss-averse behavior to form a longer-term strategic partnership in multi-attribute reverse auctions. Due to fluctuating costs of energy or labor and unintentional delivery failures like traffic jam or technology malfunctions, we consider two incomplete attributes, namely cost uncertainty and delivery risk. Integrating the loss-averse behavior of 3PLs, based on the prospect theory, the bid decision model is constructed to obtain 3PLs’ bidding strategies. The corresponding efficient and optimal scoring auctions that consist of cost-sharing contract and contingent penalty are developed to maximize the ex ante expected profit of the system or the 4PL depending on whether the 4PL is willing to cooperate or not. Theoretical analysis verified by numerical examples illustrates the advantage of the proposed mechanisms. Impacts of model parameters on the 4PL’s decision are also investigated and managerial insights are presented.

... They assumed that the network of the new SC is set "once and for all" but further price and service level modifications are possible. Rezapour et al. [41], in another research, used dynamic BLP to design an entrant SC for competition against an existing SC where demand was elastic with respect to price and distance. They modeled the problem with the strategic facility location and flow decisions and proposed exact and metaheuristic algorithms. ...

... Moreover, environmental legislation prescribes manufacturers to invest in recycling and remanufacturing process in order to decrease the need for earth' natural resources and also waste out of landfills (Qiang, 2015). For instance, Xerox Company could keep more than 145 million pounds of waste out through recycling process during two decades ago. 1 Moreover, employment growth, improving productivity, increasing competitive and economic advantages are the other results of implementing remanufacturing process which are considered as the important motivations for industrials (Eskandarpour et al., 2015;Rezapour et al., 2014;Golicic and Smith, 2013;Lee et al., 2011). ...

Increasing attention to sustainable development issues and competition between different supply chains are forcing the stakeholders to use different incentives to capture more market share. Collecting channels are one of the effective topics in the reverse competitive chains. Because of the importance of this issue, we consider two collecting reverse supply chains consist of a retailer and a manufacturer who compete together by proposing more rewards to the customers. One of these chains tries to facilitate the collecting process and obtain more market share by using the direct and traditional channels advantages. The other one uses only the traditional channel. Hence, the return rate of each channel not only depends on the self-reward but also is function of the cross-rewards suggested to the customer by the competitors in the other channels. The competitive environment in our model consists of internal and external competitions. Competition between two channels of one chain infers to internal competition, external competition that points out to competition among two supply chains. We apply three game theory structures to obtain the optimal channels rewards: Nash, Nash-Stackelberg-first supply chain, and Nash-Stackelberg-second supply chain. Finally, we comparing the results of decision variables and profit function of members under three structures through numerical analysis. Our numerical investigations show that e-channel because of less costly than traditional channel proposes more appropriate reward to customers, so this channel could obtain a more substantial share of the market. Moreover, the results reveal that highest return rate occurred under Nash scenario while Nash-Stackelberg-first supply chain and Nash-Stackelberg-second supply chain are the most economic scenarios for the first and the second supply chains, respectively.

... Consumers' attention to environmental issues has forced companies to promote their recycling capability. The development of reverse supply chains, which are well suited to sustainable supply chains, will likely increase the economic and competitive advantages of a business (Eskandarpour et al., 2015;Golicic and Smith, 2013), and the successful implementation of reverse supply chains can lead to a corresponding increase in productivity and better customer service (Rezapour et al., 2014). ...

In this paper, a two-stage reverse supply chain (RSC) is analyzed where the retailer pays rewards to customers to return obsolete products and the manufacturer refurbishes eligible returned items through remanufacturing process. Remanufacturing capacity is assumed as a stochastic variable. Under the uncertainty of remanufacturing capacity, it is possible that some inspected and eligible items could not be processed. If a bought item could not be processed, it should be salvaged at low prices and be considered a lost profit. In such situations, increasing the number of returned obsolete products is suitable where there is a high probability for enough capacity in the remanufacturing process. In this study, a stochastic model is developed to find the optimal paid reward to customers under both scenarios, including decentralized (where the retailer decides independently on reward amount) and centralized (where reward amount is determined based on the whole channel interest). By sharing the manufacturer's capacity risk, a revenue sharing contract is proposed to convince the retailer to consider uncertainty of remanufacturing capacity in deciding reward amount. Under the proposed contract, a part of retailer revenue is postponed until the remanufacturing process is completed. Non-eligible items, as well as those that cannot be processed due to insufficient capacity are not involved in revenue sharing with the retailer. Our numerical investigations reveal that the proposed scheme is able to coordinate the investigated RSC under the uncertainty of remanufacturing capacity. Contrary to the decentralized scenario, the proposed model recommends fewer paid rewards to customers when there is a high possibility of insufficient capacity in the remanufacturing process.

... Due to the increase in globalization and international competition, managing supply chains has become crucial in recent years. In this context, the challenges to minimize emissions of greenhouse gases call for major reexamination of fossil energy-based present technological paradigms favoring decisions on investments in clean energy, to support sustainable development (Cagliano et al. 2008;Brandi et al. 2013;Rezapour et al. 2014). All around the world, companies, government and different stakeholders were compelled to improve their ability to cope with the sustainability requirements when dealing with suppliers and customers. ...

In the present work, we propose a theoretical model to identify and prioritize risks involved in a biofuel supply chain. We adopt a set of indicators associated with determinant factors of the supply chain to identify risks that are characterized through a risk matrix. We consider the five largest world biodiesel producers and included China due to its global market importance and potential impacts of its growth on the environment and society. To determine the impacts and the probability of occurrence of risks, we use the Canberra distance, as metrics. To facilitate the analysis and interpretation, a convenient manner is to express the results in terms of matrices. To exemplify the potentiality of the scheme and for the sake of simplicity, a more comprehensive discussion is focused on the Brazilian case, restricted to the Technology and Innovation, and Integration, Logistics and Infrastructure determining factors (dimensions) of the biodiesel supply chain. Concerning these determining factors, the Brazilian biodiesel chain shows strong vulnerability when compared with developed and developing countries, despite that the evolution of the data over recent years indicates small improvements in Integration, Logistics and Infrastructure dimension. Although in this work the calculations are restricted to the Canberra distance, the present approach may be applied to other distances to compare or validate the results. This work presents a contribution to model vulnerability to risks, providing to policy makers and stakeholders a tool to design, analyze and improve sustainability system by measuring its risks. The study of the contribution of each indicator suggests corrections to be taken and which indicators should be prioritized.

... Nash equilibrium was used to capture the firms' behaviour along with the supply chain network topologies. Rezapour (2014) developed a bi-level model for designing an entrant supply chain in the presence of a pre-existing competing supply chain where demand is elastic with respect to price and distance. A dynamic competition was assumed between the new and pre-existing supply chains in retailers' level and probabilistic customers' behaviour. ...

In post-disaster relief, competitive emergency service providers place their stations quickly for timely rescue activities. To shorten the rescue time of the emergency services and ensure the profit of emergency service providers, an extended game model is formulated to solve the problem based on the classical Hotelling model. In the new model, logistics cost is paid by service providers who can obtain honour profit through providing service for the victims. The victims endure waiting times that consist of periods of response time and travelling time. The waiting times affect the victims' decisions and affect the equilibrium prices and profits. Numerical analysis implies that service providers obtain the highest profits on their equilibrium price when their locations are decided. Furthermore, locating both players near the ends of the disaster-affected line city is beneficial to increase the gross profits.

