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Contracting for vendor‐managed inventory with a time‐dependent stockout penalty
Abstract
We examine vendor-managed inventory contracts in a (Q, r) inventory system between a supplier and a retailer, in which a stockout penalty is charged to the supplier based on the length of the time period during which stockouts occur at the retailer. Linear and quadratic forms of the time-dependent stockout penalty are considered. For the deterministic demand case, we find that the quadratic form of time-dependent stockout penalty is equivalent to a proportional stockout penalty per unit short per unit time. For the stochastic demand case, we provide the exact cost expressions for the supplier and the retailer with a linear time-dependent stockout penalty. We also discuss how the stochastic model can be extended to the case with a quadratic time-dependent stockout penalty when there is at most one outstanding replenishment order at any point of time. We provide several interesting computational results.
... From the current research on the evaluation of supplier selection by scholars, most scholars still use AHP to construct the supplier index system; still, AHP cannot fully consider the interrelationship between the various index systems. More importantly, most of the scholars' evaluation and selection of suppliers is aimed at manufacturing companies, ignoring the high proportion of chain retail purchase costs in total costs [8][9][10][11][12]. ...
... System. On the basis of summarizing the research of scholars, a questionnaire was designed in combination with the characteristics of chain convenience stores; after distribution, recovery, and calculation, the evaluation index system of chain convenience store procurement suppliers was initially constructed [9][10][11][12][13] (as shown in Table 2). ...
The purchase cost of chain convenience stores accounts for a large proportion of the total cost. Enterprises are facing the problem of how to reasonably reduce the purchase cost while ensuring the quality of service. This paper first considers the uniqueness of chain convenience stores, draws on existing research results, and establishes an evaluation index system for chain convenience store suppliers through field research. Then, we use the principal component analysis method of selection to determine the weight of each index and make a preliminary ranking of the importance of chain convenience store suppliers. Secondly, according to the relevant weights determined by the network hierarchy method, the collected data are substituted into the multiobjective mathematical programming model to analyze the distribution of supplier procurement and calculate the procurement cost. The level of procurement expenditures accounted for by suppliers confirms the importance of suppliers. The results show that through the evaluation and ranking of suppliers and the effective management of suppliers according to the ranking results, not only the goal of cost minimization is achieved but also the reasonable service level is guaranteed, which is scientific.
... This section focuses on the application of MAM in the product maturity stage, where customer preferences are known, and the product is ordered in high volumes. However, due to demand variability, stockouts occur, resulting in penalties [110]. In certain instances, MAM is adopted as a preventive measure to avoid stockout events [53,111]. ...
Metal Additive Manufacturing (MAM) has emerged as a promising technology in the aerospace industry, enabling the production of complex components with enhanced design flexibility and reduced lead times. Concurrently, Industry 4.0 has gained significant attention for its potential to revolutionize aerospace manufacturing processes. The paper aims to cluster and review the literature on MAM in the aerospace industry, specifically focusing on its relevance to Industry 4.0 and its applicability throughout the various stages of the product life cycle for the chief purpose of matching supply with demand. Identified gaps and challenges are analyzed, highlighting the need for further research and outlining research agenda aimed at advancing the integration of MAM for Industry 4.0 in the aerospace sector. By addressing these research areas, the aerospace industry can unlock the value of MAM within an Industry 4.0 framework, leading to improved efficiency, productivity, and competitiveness.
... In order to make the collaboration work, the dominant partner is being compensated for any extra costs incurred, thus giving rise to decentralized models for supply chain coordination. Quantity discount models [4,28,30], Vendor Managed Inventory (VMI) under penalty [10,14,17,27,40,42] and Trade Credit [12] are some of the commonly used decentralized models for supply chain coordination apart from revenue sharing contract [7], buy-back contract [35] or options contract [8], etc. ...
In the just-in-time (JIT) manufacturing system, the vendors ship in small batch sizes. Hence the buyers are at an advantageous position as they can reduce their inventory holding costs. The practice of shipping in smaller batch sizes often results in the vendors incurring high costs as the number of production setups and the number of shipments increases for the vendors. The vendors could only switch to JIT mode when there is an assurance from the buyer of providing some compensation for the increased costs. This compensation from the buyer to the vendors is called ‘surcharge price’. In our work, we have studied the surcharge pricing mechanism in the presence of backorder when there is a powerful vendor and have shown that the it can coordinate a decentralized supply chain. Our study incorporates both the cases of the buyer holding full information about the vendors’ costs as well as the case of information asymmetry. In the case of full information, we have shown that the optimal order quantity in the presence of surcharge pricing is less than that of the vendor dominated scenario. At the same time, the optimal order quantity is higher than that in the buyer dominated scenario. Further, the total supply chain costs are also minimized when a surcharge pricing contract is offered in comparison to both the buyer and the vendor dominated scenarios. For the information asymmetry case, we have framed the optimal set of screening contracts and have shown that an optimal surcharge pricing contract to the vendor is free from the probability distribution of the vendor type.
