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The impact of cost uncertainty on the location of a distribution center

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Abstract

The location of a distribution center (DC) is a key consideration for the design of supply chain networks. When deciding on it, firms usually allow for transportation costs, but not supplier prices. We consider simultaneously the location of a DC and the choice of suppliers offering different, possibly random, prices for a single product. A buying firm attempts to minimize the sum of the price charged by a chosen supplier, and inbound and outbound transportation costs. No costs are incurred for switching suppliers. We first derive a closed-form optimal location for the case of a demand-populated unit line between two suppliers offering deterministic prices. We then let one of the two suppliers offer a random price. If the price follows a symmetric and unimodal distribution, the optimal location is closer to the supplier with a lower mean price. We also show the dominance of high variability: the buyer can decrease the total cost more for higher price variability for any location. The dominance result holds for normal, uniform, and gamma distributions. We propose an extended model with more than two suppliers on a plane and show that the dominance result still holds. From numerical examples for a line and a plane, we observe that an optimal location gets closer to the center of gravity of demands as the variability of any supplier's price increases.

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... Then several extended versions of this problem were investigated in literatures, such as multi-source Weber problem [18], the location problems of maximizing minimum distances, problems with barriers and so on. A rough classification of (mixed) integer programming models can be given as follows: (a) capacitated models versus uncapacitated models, (b) single-stage models versus multistage models [2,22,31,33], (c) single-commodity models versus multi-commodity models [21,26], (d) static models versus dynamic models [3], (e) deterministic models versus uncertain models [15,20,32], (f) single-source models versus multiple-source models, (g) single-objective models versus multi-objective models [12,17], (h) singlelevel models versus multi-level models [8,27]. A brief introduction and surveys of FL models appear in [18]. ...
... Note that we have to solve problem (13)- (15) for calculating q(u), which we call the oracle at u. Also note that with our assumptions its feasible set is bounded. We also have that x = 0 is feasible to the oracle; hence it has an optimal solution. ...
... We also have that x = 0 is feasible to the oracle; hence it has an optimal solution. q(u) is well-defined, but the minimizer in (13)- (15) is not necessarily unique. With some abuse of notation, we write ...
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... In the actual distribution center site selection problem, there are such factors as demand uncertainty and cost uncertainty. Rongbing Huang and Mozart B.C considered the impact of costs under the influence of different supplier prices on the location of distribution center [5]. Lixing Yang and Xiaoyu Ji studied the location problem of fuzzy environment [6]. ...
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... The location of a DC impacts the transportation of products from the first to the last level of the network. The more levels the distribution network has, the greater the need and frequency of use of this decision to reduce operating costs (Yang et al., 2007;Huang et al., 2012;Anzanello et al., 2017). With respect to d 11 , an issue that acts as a prerequisite to design an efficient DC is the planning of docks to perform the loading and unloading of materials in the facility. ...
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... (De Ligt & Wever, 1998; Huang, Menezes, & Kim, 2012(Cruijssen et al., 2007; Sutherland, 2006) Advanced Information Technology (IT) -plays an important role in collaborative transportation management. IT is critical for improving speed of information flow within the supply chain. ...