... Nash equilibrium was used to capture the firms' behaviour along with the supply chain network topologies. Rezapour (2014) developed a bi-level model for designing an entrant supply chain in the presence of a pre-existing competing supply chain where demand is elastic with respect to price and distance. A dynamic competition was assumed between the new and pre-existing supply chains in retailers' level and probabilistic customers' behaviour. ...

In post-disaster relief, competitive emergency service providers place their stations quickly for timely rescue activities. To shorten the rescue time of the emergency services and ensure the profit of emergency service providers, an extended game model is formulated to solve the problem based on the classical Hotelling model. In the new model, logistics cost is paid by service providers who can obtain honour profit through providing service for the victims. The victims endure waiting times that consist of periods of response time and travelling time. The waiting times affect the victims' decisions and affect the equilibrium prices and profits. Numerical analysis implies that service providers obtain the highest profits on their equilibrium price when their locations are decided. Furthermore, locating both players near the ends of the disaster-affected line city is beneficial to increase the gross profits.

... The model considers heterogeneous facility failure probabilities, one layer of supplier backup, and facility fortification within a finite budget. Rezapour et al. (2014) develop a bi-level model for designing an entrant SC in the presence of a pre-existing competing SC where demand is elastic with respect to price and distance. This model assumes dynamic competition between the new and pre-existing SCs in retailers' level and probabilistic customers' behaviour. ...

The understanding of the application of the theory of constraints (TOC) concepts in the management of logistics distribution is not yet consolidated in the academia and especially in the practical field. The objective of this paper was to develop and test a proposed model to support decision making regarding the feasibility of implementing TOC in managing distribution logistics. In an automotive factory, the proposed method was applied and mainly in order to perform a critical analysis of the method and the potential implementation of the TOC concepts in the management of distribution. The main results of the research allowed appointing a structured method in logical steps to be used in the practice of companies to improve their logistics performance. The research suggests the use of the method contributed to the analysis and acceptance of TOC in distribution logistics.

... Managing global supply chains has become crucial in recent years due to the increase in globalization and international competition (Cagliano et al., 2008;Rezapour et al., 2014). Complexity in designing global supply chain (GSC) networks as increased due to this expansion of GSC across borders as lead-time is necessary among supply chain facilities in order to cover greater distances. ...

How circular economy systems truly work for firms around the world is at the beginning of knowledge development. As such, this chapter aims to provide an analysis of how to concretely implement and manage innovative projects to shift from a linear to circular supply chain management. The chapter analyses the case of sustainable wooden packaging logistics implemented by Fercam Echo Labs, moving from recycling approaches to upcycling solutions for pallets and crates. The development of circular supply chain management inside the circular economy can properly guide research and practitioners' efforts in the innovative logistics packaging management arena.

The leather industry typically generates a large amount of wastewater. Leather production requires large quantities of freshwater and various chemicals are added to the water at every stage of production. The absence of proper regulatory bodies and specialized treatment plants to recycle the wastewater add to the environmental hazards caused by the industry. Due to the problems cited above and the significant cost of safe wastewater disposal, numerous manufacturers illegally discharge their chemically polluted wastewater, causing immeasurable damage to the environment and public health. Governments' failure to adopt suitable taxation and subsidy policies further aggravates the crisis and discourages manufacturers from transitioning toward sustainable production practices. As a result, the majority of manufacturers are on the brink of bankruptcy. In this study, we propose a model for a leather industry supply chain that incorporates the three pillars of sustainability which include economic viability, environmental protection, and social equity. The proposed model features flexible governmental policies and enacts a Stackelberg competition between the producers and retailers under both certain and uncertain conditions in the context of the Iranian leather industry to ensure maximum customer satisfaction. To verify the applicability of the model, it was applied to a real-world case study under uncertainty. In the end, the validity of the model was confirmed when the results were approved by a panel of industry experts.

This paper addresses a bi-level mixed-integer nonlinear programming (MINLP) model for the competitive facility location problem in a closed-loop supply chain (CLSC), in which a firm (i.e., leader) aims at entering a market by locating new distribution and collection facilities, where a competitor (i.e., follower) already exists. The goal is to find the location and attractiveness of each facility going to be established by the leader who seeks to maximize its profit while also taking the follower’s response into account. The attractiveness of each facility is a function of integer variables related to the facility’s characteristics. Customer behavior is considered to be probabilistic based on the Huff gravity-based rule. To globally optimize the model, a procedure that handles the discrete decisions of the follower’s problem is proposed. Afterward, by replacing the inner level convex program with its corresponding Karush–Kuhn–Tucker (KKT) conditions, the bi-level MINLP is converted into a single-level MINLP model, optimized by an improved branch-and-refine algorithm. Numerical experiments on randomly generated instances are conducted to illustrate the model’s applicability. Moreover, through a computational analysis of the proposed model, the amount of gain the leader makes and the follower loses due to foresight in the competition are calculated.

For the forest sector, it is important to produce wood in an efficient and cost-effective way, while at the same time satisfying customer needs. This requires careful management of the wood product supply chain; from the point of production (forest owners) to the intermediates who transform these into intermediate goods and final wood products (forest-based industries), and deliver these goods to the users. Several studies indicate that the wood product supply chain is mostly production-driven (push-strategy), but several scholars call for a more demand-oriented strategy (pull-strategy). It is, however, not always possible to implement a pull strategy. The objective of this paper is to explore to what extent the key actors in the wood supply chain consider developing a pull (or demandoriented) strategy feasible and desirable, drawing on the data of two qualitative research projects. The first project explored push and pull strategies of 30 forest holdings in different countries, using a web-survey. The second project analysed (part of) the Dutch wood supply chain based on interviews with 15 companies throughout this chain. The results clearly show that, although push strategies are dispersed along the supply chain, pull principles were also present in all stages of the chain. These strategies alternate throughout the supply chain, indicating multiple decoupling points. Most key actors in the wood supply chain considered an increase in demand orientation not possible and desirable; some even argued to be in favor of a more production---oriented strategy to avoid, a.o., unsustainable practices. Aspects as trust and innovation were also considered to be more important for supply chain improvement than a more pull-oriented strategy.

Regional and geographical differences between facilities is of paramount importance in supply chain design. However, the impact of the regions' performance on supply chain design decisions remains a relatively under-researched subject in the literature. This paper presents a hybrid methodology for designing a sustainable supply chain that is resilient to random disruptions. We propose a multi-period multi-objective optimization model that utilizes a k-means clustering method to evaluate the regions' sustainability performance. The model aims to determine sourcing and network design decisions as well as resilience strategies. To manage the operational risks associated with the supply chain, we employ a new robustness measure that eliminates the need to estimate the probability distribution of random parameters. Finally, a Benders decomposition algorithm is developed to solve the model. Practical insights are drawn from an actual case study of a downstream petrochemical industry in Iran.

The necessity for sustainable development and to support eco-friendly products have manifold the government responsibility in directing green activities. This paper theoretically studies the moderating role of government in pricing and greening decisions of chain-to-chain competition in developing substitutable green products under government involvement in supporting green product distribution and/or recycling through assigning monetary tariffs to customers and practically adjusts a real-world case study of the Iranian motorcycle industry issues. We examine two competitive supply chains (SCs) consisting of one retailer and one manufacturer under two-way logistics, i.e. forward SC that distributes green products and backward SC that collects pollutant products from the market. In addition to maximizing the profit of each SC member and minimizing government expenditure, reductions in environmental pollution are also examined. This study examines the impact of government policies in equilibrium strategies through six scenarios, based on different government elective policies, and using Nash or Stackelberg game structures. A computational analysis of the case study reveals that under more constrained budget situations, the government should resist the urge to reduce recycling tariffs, compared with distribution tariffs. The greatest reduction in environmental pollution is achievable through: government financial support only for recycling with the lowest investment rejection behavior, following a Nash game, reducing greening costs, increasing tendencies towards environmental protection, and increasing the rate of recyclable products. The greatest profit for firms is obtainable through: government financial support of distribution and recycling logistics with the lowest tendency towards environmental protection, following a Nash game, reducing greening costs, reducing the investment rejection behavior of the government, and increasing the rate of recyclable products.