This paper addresses the production scheduling and inventory management in a closed‐loop supply chain that recycles both high‐quality and low‐quality cores and makes products using cores and new raw materials. The manufacturing/remanufacturing supply chain consists of a vendor and a buyer, and they collaborate under a consignment stock (CS) agreement. We investigate and compare three operation policies under the CS agreement, covering continuous and intermittent production manners and shipments of equal and unequal batch sizes. For each operation policy, we develop a mixed integer nonlinear programming model to jointly optimize the production sequence of two classes of cores, production cycle length, shipment frequency, and shipment batch sizes, with the objective of minimizing the cost rate. By analyzing the respective decisions and conducting an extensive numerical study with various scenarios, we explore the advantages and applications of each operation policy. Based on our research findings, we provide general guidelines and criteria for operation policy selection.
This paper studies an inventory management problem for a closed-loop supply chain that is operated under a consignment stock policy and subject to a cap-and-trade regulation. The supply chain makes both new products and remanufactured products, considering that new raw materials (NRMs), cores, and finished goods (FGs) suffer from deterioration. Mixed integer nonlinear programming models are established to jointly optimize the production sequence of new products and remanufactured products, number of shipments, shipment interval, batch size of FGs, and production cycle length to minimize the total of production, shipment, inventory, deterioration, and carbon emission costs per unit time. Exploring and using the structural properties of the models, a Taylor-series based method is designed to solve the models. Finally, numerical examples and sensitivity analysis are provided to show the effects of key factors on the operational decisions and on both the economy and environment. Results indicate that the deterioration of NRMs, cores, and FGs triggers the supply chain to run short production cycles while making more frequent shipments under the consignment stock policy. Both the economic and environmental costs increase with the deterioration rates. In addition, raising the carbon-trading price can reduce carbon emissions but increase the economic cost of the supply chain, rendering the urgency in reasonably determining carbon cap and trading price.
Our work delves into supply chain coordination involving a single supplier selling a single product to multiple downstream buyers. We consider the case when the supplier proposes implementing vendor-managed inventory (VMI) for each buyer. The VMI contract involves the buyers charging a penalty to the supplier on the excess inventory whenever the supplier exceeds some pre-decided inventory threshold. Unlike the works covered predominantly in the VMI literature involving penalty, where both the penalty and the threshold are exogenous, we develop a model to determine both endogenously. In our study, the supplier deciding on the penalty and the inventory threshold needs to ensure that each of the buyers’ interests is protected, that is, none of the buyers becomes worse off from the optimal position, thereby ensuring the willing participation of all the buyers. We further compared our model with the centralized Joint Economic Lot Size (JELS) model and other existing models. We show that our model has a cost equivalence with the JELS model with unequal order intervals. We also show the superiority of our proposed model over the existing VMI models in terms of the overall costs. Finally, we examine the impact of size and ordering cost on each buyers’ costs through numerical analysis.
Multisourcing and vendor-managed inventory (VMI) programs with percentage supply allocations (PSAs) are two common practices in the electronics industry. A PSA is a prenegotiated percentage of a multisourced part's total demand, which should be provided by a supplier. For parts within Dell's supply chain for which these practices are applicable, we provide a framework to implement pull-based replenishments, verify its feasibility, and demonstrate the potential benefits via simulation. Specifically, we investigate two decisions to meet customer demand and PSAs with minimal inventory: (1) how to allocate actual customer demand among multiple suppliers, and (2) what guidelines Dell should specify to suppliers for VMI hub replenishments. For demand allocations, we propose a consumption cycle based on the PSAs. We consider a heuristic replenishment policy and develop an algorithm to compute the policy parameters, which can be used as supplier guidelines. The proposed approach presents a significant opportunity for cost savings. Dell used the results of this project (1) to address skepticism toward a pull-based approach in managing VMI replenishments, (2) to gain stakeholder support to implement a pull-based approach, and (3) to emphasize the need for a change in Dell's philosophy on managing demand allocations to suppliers and VMI hub replenishments.