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... É preciso analisar qual composição é mais econômica, mas muito comumente a operação em rede possui custo de transporte menor (CHOPRA e MEINDL, 2011;CHRISTOPHER, 1997). Além disso, Huang et al (2012) incluem os custos de transporte dos fornecedores aos CDs como fator relevante;  perecibilidade / obsolescência: se o produto, por características de sua própria composição ou mercado, tiver um reduzido período de durabilidade, seja por perecibilidade ou por obsolescência, é altamente indicado que sua disponibilidade seja mais ágil, o que é melhor garantido por meio de uma distribuição regionalizada (BAKER, 2004);  giro do produto: produtos de maior giro reduzem custos de armazenagem, mas demandam disponibilidade frequente e constante, e por isso uma estrutura de rede de distribuição é mais indicada para produtos com essas características, já que reduz a possibilidade de falta de produto pela proximidade com o seu mercado consumidor (TORRES, 2003;VIEIRA, 2009;WANKE, 2011);  tempo de trânsito / disponibilidade de frota: operações centralizadas podem apresentar maior tempo de trânsito se a área de cobertura de clientes for bastante dispersa. No entanto, pode não haver na localidade específica onde um CD regional foi estabelecido uma estrutura de transporte direto para esta distribuição local (por falta de fluxo), o que pode gerar aumentos de prazo em virtude da exigência de transbordos em grandes centros, ou a necessidade de despender frotas próprias para o atendimento eficiente (BALLOU, 2006; BOWERSOX e CLOSS, 2009);  risco de ruptura do abastecimento: como toda diluição de risco, o estabelecimento de vários CDs apresenta dois vieses: por um lado, o risco de uma ruptura no abastecimento é dividido entre os CDs, possibilitando até mesmo estratégias operacionais de atendimento entre as unidades no caso de alguma falha pontual e assim diminuindo o dano; por outro lado, a possibilidade de sua ocorrência é multiplicada pelo número de unidades, o que demanda ponderação sobre este aspecto (SCHOENHERR e TUMMALA, 2011);  sensibilidade do mercado à prazo: há mercados em que a sensibilidade ao prazo de entrega é maior do que outros, como mercados que não administram estoques no varejo, ou com tipo de venda associada ao serviço, como autopeças, informática, etc. Outros mercados consideram a agilidade importante, porém esse não é fator decisivo ou gerador de custo, como confecção, calçados, livros, etc., onde o tempo de exposição na gôndola ou vitrine é relevante, mas não se sente os impactos da indisponibilidade com tanta intensidade (ou não há a cultura de medi-los ou considerá-los como críticos). ...
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... The fuzzy TOPSIS is used to evaluate and select the best location for implementing an urban distribution centre. In Huang et al. (2012), the location of a distribution centre and the choice of suppliers offering different prices for a single product, which are possibly random, are considered simultaneously. In Mousavi & Niaki (2013), a capacitated location allocation problem is considered, in which the locations of the demands are assumed to be fuzzy, the locations follow a normal probability distribution, and the distances between the locations and the customers are taken as metrics of Euclidean. ...
... O possível motivo é que a localização de um CD influencia a escolha do fornecedor e, essas decisões de fornecimento influenciam o custo total de distribuição. Além disso, os custos relacionados ao fornecedor tornaram-se mais significativos nos últimos anos com a crescente volatilidade do mercado (Nozick;Turnquist, 2001;Huang et al. 2012). Portanto, além dos trabalhos em projeto geral de CD serem escassos, considerando também as etapas de projeto de CD, muitas fases também possuem poucas publicações, como definições de seleção de equipamentos e estratégia de operação de armazenamento, enfatizando a necessidade de estudos em todas as etapas do planejamento de projeto. ...
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Plants, distribution centers, and other facilities generally function for years or decades, during which time the environment in which they operate may change substantially. Costs, demands, travel times, and other inputs to classical facility location models may be highly uncertain. This has made the development of models for facility location under uncertainty a high priority for researchers in both the logistics and stochastic/robust optimization communities. Indeed, a large number of the approaches that have been proposed for optimization under uncertainty have been applied to facility location problems.
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In this paper, we analyze a facility location model where facilities may be subject to disruptions, causing customers to seek service from the operating facilities. We generalize the classical p-median problem on a network to explicitly include the failure probabilities, and analyze structural and algorithmic aspects of the resulting model. The optimal location patterns are seen to be strongly dependent on the probability of facility failure, with facilities becoming more centralized, or even co-located, as the failure probability grows. Several exact and heuristic solution approaches are developed. Results of numerical experiments are reported.
Article
After the work of the late Professor F. Y. Edgeworth one may doubt that anything further can be said on the theory of competition among a small number of entrepreneurs. However, one important feature of actual business seems until recently to have escaped scrutiny. This is the fact that of all the purchasers of a commodity, some buy from one seller, some from another, in spite of moderate differences of price. If the purveyor of an article gradually increases his price while his rivals keep theirs fixed, the diminution in volume of his sales will in general take place continuously rather than in the abrupt way which has tacitly been assumed.