Purpose
In this paper, multi-period location–inventory–routing problem (LIRP) considering different vehicles with various capacities has been investigated for the supply chain of red meat. The purpose of this paper is to reduce variable and fixed costs of transportation and production, holding costs of red meat, costs of meeting livestock needs and refrigerator rents.
Design/methodology/approach
The considered supply chain network includes five echelons. Demand considered for each customer is approximated as deterministic using historical data. The modeling is performed on a real case. The presented model is a linear mixed-integer programming model. The considered model is solved using general algebraic modeling system (GAMS) software for data set of the real case.
Findings
A real-world case is solved using the proposed method. The obtained results have shown a reduction of 4.20 per cent in final price of red meat. Also, it was observed that if the time periods changed from month to week, the final cost of meat per kilogram would increase by 43.26 per cent.
Originality/value
This paper presents a five-echelon LIRP for the meat supply chain in which vehicles are considered heterogeneous. To evaluate the capability of the presented model, a real case is solved in Iran and its results are compared with the real conditions of a firm, and the rate of improvement is presented. Finally, the impact of the changed time period on the results of the solution is examined.

Managing supply chain operations in a reliable manner is a significant concern for decision-makers in competitive industries. In this article, two mathematical models considering competition and integrity in a three-echelon supply chain under uncertainty are proposed. The competition is formulated as a Stackelberg game such that the distribution centers have more power than the retailers. In the first model, decisions are made about the location and number of distribution centers (DCs), allocation of retailers, and the selling price of products. In the second model, based on the real world, the probability of risk and failure for the distribution centers are considered. Backup facilities should be established for unreliable facilities to meet the demands of retailers during disruption. To capture uncertainty, a two-stage stochastic approach is applied to model the problems. The first stage of the model belongs to the strategic planning and is not affected by randomness, while the second stage deals with tactical decisions depending on the realization of the first stage's random vector. In order to solve the problem, a hybrid genetic algorithm has been applied to large-scale problems. Numerical experiments have been conducted to assess the effectiveness of the proposed algorithm. Next, a sensitivity analysis is performed to recognize the most important parameters and evaluate the accuracy of our approach. Finally, to demonstrate the applicability of the model, the proposed model was implemented on the data of Alborz Pharmaceutical Company.

We address an intra-supply chain competition where a producer and resellers competing to achieve their goals, while taking into consideration the uncertainties and disruption risks. We utilize a bi-level multi-objective programming approach for designing a competitive supply chain network. A hybrid solution approach, combining the compromise programming and Benders
decomposition methods, is developed to solve the model. Furthermore, an efficient inequality constraint is proposed to cope with the computational complexity of the bi-level model. To explore
the practical application of the model, a real-world case example is discussed. Finally, the scalability of the solution approach is illustrated for large-scale problems.

Resilience to disruptions and sustainability are both of paramount importance to supply chains. However, the interactions between the two have not been thoroughly explored in the academic literature. We attempt to contribute to this area by presenting a hybrid methodology for the design of a sustainable supply network that performs resiliently in the face of random disruptions. A stochastic bi-objective optimisation model is developed that utilises a fuzzy c-means clustering method to quantify and assess the sustainability performance of the suppliers. The proposed model determines outsourcing decisions and resilience strategies that minimise the expected total cost and maximise the overall sustainability performance in disruptions. Important managerial insights and practical implications are obtained from the model implementation in a case study of plastic pipe industry.

In a competitive environment, supply chains are competing with each other to gain the market share and competition is a critical factor influencing the supply chain network structure. The current paper presents a variational inequality formulation and provides the results for a competitive supply chain network design model. The new-entrant supply chain competes against an existing one in a non-cooperative behavior. The networks include raw material suppliers, manufacturers, retailers, and the same demand markets. The manufacturers produce multiple products with deterministic, price-dependent demand. The goal is to maximize the future revenue of both chains. The problem is modeled by mathematical programming and the governing Nash equilibrium conditions are derived. Then, a finite-dimensional variational inequality formulation is presented to solve the equilibrium problem. Qualitative properties of the equilibrium pattern are provided to establish existence and uniqueness results under reasonable conditions. The modified projection algorithm is used to solve the variational inequality problem. A numerical example is presented in order to show the efficiency of the proposed model and to investigate the behavior of the model under different conditions.

This paper presents the competitive supply chain network design problem in which \(n\) decentralized supply chains simultaneously enter the market with no existing rival chain, shape their networks and set wholesale and retail prices in competitive mode. The customer demand is elastic and price dependent, customer utility function is based on the Hoteling model and the chains produce identical or highly substitutable products. We construct a solution algorithm based on bi-level programming and possibility theory. In the proposed bi-level model, the inner part sets the prices based on simultaneous extra- and Stackleberg intra- chains competitions, and the outer part shapes the networks in cooperative competitions. Finally, we use a real-word study to discuss the effect of the different structures of the competitors on the equilibrium solution. Moreover, sensitivity analyses are conducted and managerial insights are offered.

In a global and competitive economy, efficient supply networks are essential for modern enterprises. Horizontal cooperation (HC) concepts represent a promising strategy to increase the performance of supply chains. HC is based on sharing resources and making joint decisions among different agents at the same level of the supply chain. This paper analyzes different cooperation scenarios concerning integrated routing and facility-location decisions in road transportation: (a) a noncooperative scenario in which all decisions are individually taken (each enterprise addresses its own vehicle routing problem [VRP]); (b) a semicooperative scenario in which route-planning decisions are jointly taken (facilities and fleets are shared and enterprises face a joint multidepot VRP); and (c) a fully cooperative scenario in which route-planning and facility-location decisions are jointly taken (also customers are shared, and thus enterprises face a general location routing problem). Our analysis explores how this increasing level of HC leads to a higher flexibility and, therefore, to a lower total distribution cost. A hybrid metaheuristic algorithm, combining biased randomization with a variable neighborhood search framework, is proposed to solve each scenario. This allows us to quantify the differences among these scenarios, both in terms of monetary and environmental costs. Our solving approach is tested on a range of benchmark instances, outperforming previously reported results.

This study investigates equilibrium between green and non-green product types under different government intervention schemas. To this end, we establish production competition models of a set of green and non-green supply chains (GSCs and NGSCs, respectively). GSCs and NGSCs are two-echelon supply chains (SCs) that present green and non-green types of a product to a market, respectively. We consider two schemas of governmental intervention: direct tariffs (DTs) and tradable permits (TPs), both with and without baselines. This research seeks to evaluate how the GSCs and NGSCs respond to the DT or TP schemas. To establish the best SC response strategies, we formulate three-level non-linear programming problems for four possible governmental intervention scenarios. We find that this problem is multidimensional with different system stakeholders including the government, SCs, consumers, and the environment. In fact, different schemas result in different satisfaction levels of stakeholders. Thus, an appropriate schema can be selected by considering corresponding effects on the stakeholders. The comprehensive evaluation of a case study on residential building construction SCs yields significant managerial insights.