We consider a supply chain where a vendor manages its multiple retailers' stocks under a vendor managed inventory (VMI) contract that specifies upper stock limits at the retailers' premises and overstock costs for exceeding those limits. We formulate a mixed integer nonlinear program that minimizes total supply chain costs and allows unequal shipment frequencies to the retailers. We develop an algorithm to solve its relaxed version which provides a lower bound cost solution. We propose a cost efficient heuristic procedure to generate delivery schedules to the retailers. We conduct a sensitivity analysis to provide insights on the performance of the proposed heuristic. Results show that our heuristic finds optimal or near optimal solutions, and it proposes substantial savings compared to the total supply-chain cost in the cases where there is no VMI and where there is VMI but with equal shipment frequencies to retailers.
We study a single-item r q inventory system, where r is the reorder point and q is the order quantity. The demand is a compound-Poisson process. We investigate the behavior of the optimal policy parameters and the long-run average cost of the system in response to stochastically shorter or less-variable lead times. We show that although some of the properties of the base-stock system can be extended to this more general model, some cannot. The same findings also apply when the comparison is conducted on the lead-time demand distributions.
This paper models a type of vendor-managed inventory (VMI) agreement that occurs in practice called a (z, Z) contract. We investigate the savings due to better coordination of production and delivery facilitated by such an agreement. The optimal behavior of both the supplier and the retailer are characterized. The optimal replenishment and production policies for a supplier are found to be up-to policies, which are shown to be easily computed by decoupling the periods when the supplier outsources from those when the supplier does not outsource. A simple application of the newsvendor relation is used to define the retailer's optimal policy. Numerical analysis is conducted to compare the performance of a single supplier and a single retailer operating under a (z, Z) VMI contract with the performance of those operating under traditional retailer-managed inventory (RMI) with information sharing. Our results verify some observations made in industry about VMI and show that the (z, Z) type of VMI agreement performs significantly better than RMI in many settings, but can perform worse in others.
The paper introduces an option contract to improve the performance of a vendor-managed inventory (VMI) supply chain under yield uncertainty. We first assume that there is a deterministic demand and find that the option contract can coordinate the supply chain and arbitrarily allocate coordinated profit among members. Compared with a subsidy contract, we then investigate the relationship between the option contract and the subsidy contract in the paper. When a replenishment tactic is considered in the model, supply chain coordination and Pareto improvement can be achieved by introducing the option contract. The paper further shows that the option contract also can effectively coordinate the supply chain when demand is stochastic. Numerical studies are conducted to illustrate our models and validate our findings.
Vendor-managed inventory (VMI) is a business practice in which the supplier manages the inventory at the customer's premises and makes replenishment decisions. VMI has been extensively studied over a short period of time since it was successfully implemented in the industry in the late 1980s. In this paper, we classify and review theoretical and empirical studies on VMI. In particular, we provide three classifications of theoretical papers focusing on the contractual agreement between supply chain partners, drivers of the benefits of VMI, and research approaches, while we classify empirical papers based on their research purposes and methodologies. One of our findings is that most theoretical studies examine event-based VMI contracts such as (z, Z)-Type contracts, while the penalties/rewards are based on long-Term performance in many VMI agreements observed in practice. We also find that most theoretical studies focus on cost reductions from VMI and their drivers, while empirical studies report various benefits of VMI such as lower inventory and fewer stockouts. We suggest several future research directions based on our literature review.
We examine vendor-managed inventory (VMI) systems with stockout-cost sharing between a supplier and a customer using an EOQ model with shortages allowed under limited storage capacity, in which a stockout penalty is charged to the supplier when stockouts occur at the customer. In the VMI systems the customer and the supplier minimize their own costs in designing a VMI contract and making replenishment decisions, respectively. We compare the VMI systems with an integrated supplier-customer system where the supply chain total cost is minimized. We show that VMI with stockout-cost sharing and the integrated supplier-customer system result in the same replenishment decisions and system performance if and only if the supplier's reservation cost is equal to the minimum supply chain total cost of the integrated system. On the other hand, we also show how VMI along with fixed transfer payments as well as stockout-cost sharing can lead to the supply chain coordination regardless of the supplier's reservation cost. We also provide several interesting computational results. © 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS).