Article
This note deals with the optimal locations of a given number of facilities when customers’ behavior is described by a probabilistic choice model. In this context, the principle of median location is generalized. The optimal locations are determined in the case of the multinomial logit for different numbers of facilities.
Article
Suppose n facilities are to be located on a line segment so as to minimize cost function. One might expect that the facilities' optimal locations have the following interleaving property: if one of the n facilities is removed and if the locations of the others are shifted by reoptimizing, each remaining facility's location shifts toward the location of the one removed, but not farther toward it than the original location of the adjacent facility. This work presents two models whose solutions have this interleaving property and four examples of such models. An additive criterion is used in one model, a minimax criterion in the other. In the additive model, the minimum cost is a convex function of n multiplied by (times) , in the minimax model, it is nonincreasing.
Article
Uncertainties abound within a supply chain and have big impacts on its performance. We propose an integrated model for a three-tiered supply chain network with one supplier, one or more facilities and retailers. This model takes into consideration the unreliable aspects of a supply chain. The properties of the optimal solution to the model are analyzed to reveal the impacts of supply uncertainty on supply chain design decisions. We also propose a general solution algorithm for this model. Computational experience is presented and discussed. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007
Article
Supply chain management is becoming an increasingly important issue, especially when in most industries the cost of materials purchased comprises 40-60% of the total sales revenue. Despite the benefits cited for single sourcing in the popular literature, there is enough evidence of industries having two/three sources for most parts. In this paper we address the operational issue of quantity allocation between two uncertain suppliers and its effects on the inventory policies of the buyer. Based on the type of delivery contract a buyer has with the suppliers, we suggest three models for the supply process. Model I is a one-delivery contract with all of the order quantity delivered either in the current period with probability beta, or in the next period with probability 1 - beta. Model II is also a one-delivery contract with a random fraction of the order quantity delivered in the current period; the portion of the order quantity not delivered is cancelled. Model III is similar to Model Il with the remaining quantity delivered in the next period. We derive the optimal ordering policies that minimize the total ordering, holding and penalty costs with backlogging. We show that the optimal ordering policy in period n for each of these models is as follows: for x greater-than-or-equal-to u(n)BAR order nothing; for v(n)BAR less-than-or-equal-to X < u(n)BAR, use only one supplier; and for x < v(n)BAR, order from both suppliers. For the limiting case in the single period version of Model I, we derive conditions under which one would continue ordering from one or the other or both suppliers. For Model II, we give, sufficient conditions for not using the second (more expensive) supplier when the demand and yield distributions have some special form. For the single period version of Models II and III with equal marginal ordering costs we show that the optimal order quantities follow a ratio rule when demand is exponential and yields are either normal or gamma distributed.
Article
When supply lead times are uncertain, the simultaneous procurement from two sources offers savings in inventory holding and shortage costs. Economies are achieved if these savings outweigh the increase in ordering costs. In this paper we analyze dual sourcing in the context of the "reorder point, order quantity" inventory model with constant demand and stochastic lead times and compare it with single sourcing. Two cases are studied, using the uniform and the exponential distributions, which may be thought of as two extreme ways of representing stochastic lead times. In our two-vendor model, the order quantity is split equally between the two vendors and the split orders are placed simultaneously when the inventory position reaches the reorder level. A comparison of the total expected costs suggests that when the uncertainty in the lead times is high and the ordering costs are low, dual sourcing could be cost effective.
Chapter
We review inventory models that use multiple sourcing (diversification) to deal with upstream (supply) uncertainty. To provide a structured review, we identify three sources of supply uncertainty as follows: supply timing, supply quantity (or quality), and purchase price. Then, we summarize the main results that exist in the literature. Finally, based on our observations, we provide directions for future research.