A two-stage algorithm is developed for the competitive supply chain network design problem in which two competitors simultaneously enter the market with no existing rival chain, shape their networks, and set attractiveness of their opened distribution centres to maximize their profits. The customer behaviour is based on the Huff gravity-based rule.
The proposed algorithm is constructed based on the Lemke and Howson algorithm and variational inequality formulation with the help of bi-level programming, the modified projection method, and the possibility theory. We derive the equilibrium condition and establish the finite dimensional variational inequality formulation, and provide properties of the equilibrium patterns in terms of the results of existence and uniqueness. Finally, we generate some instances and use a real world study to discuss the effect of the different structures of the competitors, namely centralized, decentralized, cooperative, or unknown modes, on the equilibrium solution.

We develop price-energy-saving competition and cooperation models for two green supply chains (GSCs) under government financial intervention. First, we study the best response strategies of the chains for the given tariffs of a government. Second, we formulate 16 mathematical programming models regarding governments’ energy-saving, social welfare, and revenue-seeking policies. We find that the government can orchestrate GSCs to fulfil the financial, social, and environmental objectives by an appropriate tariff mechanism. Moreover, cooperation in a GSC and between GSCs may facilitate the government’s sustainable development policies. A comprehensive analysis on case study of brick production GSCs reveals some important managerial insights.

In general, vaccines are recognized as an important means to protect populations against infectious diseases. We show that vaccines do not behave like commodity goods and elaborate on the key issues for vaccine supply chain design. This paper reviews the literature on model-based supply chain network design in order to identify the applicability of these models to the key issues of the design of a vaccine supply chain. We study whether the decisions at strategic, tactical and operational levels of the reviewed literature are able to address vaccine supply chain key issues as limited shelf life, cold chain distribution and accessing remote areas. Furthermore, we provide an overview of how uncertainty is incorporated in the reviewed literature and is able to incorporate disease epidemics, tender procurement, lead time variability and demand variability. Our future vaccine supply chain network needs to be sustainable, hereby taking the preferences of different stakeholders into account for obtaining a set of economical, technological and value key performance indicators that need to be satisfied by the design. Finally, we discuss the real-life applicability of the research up to now and discuss similarities and dissimilarities of vaccine supply chains with other pharmaceutical supply chains.

In this paper, a novel multi-objective mathematical model is developed to solve a capacitated single-allocation hub location problem with a supply chain overview. Three mathematical models with various objective functions are developed. The objective functions are to minimize: (a) total transportation and installation costs, (b) weighted sum of service times in the hubs to produce and transfer commodities and the tardiness and earliness times of the flows including raw materials and finished goods, and (c) total greenhouse gas emitted by transportation modes and plants located in the hubs. To come closer to reality, some of the parameters of the proposed mathematical model are regarded as uncertain parameters, and a robust approach is used to solve the given problem. Furthermore, two methods, namely fuzzy multi-objective goal programming (FMOGP) and the Torabi and Hassini's (TH) method are used to solve the multi-objective mathematical model. Finally, the concluding part presents the comparison of the obtained results.

This paper considers a supply chain where a manufacturer sells its product through a retailer. In such a market, a potential entrant can make a substitute product by imitating the incumbent's product and then sells it to the common market with one of three alternative entry modes: (i) selling through the incumbent's retailer, (ii) selling through another independent retailer, or (iii) selling directly to consumers. Faced with the entrant's entry, the manufacturer has managed to offer a value-added service to add to its product's value at a cost. We investigate the entrant's optimal entry mode when the manufacturer offers profit-sharing contracts to the retailer and when it does not, and discuss the impact of the potential invader's entry on the incumbent firms' performances. The results show that: (1) the entrant sells directly to consumers when faced with weak value competition, and sells through another retailer against fierce value competition. (2) If the value competition is relatively fierce and the efficiency of the value-added service is relatively high as well, the incumbent firms can benefit from the new entry. (3) A profit-sharing contract, as a coordination policy, can fully coordinate the incumbent supply chain no matter whether there exists a potential entrant or not, yet the entry can affect the distribution of the profits between the incumbent manufacturer and retailer.

This paper investigates the network design problem of a two-level supply chain (SC), which is applicable for industries such as automotive, fuel and tire manufacturing. Models presented in this paper aim at locating retail facilities of a SC and identifying their required capacities in the presence of existing competing retailers of a rival SC. We consider feasible locating space of the retail facilities on the continuous plane with bounded constraints and static competition among the rivals of the markets with deterministic demands. The problem is used for both essential and luxury product cases; hence, we consider elastic and inelastic demands, both. The models discussed in this paper are non-linear and non-convex which are difficult to solve. We use interval branch-and-bound as optimization algorithm for small size single-retailer problems; but for large-scale, multi-retailer problems we need to have more efficient methods. Therefore, we apply a heuristic algorithm (H1), a simulated annealing (SA) algorithm, an interior point (IP) algorithm, a genetic algorithm (GA) and a pattern search algorithm for solving multi-retailer problem with elastic and inelastic demands. Computational results obtained from performing different solution approaches for both elastic and inelastic show that mostly IP, PS, and H1 methods outperform the other approaches. The computational results on a real-life case are also promising. Several extended mathematical models and an example of a typical case with details are presented in the appendix of the paper.

We consider a spatial interaction model for locating a set of new facilities that compete for customer demand with each other, as well as with some pre-existing facilities to capture the "market expansion" and the "market cannibalization" effects. Customer demand is assumed to be a concave non-decreasing function of the total utility derived by each customer from the service offered by the facilities. The problem is formulated as a non-linear Knapsack problem, for which we develop a novel solution approach based on constructing an efficient piecewise linear approximation scheme for the objective function. This allows us to develop exact and α-optimal solution approaches capable of dealing with relatively large-scale instances of the model. We also develop a fast Heuristic Algorithm for which a tight worst-case error bound is established.

A model for designing the network of a new entrant supply chain under inelastic demand and in the presence of pre-existing competing chains is proposed. These supply chains provide an identical product for a market area. The model considers the location of distribution centres and retail outlets on a discrete set of potential locations. The assumptions of the model are: (1) static competition between the new and pre-existing chains and (2) a probabilistic customer behaviour based on an attraction function depending on both the location and the quality of the retailers. This model also incorporates the impact of the facilities’ location decisions on the operational inventory and shipment decisions. The resulting model is formulated as a mixed integer non-linear programme (MINLP). To solve the MINLP it is transformed to a linear one. We illustrate the model, discuss the results of a real-world case, and investigate the effectiveness of the proposed algorithm using randomly generated examples.

This paper studies a distribution system in which a manufacturer supplies a common product to two independent retailers, who in turn use service as well as retail price to directly compete for end customers. We examine the drivers of each firm's strategy, and the consequences for total sales, market share, and profitability. We show that the relative intensity of competition with respect to each competitive dimension plays a key role, as does the degree of cooperation between the retailers. We discover a number of insights concerning the preferences of each party regarding competition. For instance, there will be circumstances under which both retailers would prefer an increase in competitive intensity. Our analysis generalizes existing knowledge about manufacturer wholesale pricing strategies, and rationalizes behaviors that would not be evident without both price and service competition. Finally, we characterize the structure of wholesale pricing mechanisms that can coordinate the system, and show that the most commonly used formats (those that are linear in the order quantity) can achieve coordination only under very limiting conditions.

In this paper, we develop a supply chain network model consisting of manufacturers and retailers in which the demands associated with the retail outlets are random. We model the optimizing behavior of the various decision-makers, derive the equilibrium conditions, and establish the finite-dimensional variational inequality formulation. We provide qualitative properties of the equilibrium pattern in terms of existence and uniqueness results and also establish conditions under which the proposed computational procedure is guaranteed to converge. Finally, we illustrate the model through several numerical examples for which the equilibrium prices and product shipments are computed. This is the first supply chain network equilibrium model with random demands for which modeling, qualitative analysis, and computational results have been obtained.