In this paper, we propose an option contract for a two-echelon supply chain operating under vendor-managed inventory (VMI). We find that the supply chain coordination and Pareto improvement can be achieved synchronously. As a comparison, a subsidy contract is introduced to coordinate the supply chain. The paper further considers the influence of a replenishment tactic on the performance of the supply chain. After introducing a replenishment tactic, the supply chain can replenish the products to satisfy unmet demand during the selling season. We further use an option contract to coordinate the supply chain, and a Pareto improvement can be gained. All our findings are numerically illustrated.
This paper presents a stochastic inventory model for situations in which, during a stockout period, a fraction β of the demand is backordered and the remaining fraction 1 - β is lost. The model is suggested by the customers' different reactions to a stockout condition: during the stockout period, some patient customers wait until their demand is satisfied, while other impatient or urgent customers cannot wait and have to fill their demand from another source. The cost of a backorder is assumed to be proportional to the length of time for which the backorder exists, and a fixed penalty cost is incurred per unit of lost demand. Based on a heuristic treatment of a lot-size reorder-point policy, a mathematical model representing the average annual cost of operating the inventory system is developed. The optimal operating policy variables minimizing the average annual cost can be calculated iteratively. At the extremes β = 1 and β = 0, the model presented reduces to the usual backorders and lost sales case, respectively.
Firms such as Wal-Mart and Campbell’s Soup have successfully implemented vendor managed inventory (VMI). Articles in the trade press and academic literature often begin with the premise that VMI is ’beneficial’; but beneficial to which party and under what conditions? We consider in this paper a vendor V that manufactures a particular product at a unique location. That item is sold to a single retailer, the customer C. Three cases are treated in detail: independent decision making (no agreement between the parties); VMI, whereby the supplier V initiates orders on behalf of C; and central decision making (both vendor and customer are controlled by the same corporate entity). Values of some cost parameters may vary between the three cases and each case may cause a different actor to be responsible for particular expenses. Under a constant demand rate, optimal solutions are obtained analytically for the customer’s order quantity, the vendor’s production quantity, hence the parties’ individual and total costs in the three cases. Inequalities are obtained to delineate those situations in which VMI is beneficial.
The most common measure of effectiveness used in determining the optimal (s, S) inventory policies is the total cost function per unit time, E(s, Δ), Δ = S − s. In stationary analysis, this function is constructed through the limiting distribution of on-hand inventory, and it involves some renewal-theoretic elements. For Δ ≥ 0 given, E(s, Δ) turns out to be convex in s, so that the corresponding optimal reorder point, s 1 (Δ), can be characterized easily. However, E(s 1 (Δ), Δ) is not in general unimodal on Δ ≥ 0. This requires the use of complicated search routines in computations, as there is no guarantee that a local minimum is global.
Both for periodic and continuous review systems with constant lead times, full backlogging and linear holding and shortage costs, we prove in this paper that E′(s 1 (Δ), Δ) = 0, Δ ≥ 0, is both necessary and sufficient for a global minimum (E(s 1 (Δ), Δ) is pseudoconvex on Δ ≥ 0) if the underlying renewal function is concave. The optimal stationary policy can then be computed efficiently by a one-dimensional search routine. The renewal function in question is that of the renewal process of periodic demands in the periodic review model and of demand .sizes in the continuous review model.
Vendor-managed inventory (VMI) represents the methodology through which the upstream stage of a supply chain (vendor) takes responsibility for managing the inventories at the downstream stage (customer) based on previously agreed limits. VMI is another method by which supply chains can be managed, and, owing to centralised decision-making and constant information sharing, the benefits are much higher than in traditional supply chain case. However, there exists a lack of research that identifies the dimensions of VMI, benefits of VMI, methods, and levels used in the VMI environment. The focus of this paper is to explore the existing literature on VMI, to categorise it according to the criteria evaluated, and to present a systematic review. In this study, we have classified the review into three categories such as dimension-based, methodology-based, and level-based. From the thorough literature review, we have identified six dimensions of VMI: namely, inventory, transportation, manufacturing, general benefits, coordination/collaboration, and information sharing. In addition, there are, three methodological classifications: modelling, simulation, and case studies. Finally, we will consider the level-based classification. Based on the review, several recommendations that improve the performance of VMI are presented.