Chapter
We study the problem of finding the global minimum of the difference between two convex functions f(x)−g(y), under linear constraints of the form: x∈X, y∈Y, Ax+By+c≤0, where X Ì \mathbbRn1 , Y Ì \mathbbRn2 X \subset \mathbb{R}^{n_1 } , Y \subset \mathbb{R}^{n_2 }, are convex polyhedral sets. The proposed solution method consists in converting the problem into a concave minimization problem in \mathbbRn2 + 1\mathbb{R}^{n_2 + 1} and applying the outer approximation method to the latter problem. Using a special type of separating hyperplanes the same result could also be obtained by applying the generalized Benders’ decomposition method with a proper change of variable in the master problem. As specialized to the indefinite quadratic programming problem, the algorithm is convergent, provided only the set Y 0={y∈Y:(∃x∈X) Ax+By+c≤0} is bounded.
Article
In this paper, we present a stochastic version of the location model with risk pooling (LMRP) that optimizes location, inventory, and allocation decisions under random parameters described by discrete scenarios. The goal of our model (called the stochastic LMRP, or SLMRP) is to find solutions that minimize the expected total cost (including location, transportation, and inventory costs) of the system across all scenarios. The location model explicitly handles the economies of scale and risk-pooling effects that result from consolidating inventory sites. The SLMRP framework can also be used to solve multi-commodity and multi-period problems.We present a Lagrangian-relaxation–based exact algorithm for the SLMRP. The Lagrangian subproblem is a non-linear integer program, but it can be solved by a low-order polynomial algorithm. We discuss simple variable-fixing routines that can drastically reduce the size of the problem. We present quantitative and qualitative computational results on problems with up to 150 nodes and 9 scenarios, describing both algorithm performance and solution behavior as key parameters change.
Article
This paper considers multiple-supplier single-item inventory systems, where the item acquisition lead times of suppliers and demand arrival are random, and backorder is allowed. The acquisition takes place when the inventory level depletes to a reorder level, and the order is split among multiple suppliers. The acquisition lead times may have different distributions, the unit purchasing prices from suppliers may be different, and thus the order quantities for different suppliers may be different. The problem is to determine the reorder level and order quantity for each supplier so that the expected total cost per unit time, consisting of the fixed ordering cost, procurement cost, inventory holding cost and shortage cost, is minimized. We develop a mathematical model describing the system in detail. We also conduct extensive numerical experiments to analyze the advantages and distinct characteristics of multiple-supplier systems.
Article
Supply chain management (SCM) has become an important management paradigm. As supply chain members are often separate and independent economic entities, a key issue in SCM is to develop mechanisms that can align their objectives and coordinate their activities so as to optimize system performance. In this paper, we provide a review of coordination mechanisms of supply chain systems in a framework that is based on supply chain decision structure and nature of demand. This framework highlights the behavioral aspects and information need in the coordination of a supply chain. The identification of these issues points out several directions of future research in this area.
Article
Historically, the three fundamental stages of the supply chain, procurement, production and distribution, have been managed independently, buffered by large inventories. Increasing competitive pressures, and market globalization are forcing firms to develop supply chains that can quickly respond to customer needs. To remain competitive, these firms must reduce operating costs while continuously improving customer service. With recent advances in communications and information technology, as well as a rapidly growing array of logistics options, firms have an opportunity to reduce operating costs by coordinating the planning of these stages. In this paper, we review the literature addressing coordinated planning between two or more stages of the supply chain, placing particular emphasis on models that would lend themselves to a total supply chain model. Finally, we suggest directions for future research.
Article
This paper extends the location-allocation formulation by making the cost charged to users by a facility a function of the total number of users patronizing the facility. Users select their facility based on facility charges and transportation costs. We explore equilibria where each customer selects the least expensive facility (cost and transportation) and where the facility is at a point that minimizes travel costs for its customers. The problem in its general form is quite complex. An interesting special case is studied: facilities and customers are located on a finite line segment and demand is distributed on the line by a given density function.