We consider a supply chain in which two suppliers compete for supply to a customer. Pricing and delivery-frequency decisions in the system are analyzed by two three-stage noncooperative games with different decision rights designated to the parties involved. The customer first sets the price (or delivery frequency) for each supplier. Then, the suppliers offer the delivery frequencies (or prices) simultaneously and independently. Finally, the customer determines how much demand to allocate to each of the suppliers. We show that delivery frequency, similar to delivery speed in time-based competition, can be a source of competitive advantage. It also allows firms that sell identical products to offer complementary services to the customer because she can lower her inventory with deliveries from more suppliers. In general, higher delivery frequencies lower the value of getting deliveries from the second supplier and therefore intensify price competition. Assuming the cost structures do not change and the suppliers are identical, we show that when the customer controls deliveries, she would strategically increase delivery frequencies to lower prices. The distortion in delivery frequencies is larger and the overall performance of the supply chain is lower when the customer, not the suppliers, controls deliveries. Moreover, the customer is better off under delivery competition, while the suppliers are better off under price competition.

In this paper, we model a manufacturer that contracts with two retailers, who then choose retail prices and stocking quantities endogenously in a Bayesian Nash equilibrium. If the manufacturer designs a contract that is accepted by both retailers, it sets the wholesale price as a compromise between two conflicting roles: reducing intrabrand retail price competition and inducing retailers to stock closer to first-best levels (that is, optimum for the supply chain as a whole). In equilibrium, fill rates are less than first best. If, on the other hand, the manufacturer eliminates retail competition by designing a contract accepted by only one retailer, the assignment of consumers to retailers is inefficient. In either equilibrium, the performance of the supply chain is strictly less than first best. However, the manufacturer achieves first-best retail prices and fill rates if it can subsidize the retailers' leftover inventory. Absent such subsidies, the two-retailer equilibrium arises when the two retailers compete less intensively. In that equilibrium, numerical results indicate that the value of subsidizing unsold inventory is increasing in demand uncertainty, intensity of retail competition, and salvage value of inventory, and is decreasing in manufacturing cost and opportunity cost of shelf space.

In this paper, we present a supply chain network model with multiple tiers of decision-makers, consisting, respectively, of manufacturers, distributors, and retailers, who can compete within a tier but may cooperate between tiers. We consider multicriteria decision-making for both the manufacturers and the distributors whereas the retailers are subject to decision-making under uncertainty since the demands associated with the product are random. We derive the optimality conditions for the decision-makers, establish the equilibrium conditions, and derive the variational inequality formulation. We then utilize the variational inequality formulation to provide both qualitative properties of the equilibrium product shipment, service level, and price pattern and to propose a computational procedure, along with convergence results. This is the first supply chain network model to capture both multicriteria decision-making and decision-making under uncertainty in an integrated equilibrium framework.

Preface. Glossary of Notation. I: Theory of Projected Dynamical Systems. 1. Introduction and Overview. 2. Projected Dynamical Systems. 3. Stability Analysis. 4. Discrete Time Algorithms. 5. Oligopolistic Market Equilibrium. 6.Spatial Price Equilibrium. 7. Elastic Demand Traffic Equilibrium. 8. Fixed Demand Traffic Equilibrium. Index.

In the maritime industry, the stakeholders comprising the port authorities, shipping companies, and port operators often compete and collaborate within an ecological system. This paper investigates the competition and cooperation strategies amongst three parties: two major container hub ports and the shipping companies. This research develops a game theoretic network design model which considers three scenarios: (i) perfect competition between the hub ports, (ii) perfect cooperation between the hub ports, and (iii) cooperation between the shipping companies and the hub ports as a whole. The scenarios are tested using empirical data from two leading Asian hub ports: Singapore and Hong Kong. An interval branch and bound is designed to solve the models.

Preface. I: Theory and Fundamentals. 1. Variational Inequality THeory. 2. Algorithms. II: Partial Equilibrium - Perfect Competition. 3. Spatial Price Equilibrium. 4. Traffic Network Equilibrium. 5. Migration Equilibrium. III: Partial Equilibrium - Imperfect Competition. 6. Oligopolistic Market Equilibrium. 7. Environmental Networks. 8. Knowledge Network Equilibrium. IV: General Equilibrium. 9. Walrasian Price Equilibrium. 10. Financial Equilibrium. V: Estimation. 11. Constrained Matrix Problems. A. Problems.

We consider the general traffic equilibrium network model where the travel cost on each link of the transportation network may depend on the flow on this as well as other links of the network. The model has been designed in order to handle situations where there is interaction between traffic on different links e.g., two-way streets, intersections or between different modes of transportation on the same link. For this model, we use the techniques of the theory of variational inequalities to establish existence of a traffic equilibrium pattern, to design an algorithm for the construction of this pattern and to derive estimates on the speed of convergence of the algorithm.

In this article, we consider the general multimodal traffic equilibrium model with elastic demands. The link travel costs may depend upon the entire load pattern and the travel demands associated with each origin-destination pair and mode may depend upon travel costs associated with every origin-destination pair and every mode of transportation. For this model, we define the concepts of user-optimality and equilibrium. We establish, by means of a constructive proof motivated by the theory of variational inequalities, the existence of a unique equilibrium under appropriate monotonicity conditions. We then show that the existence proof induces an algorithm for the computation of equilibrium traffic patterns. The algorithm proceeds by iteration, each step of which amounts to computing the equilibrium pattern for a single modal linear traffic equilibrium problem with elastic demands. We derive estimates for the speed of convergence.

We consider a market with two competing supply chains, each consisting of one wholesaler and one retailer. We assume that the business environment forces supply chains to charge similar prices and to compete strictly on the basis of customer service. We model customer service competition using game-theoretical concepts. We consider three competition scenarios between the supply chains. In the uncoordinated scenario, individual members of both supply chains maximize their own profits by individually selecting their service and inventory policies. In the coordinated scenario, wholesalers and retailers of each supply chain coordinate their service and inventory policy decisions to maximize supply chain profits. In the hybrid scenario, competition is between one coordinated and one uncoordinated supply chain. We discuss the derivation of the equilibrium service strategies, resulting inventory policies, and profits for each scenario, and compare the equilibria in a numerical study. We find that coordination is a dominant strategy for both supply chains, but as in the prisoner's dilemma, both supply chains are often worse off under the coordinated scenario relative to the uncoordinated scenario. The consumers are the only guaranteed beneficiaries of coordination.

We consider a two-player, sequential location game in d-dimensional Euclidean space with arbitrarily distributed consumer demand. The objective for each player is to select locations so as to maximize their market share—the mass of consumers in the vicinity of their chosen locations. At each stage, the two players (Leader and Follower) choose one location each from a feasible set in sequence. We first show that (i) if the feasible locations form a finite set in R d , Leader (the first mover) must obtain at least a 1 d+1 fraction of the market share in equilibrium in the single-stage game, and there exist games in which Leader obtains no more than 1 d+1 ; (ii) in the original Hotelling game (uniformly distributed consumers on the unit interval), Leader obtains 1 2 even in the multiple stage game, using a strategy which is oblivious of Follower's locations. Furthermore, we exhibit a strategy for Leader, such that even if she has no information about the number of moves, her payoff must equal at least half the payoff of the single-stage game.

Optimization models, especially nonlinear optimization models, have been widely used to solve integrated supply chain design problems. In integrated supply chain design, the decision maker needs to take into consider-ation inventory costs and distribution costs when the number and locations of the facilities are determined. The objective is to minimize the total cost that includes location costs and inventory costs at the facilities, and distribution costs in the supply chain. We provide a survey of recent developments in this research area.