In this paper, a mathematical model for the single‐vendor single‐buyer problem under VMI configuration is considered. In particular, the contractual agreement between the vendor and buyer is explicitly included. This contract includes an upper limit on the buyer's inventory level such that the vendor is penalised for items exceeding this limit. The purpose of this upper bound is to protect the buyer against excessive inventory. An algorithm is devised to solve the proposed model. Moreover, sensitivity analysis is conducted to show the effect of key parameters of the model on the optimal solution.
Using a unique, item-level data set, we examined benefits to downstream firms (distributors) from the decision-transfer component of vendor-managed inventory (VMI), the feature that distinguishes VMI from other information-sharing, collaborative supply chain programs. Our major findings are that the decision-transfer component of VMI adds significant benefits to the downstream firm in terms of inventory and stockout reductions above and beyond information sharing, and that these two benefits may be realized at different times following VMI implementation; that is, inventory reduction, initially, may be the major benefit to distributors from VMI, while the benefits of stockout reduction may more likely be realized after the first year of implementation. In addition, VMI provides benefits to the upstream firm (manufacturer) by reducing the downstream firm's inventory variability, a likely contributor to the bullwhip effect. Based on our empirical analysis, the decision-transfer component of VMI, on average, reduces inventory levels by 7%, stockouts by 31%, and inventory variability by 9%.
In this paper, we have considered a vendor-managed inventory (VMI) arrangement in a supply chain (SC), where the buyer imposes a penalty for shipments exceeding an upper limit. We have shown as how the industry practice of VMI under penalty can be used as a SC coordination mechanism. The vendor can influence the buyer to increase the batch size without making the buyer worse off. We also discuss how such a penalty scheme may be derived. Further, we have established the equivalence of VMI under deterministic demand with that of quantity discount models, thus highlighting the need to incorporate both cooperation and coordination perspectives while analysing SC collaboration mechanisms.
Vendor managed inventory (VMI) is a supply chain partnership strategy that allows a supplier to place orders on behalf of its customers. This paper considers a supply chain composed of a single vendor and multiple retailers operating under a VMI contract that specifies limits on retailers' stock levels. We address the problem of synchronizing the vendor's cycle time with the buyers' unequal ordering cycles by developing a mixed integer non-linear program that minimizes the joint relevant inventory costs under storage restrictions. We also propose a cost efficient heuristic to solve the developed optimization problem. We conducted computational experiments to assess the reduction in the total supply chain costs resulting from relaxing the restriction of equal ordering cycles. It is found that the heuristic generates greater cost savings in cases of increased variability in retailers' demand and cost parameters.
We examine the problem of designing a vendor-managed inventory (VMI) contract with consignment stock and stockout-cost sharing in a (Q, r) inventory system between a supplier and a retailer. In particular, the contract specifies fixed and proportional penalties charged to the supplier when stockouts occur at the retailer. The retailer chooses the penalties and offers the contract to the supplier, and the supplier can accept or reject the contract. If he accepts it, the supplier manages the inventory at the retailer and makes replenishment decisions. For the deterministic demand we characterize the optimal contract for the retailer and the corresponding optimal inventory policy for the supplier. Our computational study for the deterministic and stochastic demands provides several interesting results. In particular, it suggests that VMI may result in significant cost savings for both the retailer and the supplier, but that the retailer may not always benefit from VMI. Our study also sheds lights on the relationship between VMI and replenishment leadtime and the value of information sharing on the retailer's stockout quantity in VMI contracting.
We consider inventory systems which are governed by an (r,q) or (r,nq) policy. We derive general conditions for monotonicity of the three optimal policy parameters, i.e., the optimal reorder level, order quantity and order-up-to level, as well as the optimal cost value, as a function of the various model primitives, be it cost parameters or complete cost rate functions or characteristics of the demand and leadtime processes. These results are obtained as corollaries from a few general theorems, with separate treatment given to the case where the policy parameters are continuous variables and that where they need to be restricted to integer values. The results are applied both to standard inventory models and to those with general shelf age and delay dependent inventory costs.
We consider single-item (r, q) and (s, T) inventory systems with integer-valued demand processes. While most of the inventory literature studies continuous approximations of these models and establishes joint convexity properties of the policy parameters in the continuous space, we show that these properties no longer hold in the discrete space, in the sense of linear interpolation extension and L♮-convexity. This nonconvexity can lead to failure of optimization techniques based on local optimality to obtain the optimal inventory policies. It can also make certain comparative properties established previously using continuous variables invalid. We revise these properties in the discrete space.