Article
We research the management approach that quantitatively combines decisions that affect different planning horizons--namely, the strategic and operational ones--and simultaneously derive the optimal values of these decisions. The system we investigate comprises retail outlets and customers in an infinite-horizon setting. Both retail outlets and customers are located on a finite homogenous line segment. The total demand posed by customers is normally distributed with known mean and variance. To optimally design and operate such a system, we need to determine the optimal values of the number of retail outlets, the location of each retail outlet, and the replenishment inventory levels maintained at each retail outlet. We analyze the system from an expected cost point of view, considering the fixed costs of operating the retail outlets, the expected holding and shortage costs, and the expected delivery costs. We show that all decisions can be represented as a function of the number of retail outlets. Moreover, we show that the system's expected cost function is quasi-convex in the number of retail outlets. We compare our model to a model that does not integrate these decisions at once. We show the advantage of our approach on both the solution and objective spaces. We propose an exact quantification of this advantage in terms of the cost and problem parameters. In addition, we point out several managerial insights.
Article
This paper examines capacitated facility location problems on a straight line. To serve a customer, a facility must be located within a corresponding customer neighborhood. The fixed costs of locating facilities and the unit production costs of serving a customer from a facility can depend upon their locations on the line. We discuss the computational complexity of several capacitated location models. For capacitated problems on a line with non-nested customer intervals, and for general capacitated problems that satisfy a certain “monotonicity” property, we develop polynomial-time dynamic programming algorithms for (i) locating minimum cost facilities to serve all customers, and (ii) maximizing the profit by locating up to q facilities that serve some or all customers with idiosyncratic returns, penalties and demands.
Article
Facility location decisions play a critical role in the strategic design of supply chain networks. In this paper, a literature review of facility location models in the context of supply chain management is given. We identify basic features that such models must capture to support decision-making involved in strategic supply chain planning. In particular, the integration of location decisions with other decisions relevant to the design of a supply chain network is discussed. Furthermore, aspects related to the structure of the supply chain network, including those specific to reverse logistics, are also addressed. Significant contributions to the current state-of-the-art are surveyed taking into account numerous factors. Supply chain performance measures and optimization techniques are also reviewed. Applications of facility location models to supply chain network design ranging across various industries are presented. Finally, a list of issues requiring further research are highlighted.
Article
This study examined whether acute alcohol (EtOH) intoxication before burn injury potentiates postburn intestinal tissue damage and whether neutrophils have any role in the damage under those conditions. Male rats ( approximately 250 g) were gavaged with EtOH to achieve a blood EtOH level of approximately 100 mg/dL or with saline and received either approximately 12.5% or approximately 25% total body surface area (TBSA) burn or sham injury. Rats were killed at 4 or 24 h after injury, and various parameters were measured. As compared with sham animals, burn injury alone (regardless of size) resulted in a significant increase in intestinal tissue myeloperoxidase (MPO; an index of neutrophil infiltration) activity and IL-18 levels 4 h after injury. Furthermore, rats receiving 25% TBSA, but not 12.5%, burn exhibited intestine edema. The IL-18 and MPO activity were normalized at 24 h after injury in rats receiving 12.5% TBSA burn, whereas these parameters remained elevated at 24 h in rats with 25% burn. The presence of EtOH in rats at the time of burn injury exacerbated the levels of IL-18, MPO activity, and edema at 4 and 24 h after burn injury. Treatment of rats with anti-IL-18 antibodies or with antineutrophil antiserum prevented the increase in the above parameters after EtOH and burn injury, except that the depletion of neutrophils did not prevent the IL-18 increase. In summary, these findings suggest that acute EtOH intoxication exacerbates postburn intestinal tissue damage after burn injury, and that it is, in part, neutrophil mediated.
Article
We study a production-inventory system with multiple unreliable supply sources. Through inspection and rework the system can improve the quality of the units received from the supply sources. There are two interleaved decisions: the replenishment quantities from the sources and the inspection-rework quantities among the units received. We show the optimal solution to the replenishment decision can be efficiently derived from a greedy algorithm, and inspection-rework is optimally applied to a single source identified by the algorithm. Furthermore, in the case of linear cost functions, it is optimal to place orders from two supply sources, i.e., dual sourcing is optimal. The results extend to the infinite-horizon case, where an order-up-to policy is optimal. The model also readily adapts to situations in which the supply imperfection takes the form of a reduced delivery quantity (yield loss).
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