Supply chains often consist of several tiers, with different numbers of firms competing at each tier. A major determinant of the structure of supply chains is the cost structure associated with the underlying manufacturing process. In this paper, we examine the impact of fixed and variable costs on the structure and competitiveness of supply chains with a serial structure and price-sensitive linear deterministic demand. The entry stage is modeled as a simultaneous game, where the players take the outcomes of the subsequent post-entry (Cournot) competition into account in making their entry decisions. We derive expressions for prices and production quantities as functions of the number of entrants at each tier of a multitier chain. We characterize viability and stability of supply-chain structures and show, using lattice arguments, that there is always an equilibrium structure in pure strategies in the entry game. Finally, we examine the effects of vertical integration in the two-tier case. Altogether, the paper provides a framework for comparing a variety of supply-chain structures and for studying how they are affected by cost structures and by the number of entrants throughout the chain.

This paper is concerned with the supply chain network equilibrium models proposed by Nagurney et al. [Nagurney, A., Dong, J., Zhang, D., 2002. A supply chain network equilibrium model. Transportation Research 38E, 281-303] and Dong et al. [Dong, J., Zhang, D., Nagurney, A., 2004. A supply chain network equilibrium model with random demands. European Journal of Operational Research 156, 194-212]. It demonstrates that these models possess the unconstrained continuously differentiable minimization formulations, whose any stationary point is the solution of the corresponding model. Accordingly, not only is the Quasi-Newton algorithm capable of finding a solution of the model, but also it can overcome the difficulty experienced by the modified projection method in choosing an appropriate predetermined step size. In addition, 11 benchmark examples are employed to show the advantage of the unconstrained minimization formulation.

The variational inequality problem has been utilized to formulate and study a plethora of competitive equilibrium problems in different disciplines, ranging from oligopolistic market equilibrium problems to traffic network equilibrium problems. In this paper we consider for a given variational inequality a naturally related ordinary differential equation. The ordinary differential equations that arise are nonstandard because of discontinuities that appear in the dynamics. These discontinuities are due to the constraints associated with the feasible region of the variational inequality problem. The goals of the paper are two-fold. The first goal is to demonstrate that although non-standard, many of the important quantitative and qualitative properties of ordinary differential equations that hold under the standard conditions, such as Lipschitz continuity type conditions, apply here as well. This is important from the point of view of modeling, since it suggests (at least under some appropriate conditions) that these ordinary differential equations may serve as dynamical models. The second goal is to prove convergence for a class of numerical schemes designed to approximate solutions to a given variational inequality. This is done by exploiting the equivalence between the stationary points of the associated ordinary differential equation and the solutions of the variational inequality problem. It can be expected that the techniques described in this paper will be useful for more elaborate dynamical models, such as stochastic models, and that the connection between such dynamical models and the solutions to the variational inequalities will provide a deeper understanding of equilibrium problems.

A model for the optimal location of new facilities in a competitive market is introduced under the hypothesis that customers' behavior can be modeled by random utility functions. It means that the company, that wished to locate, uses a random utility model to forecast the market share of a location. Therefore the company cannot forecast the behavior of every customer in a deterministic fashion, but is able to embed him by a probability distribution. Three formulations are proposed to compute upper bounds of the objective function and compared in a numerical simulation. A branch and bound method is developed and tested on examples with up to 50 potential locations, and a Variable Neighborhood Search heuristic is proposed to solve larger instances.

This paper analyzes channel pricing in multiple distribution channels under competition between a national brand (NB) and a store brand (SB), where an NB can be distributed both through a direct channel (e-channel) and an indirect channel (local stores) but an SB can be distributed only through an indirect channel. We first explore cross-brand and cross-channel pricing policies. Formulating the problem as a Nash pricing game, we reach two findings: (1) brand loyalty building is profitable for both an NB and an SB; and (2) marketing decisions are more restrictive for an NB channel than they are for the SB channel. We next assess supply chain coordination and reach two findings: (1) wholesale price change does not coordinate the supply chain and (2) an appropriate combination of markup and markdown prices can achieve both supply chain coordination and a win–win outcome for each channel.

This paper develops an adverse selection model for a two-stage supply chain with one supplier, one retailer, and a potential outside entrant supplier who makes a partially substitutable product. The work is different from most research on entry deterrence that only considers a single-stage model. Our main interest is to investigate how the incumbent supplier can strategically maximize her profit by a wholesale pricing policy when facing the potential entrant. We focus on a model where the entrant supplier will sell her product through the same incumbent retailer. We derive the optimal decisions for each player and study the comparative statics of the equilibrium. To investigate how the supply chain structure may affect the deterrence strategy of the incumbent supplier, we also consider three alternative models with different channel structures, when both suppliers sell their products directly, when the entrant has another independent retailer, and when the entrant sells her product directly. Through the comparison, we find that the existence of the common downstream retailer often enhances the deterring motivation of the incumbent supplier.

This paper investigates how firms should select their production sites, capacities and quantities under rivalry. There are assumed to be a finite number of discrete potential location sites and a finite number of discrete markets, which may or may not coincide. Firms first decide either simultaneously or sequentially whether and where to establish a production site. The fixed cost of opening a facility and the marginal cost of production both depend on where the facility is located. Firms then choose capacity and a production quantity for each market. Prices in each market are determined by the total quantity available at that location via the Cournot mechanism. This formulation thus addresses multi-market, oligopolistic spatial competition with heterogeneity in production and logistics costs.We then analyze the Nash equilibria of the entry game and provide sufficient conditions for the existence of equilibria in the simultaneous entry game. At equilibrium, firms may not produce for all markets and may have limited market areas; however, these areas may overlap, so that there are multiple suppliers in any market. In general, there may not be a first mover advantage and early entrants may earn lower profits than later entrants.

We consider a competitive location problem in which a new firm has to make decisions on the locations of several new facilities as well as on its price setting in order to maximise profit. Under the assumption of discriminatory prices, competing firms set a specific price for each market area. The customers buy one unit of a single homogeneous price-inelastic product from the facility that offers the lowest price in the area the consumers belong to. Three customer choice rules are considered in order to break ties in the offered prices. We prove that, considering long-term competition on price, this problem can be reduced to a problem with decisions on location only. For each one of the choice rules the location problem is formulated as an integer programming model and a parametric analysis of these models is given. To conclude, an application with real data is presented.

This paper examines a competitive facility location problem occurring in the plane. A new gravity-based utility model is developed, in which the capacity of a facility serves as its measure of attractiveness. A new problem formulation is given, having elastic gravity-based demand, along with capacity, forbidden region, and budget constraints. Two solution algorithms are presented, one based on the big square small square method, and the second based on a penalty function formulation using fixed-point iteration. Computational testing is presented, comparing these two algorithms along with a general-purpose nonlinear solver.Scope and purposeIn a competitive business environment where products are not distinguishable, facility location plays an important role in an organization's success. This paper examines a firm's problem of selecting the locations in the plane for a set of new facilities such that market capture is maximized across all of the firm's facilities (both new and pre-existing). Customers are assumed to divide their demand among all competing facilities according to a utility function that considers facility attractiveness (measured by facility capacity for satisfying demand) and customer-facility distance. The level of customer demand is assumed to be a function of the facility configuration. Three types of constraints are introduced, involving facility capacity, forbidden regions for new facility location, and a budget function. Two solution algorithms are devised, one based on branch-and-bound methods and the other based on penalty functions. Computational testing is presented, comparing these two algorithms along with a general-purpose nonlinear solver.