The article presents a stochastic inventory model for situations in which, during a stockout period, a fraction beta of the demand is backordered and the remaining fraction 1 minus beta is lost. The model is suggested by the customers' different reactions to a stockout condition: during the stockout period, some patient customers wait until their demand is satisfied, while other impatient or urgent customers cannot wait and have to fill their demand forom another source. The cost of a backorder is assumed to be proportional to the length of time for which the backorder exists, and a fixed penalty cost is incurred per unit of lost demand. Based on a heuristic treatment of a lot-size reorder-point policy, a mathematical model representing the average annual cost of operating the inventory system is developed. The optimal operating policy variables minimizing the average annual cost can be calculated iteratively.
The reorder point/reorder quantity policies, also referred to as (r,Q) policies, are widely used in industry and extensively studied in the literature. However, for a period of almost 30 years there has been no efficient algorithm for computing optimal control parameters for such policies. We present a surprisingly simple and efficient algorithm for the determination of an optimal (r * ,Q * ) policy. The computational complexity of the algorithm is linear in Q * . For the most prevalent case of linear holding, backlogging and stockout penalty costs (in addition to fixed order costs), the algorithm requires at most (6r * +13Q * ) elementary operations (additions, comparisons and multiplications), and hence, no more than 13 times the amount of work required to do a single evaluation of the long-run average cost function in the point (r * ,Q * ).
Purpose
The purpose of this paper is to define the standard structure of a vendor managed inventory (VMI) agreement, which can be used as a guideline for the early definition of the agreement.
Design/methodology/approach
Starting from an industrial application of relevance, the information flow and the technical details, which are to be defined before the operation startup, are identified and discussed. These data are used as the key points for the definition of the basic frame of the agreement. A particular emphasis is given to the “Technical Specification” and the “Service Level Agreement” sections.
Findings
It is shown that a VMI agreement should be arranged into parts dealing with the generic and legal sides of the agreement, whereas the technical aspects and the relation‐specific topics should be addressed in the annexes. This increases the flexibility of the agreement in that, as the VMI relationship evolves over time, changes will affect only the annexes leaving the main body of the agreement unaltered.
Practical implications
The proposed agreement has a flexible structure and can be easily adopted by the personnel involved to correctly define and implement VMI in several industrial fields.
Originality/value
By approaching VMI from a practical point of view, this paper identifies the main issues that must be covered in the agreement to fit the needs of both parties and to assure benefits on both sides.
Purpose – To highlight how vendor managed inventory (VMI) can be extended both upstream and downstream in the supply network to co-ordinate the material and information flows among a number of different suppliers, manufacturing and distribution plants (“extended VMI”). Design/methodology/approach – The research is based on data and information gathered during an in-depth case study within the supply network co-ordinated by GlaxoSmithKline, one of the world's leading research-based pharmaceutical and healthcare companies. Findings – Defines the peculiarities and the requisites of the extended VMI as to: the information flows supporting the relationships among the supply network members; the information systems, supporting the data collection, management, diffusion and elaboration; the performance monitoring system, highlighting the benefits for each supply network member as well as avoiding opportunistic behaviours. Research limitations/implications – The research intends to offer an original contribution to the stream of research on VMI, explaining the peculiarities and the requisites of the extended VMI. Future research should seek to consider the extended VMI in light of some supply chain management (SCM) practices which have emerged in recent years, such as collaborative planning, forecasting and replenishment. Moreover, a second research opportunity lies in investigating the mixes of SCM initiatives – among which is also the extended VMI – needing launch in a perspective of optimisation of the whole supply network. Practical implications – The case reported here and the research findings should offer guidance for managers facing the decision-making process concerning the implementation of the VMI both upstream and downstream in the supply network. Originality/value – Most authors tend to consider VMI at the dyadic level, namely as an approach for managing materials and information flows between one or more customers and their immediate suppliers. Instead, this research adopts a supply network perspective, seeking to explain how VMI can be extended both upstream and downstream and considering the supply network as a whole rather than as a series of dyads.
In the modern supplier-customer relationship, Vendor Managed Inventory (VMI) is used to monitor the customer's inventory replenishment. Despite the large amount of literature on the subject, it is difficult to clearly define VMI and the main associated processes. Beyond the short-term pull system inventory replenishment often studied in academic works, partners have to share their vision of the demand, their requirements and their constraints in order to fix shared objectives for the medium/long-term. In other words, the integration of VMI implies consequences for the collaborative process that links each partner's different planning processes. In this article we propose a literature review of VMI. Based on the conceptual elements extracted from this analysis, we suggest a VMI macro-process that summarises both operational and collaborative elements of VMI.