In this paper, we develop a supply chain network model consisting of manufacturers and retailers in which the demands associated with the retail outlets are random. We model the optimizing behavior of the various decision-makers, derive the equilibrium conditions, and establish the finite-dimensional variational inequality formulation. We provide qualitative properties of the equilibrium pattern in terms of existence and uniqueness results and also establish conditions under which the proposed computational procedure is guaranteed to converge. Finally, we illustrate the model through several numerical examples for which the equilibrium prices and product shipments are computed. This is the first supply chain network equilibrium model with random demands for which modeling, qualitative analysis, and computational results have been obtained.

A chain wants to set up a single new facility in a planar market where similar facilities of competitors, and possibly of its own chain, are already present. Fixed demand points split their demand probabilistically over all facilities in the market proportionally with their attraction to each facility, determined by the different perceived qualities of the facilities and the distances to them, through a gravitational or logit type model. Both the location and the quality (design) of the new facility are to be found so as to maximise the profit obtained for the chain. Several types of constraints and costs are considered.Two solution methods are developed and tested. The first is a repeated local optimisation heuristic, extending earlier proposals to the supplementary design question and the presence of locational constraints. The second is an exact global optimisation technique based on reliable computing using interval analysis, incorporating several novel features. An example and comparative computational results demonstrate that this difficult and very multi-modal problem can be solved by such techniques. The local optimisation method turns out not to be very robust in its results, even after numerous repetitions, whereas the global optimisation method yields very useful and complete information on guaranteed near to optimal solutions after an important but still quite acceptable computational effort.

We consider models for duopolistic competitive supply chain network designing with sequential acting and variable delivered prices. These models design a multi-tier chain operating in markets under deterministic price-depended demands and with a rival chain present. The existing rival chain tends to open some new retailers to recapture some income in a near future. These rival chains’ structures are assumed to be set “once and for all” in a sequential manner but further price adjustments are possible.This problem is modeled for each of the following two strategies: (1) the von Stackelberg strategy in which we assume the existing chain will choose its future entry sites in the way to optimize its market share. This problem is modeled by a linear binary bi-level program and solved by a combinatorial meta-heuristic. (2) the minimum regret strategy in which we assume the existing chain’s future entry sites are totally unpredic, it is playing a “game against nature”. This problem is modeled by linear binary programs.

In this paper, we consider the dynamics of a global supply chain network economy in the presence of risk and uncertainty in which distinct speeds of adjustment are included. We assume three tiers of decision-makers: manufacturers, distributors, and retailers, who acquire the product in order to satisfy the demand at the demand markets. The manufacturers, distributors, and retailers may be based in the same or in different countries and may transact in different currencies. We allow for electronic transactions in the form of electronic commerce between the manufacturers and the retailers as well as between the distributors and the retailers since the retailers may be physical or virtual. In addition, supply-side risk and demand-side risk are handled in our formulation with the former being expressed as a multicriteria decision-making problem for each manufacturer and distributor (with distinct weights associated with the criteria) and the latter being handled with the use of uncertain demands. The proposed framework allows for the modeling and theoretical analysis of such global supply chain networks, which involve competition within a tier of decision-makers but cooperation between tiers. Numerical examples are provided for illustrative purposes.

In this paper we propose five heuristic procedures for the solution of the multiple competitive facilities location problem. A franchise of several facilities is to be located in a trade area where competing facilities already exist. The objective is to maximize the market share captured by the franchise as a whole. We perform extensive computational tests and conclude that a two-step heuristic procedure combining simulated annealing and an ascent algorithm provides the best solutions.

In this paper, we develop an integrated framework for the modeling of reverse supply chain management of electronic waste, which includes recycling. We describe the behavior of the various decision-makers, consisting of the sources of electronic waste, the recyclers, the processors, as well as the consumers associated with the demand markets for the distinct products. We construct the multitiered e-cycling network equilibrium model, establish the variational inequality formulation, whose solution yields the material flows as well as the prices, and provide both qualitative properties of the equilibrium pattern as well as numerical examples that are solved using the proposed algorithm.

We adapt the competitive location model based on maximal covering to include the knowledge that a competitor will enter the market later with a single new facility. The objective is to locate facilities under a budget constraint in order to maximise the remaining market share after the competitor's later entry.We develop mixed zero–one programming formulations for each of the following three strategies: the maxmin strategy where the worst possible competitor choice is considered, the minimum regret strategy, and the von Stackelberg strategy in which the competitor also optimises its market share. Some computational results show the feasibility and limits of these models.

New location models are presented here for exploring the reduction of facilities in a region. The first of these models considers firms ceding market share to competitors under situations of financial exigency. The goal of this model is to cede the least market share, i.e., retain as much of the customer base as possible while shedding costly outlets. The second model considers a firm essentially without competition that must shrink it services for economic reasons. This firm is assumed to close outlets so that the degradation of service is limited. An example is offered within a competitive environment to demonstrate the usefulness of this modeling approach.

In this paper we present the problem of locating a facility when competition from another facility is taken into consideration. Two problems are addressed here. One is the location of a new facility that will attract the most buying power from an existing facility. The other is the location of a facility that will secure the most buying power againts the best location of competing facility to be set up in the future.

In this paper, we consider the relationship between supply chain network equilibrium and transportation network equilibrium. We demonstrate that a supply chain network equilibrium model introduced earlier can be reformulated as a transportation network equilibrium model with elastic demands through a supernetwork reformulation of the former. This equivalence allows us to transfer the wealth of methodological tools developed for transportation network equilibrium modeling, analysis, and computation to the study of supply chain networks. To illustrate the power of the results, we then apply an algorithm developed for the solution of transportation network equilibrium problems with elastic demands to compute the product shipments and demand market prices in several numerical supply chain network examples taken from the existing literature.

In this paper a model for the location of a retail facility anywhere in the plane is presented. Existing location papers suggest that marketers can evaluate a set of potential sites for the location of a new facility. The site that maximizes the market share captured is selected. However, the best site for the new facility may not be included in the user provided set of potential sites. Finding the best location anywhere in the plane requires the analysis of the market share function which is addressed in this paper. In addition, a sensitivity analysis of both the best location and the market share captured is provided. Computational experiments illustrate the properties of this function and its sensitivity to the data parameters. The analysis shows that the market share captured by the facility (existing or new) is sensitive to both facility location and attractiveness.

We consider n demand points on a tree network. Two competitive companies plan to construct their own facilities on this network in a certain order. We assume that the weights of demand points at the entry time of the follower, used by the leader in his decision, are stochastic. We also assume that each customer utilizes the nearest facility to him. The objective of each company is to locate its facility so as to maximize the captured buying power after the follower’s entry. We analyze the problems and present an efficient solution procedure to find a Stackelberg equilibrium solution.

In this paper, we study competition in multiechelon supply chains with an assembly structure. Firms in the supply chain are grouped into homogenous sectors (nodes) that contain identical firms with identical production capabilities that all produce exactly one undifferentiated product (that may itself be a ÜkitÝ of components). Each sector may use several inputs to produce its product, and these inputs are supplied by different sectors. The production process within any sector is taken to be pure assembly in fixed proportions. The number of firms in each sector is known. The demand curve for the final product is assumed to be linear, as are production costs in all sectors. Competition is modeled via a Ücoordinated successive CournotÝ model in which firms choose production quantities for their downstream market so as to maximize profits, given prices for all inputs and all complementary products. Production quantities for sectors supplying the same successor are coordinated through pricing mechanisms, so that complementary products are produced in the right proportions. Under these assumptions, equilibrium prices for any multiechelon assembly network are characterized by a system of linear equations. We derive closed-form expressions for equilibrium quantities and prices in any two-stage system (i.e., a system with multiple input sectors and a single assembly sector). We show that any assembly structure can be converted to an equivalent (larger) structure in which no more than two components are assembled at any node. Finally, large structures can be solved either by direct solution of the characteristic linear equations or through an iterative reduction (compression) to smaller structures.

Vendor-managed inventory (VMI) is emerging as a significant development in the recent trend towards collaboration and information sharing in supply chain management. Transfer of inventory monitoring and other overhead costs to manufacturers and continuous replenishment of retailer inventory are commonly cited as potential benefits that VMI offers to retailers. We provide a new explanation in this paper for why retailers might be interested in VMI. We show that VMI intensifies the competition between manufacturers of competing brands and that the increased competition benefits a retailer that stocks these brands. Competition arises because of brand substitution; that is, some consumers may switch to another brand if their "preferred" brand is out of stock. The manufacturer whose brand is out of stock thus risks losing sales from those consumers who buy the competing brand. Consequently, each manufacturer has an incentive to keep a higher stock of its own brand, not only to satisfy the demand from its customers, but also the spillover demand that arises if a competing brand goes out of stock. When the retailer makes the stocking-level decisions, the competition is mitigated by the pooling of demands at the retailer. VMI restores the competition between the manufacturers and benefits the retailer.

This paper considers network supply chains with price dependent demand by modelling them as large acyclic networks. Such large networks are common in the automobile and apparel industries. We develop a model to analyze the effect of these large scale problems involving long sequences of contracts, and show that contract leadership, as well as leader position in the network affect the performance of the entire supply chain. We generalize Spengler (1950) to a game on a "contract tree" for a particular supply chain and extend the concept of double marginalization so that it can be applied in the form of a transformation to each contract that is offered by one member to another in the "contract tree". We construct an algorithm to find the equilibrium solution, and derive the optimal location of the leader ("optimal" being that leader location which maximizes total supply chain profits). Our work formalizes many intuitive insights; for example, member profits are determined by system-wide rather than individual costs. Finally, we model Cournot competition between competing supply chains (both two heterogeneous trees and multiple identical trees) and show the effect of changes in leader position as well as cost structure on the equilibrium.

We propose a multi-site location-allocation model for selecting locations in competitive service systems. Examples are typical franchise systems or retailers with multiple outlets. The proposed objective function maximizes a measure of spatial utility of users subject to constraints on waiting time of users and budget of the multi-site facility owners. The intent is to provide model support in assisting with decisions by one multi-facility owner about locating new sites or closing current sites in the presence of one or more competitors, each of which control several sites. Algorithms and spatial data necessary for solving the problem are described. The model is described in the context of locating bank branches though it is applicable in many other contexts.

We develop a new framework for location of competitive facilities by introducing non-constant expenditure functions into spatial interaction location models. This framework allows us to capture two key effects – market expansion and cannibalization – within the same model.
We develop algorithmic approaches for finding optimal or near-optimal solutions for several models that arise from choosing a specific form of the expenditure functions.

In a decentralized supply chain, with long-term competition between independent retailers facing random demands and buying from a common supplier, how should wholesale and retail prices be specified in an attempt to maximize supply-chain-wide profits? We show what types of coordination mechanisms allow the decentralized supply chain to generate aggregate expected profits equal to the optimal profits in a centralized system, and how the parameters of these (perfect) coordination schemes can be determined. We assume that the retailers face stochastic demand functions that may depend on all of the firms' prices as well as a measure of their service levels, e.g., the steady-state availability of the products. We systematically compare the coordination mechanisms when retailers compete only in terms of their prices, and when they engage in simultaneous price and service competition.

This paper develops an equilibrium model to design a centralized supply chain network operating in markets under deterministic price-depended demands and with a rival chain present. The two chains provide competitive products, either identical or highly substitutable, for some participating retailer markets.We model the optimizing behavior of these two chains, derive the equilibrium conditions, and establish the finite-dimensional variational inequality formulation, and solve it using a modified projection method. We provide properties of the equilibrium pattern in terms of the existence and uniqueness results. Our model also considers the impacts of the strategic facility location decisions on the tactical inventory and shipment decisions. Finally, we illustrate the model through a numerical example and discuss how the prices, costs, incomes, and profits behave with respect to key marketing activities, such as advertising, brand positioning, and brand loyalty.

This paper develops a stochastic general equilibrium inventory model for an oligopoly, in which all inventory constraint parameters are endogenously determined. We propose several systems of demand processes whose distributions are functions of all retailers' prices and all retailers' service levels. We proceed with the investigation of the equilibrium behavior of infinite-horizon models for industries facing this type of generalized competition, under demand uncertainty.
We systematically consider the following three competition scenarios. (1) Price competition only: Here, we assume that the firms' service levels are exogenously chosen, but characterize how the price and inventory strategy equilibrium vary with the chosen service levels. (2) Simultaneous price and service-level competition: Here, each of the firms simultaneously chooses a service level and a combined price and inventory strategy. (3) Two-stage competition: The firms make their competitive choices sequentially. In a first stage, all firms simultaneously choose a service level; in a second stage, the firms simultaneously choose a combined pricing and inventory strategy with full knowledge of the service levels selected by all competitors. We show that in all of the above settings a Nash equilibrium of infinite-horizon stationary strategies exists and that it is of a simple structure, provided a Nash equilibrium exists in a so-called reduced game.
We pay particular attention to the question of whether a firm can choose its service level on the basis of its own (input) characteristics (i.e., its cost parameters and demand function) only. We also investigate under which of the demand models a firm, under simultaneous competition, responds to a change in the exogenously specified characteristics of the various competitors by either: (i) adjusting its service level and price in the same direction, thereby compensating for price increases (decreases) by offering improved (inferior) service, or (ii) adjusting them in opposite directions, thereby simultaneously offering better or worse prices and service.

We consider a two-echelon distribution system in which a supplier distributes a product toN competing retailers. The demand rate of each retailer depends on all of the retailers' prices, or alternatively, the price each retailer can charge for its product depends on the sales volumes targeted by all of the retailers. The supplier replenishes his inventory through orders (purchases, production runs) from an outside source with ample supply. From there, the goods are transferred to the retailers. Carrying costs are incurred for all inventories, while all supplier orders and transfers to the retailers incur fixed and variable costs. We first characterize the solution to the centralized system in which all retailer prices, sales quantities and the complete chain-wide replenishment strategy are determined by a single decision maker, e.g., the supplier. We then proceed with the decentralized system. Here, the supplier chooses a wholesale pricing scheme; the retailers respond to this scheme by each choosing all of his policy variables. We distinguish systematically between the case of Bertrand and Cournot competition. In the former, each retailer independently chooses his retail price as well as a replenishment strategy; in the latter, each of the retailers selects a sales target, again in combination with a replenishment strategy. Finally, the supplier responds to the retailers' choices by implementing his own cost-minimizing replenishment strategy. We construct a perfect coordination mechanism. In the case of Cournot competition, the mechanism applies a discount from a basic wholesale price, based on thesum of three discount components, which are a function of (1) annual sales volume, (2) order quantity, and (3) order frequency, respectively.

We consider a competitive facility location problem with two players. Players alternate placing points, one at a time, into the playing arena, until each of them has placed n points. The arena is then subdivided according to the nearest-neighbor rule, and the player whose points control the larger area wins. We present a winning strategy for the second player, where the arena is a circle or a line segment. We permit variations where players can play more than one point at a time, and show that the first player can ensure that the second player wins by an arbitrarily small margin.