Using a system-point (SP) method of level crossings, we derive the stationary distribution of the inventory level (stock on hand) in a continuous-review inventory system with compound Poisson demand, Erlang as well as hyperexponentially distributed lead times, and lost sales. This distribution is then used to formulate long-run average cost functions with/without a service level constraint. Some numerical results are also presented, and compared with the Hadley and Whitin heuristic. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 259–278, 1998
The exact expression is derived for the average stationary cost of a (Q,R) inventory system with lost sales, unit Poisson demands, Erlang-distributed lead times, fixed order cost, fixed cost per unit lost sale, linear holding cost per unit time, and a maximum of one order outstanding. Explicit expressions for the state probabilities and a fast method of calculating them are obtained for the case of Q greater than R. Exponential lead times are analyzed as a special case. A simple cyclic coordinate search procedure is used to locate the minimum cost policy. Examples of the effect of lead time variability on costs are given.
For most order quantity/reorder point inventory systems, the stochastic model, which specifies the demands as stochastic processes, is often more accurate than its deterministic counterpart—the EOQ model. However, the application of the stochastic model has been limited because of the absence of insightful analytical results on the model.
This paper analyzes the stochastic order quantity/reorder point model in comparison with a corresponding deterministic EOQ model. Based on simple optimality conditions for the control variables derived in the paper, a sensitivity analysis is carried out, and a number of basic qualitative properties are established for the optimal control parameters. Our main results include the following: (1) in contrast to the deterministic EOQ model, the controllable costs of the stochastic model due to selection of the order quantity (assuming the reorder point is chosen optimally for every order quantity) are actually smaller, while the total costs are clearly larger; the optimal order quantity is larger, but the difference is relatively small when the quantity is large; the cost performance is even less sensitive to choices of the order quantity; (2) the relative increase of the costs incurred by using the quantity determined by the EOQ instead of the optimal from the stochastic model is no more than 1/8, and vanishes when the ordering costs are significant relative to other costs.
We argue that standard approximations for two often-used inventory service-level measures may perform poorly in many situations. Then we confirm the long-standing conjecture that the (relatively) exact formulas for these quantities are convex functions of the relevant control variables. Both results suggest the exact expressions should be seriously considered in practical work.
A method is developed to calculate an (s, S) policy that minimizes the average stationary cost in an inventory system with: constant lead time, fixed order cost, linear holding cost per unit time, linear penalty cost per unit short, discrete compound Poisson demand, and lost sales. It is assumed that at most one order is outstanding, or equivalently that S - s > s. The procedure is compared to several easier-to-compute approximate solutions, including one that assumes backordering. Examples are given that reveal that although the backorder solution is different than the lost sales one, the cost penalty of using it in the lost sales situation is small.
Vendor-managed inventory (VMI) is a well-known industry practice for supply chain collaboration. In this paper we consider a periodic-review stochastic inventory model to examine the benefits of VMI in a global environment, in which the supplier and the retailer face exchange rate uncertainty and incur different fixed ordering costs. Our study suggests that, despite of all the inventory costs transferred from the retailer, the supplier can benefit from VMI by achieving economies of scale in production/delivery. It also suggests that the supply chain total cost always decreases under VMI and the reduction of the supply chain total cost is larger when there is exchange rate uncertainty, compared with the case of no exchange rate uncertainty. We also provide some analytical results, including the optimality of a state-dependent (s, S) policy for the supplier.
Based on continuous review (r, Q) policy, this paper deals with contracts for vendor managed inventory (VMI) program in a system comprising a single vendor and a single retailer. Two business scenarios that are popular in VMI program are "vendor with ownership" and "retailer with ownership". Taking the system performance in centralized control as benchmark, we define a contract "perfect" if the contract can enable the system to be coordinated and can guarantee the program to be trusted. A revenue sharing contract is designed for vendor with ownership, and a franchising contract is designed for retailer with ownership. Without consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the other one is a perfect contract. With consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the performance of the other one depends on system parameters.
We analyze decentralized supply chains that follow general continuous review (Q, R) inventory policies subject to vendor-managed inventory agreements where the supplier chooses the order quantity Q, and the retailer chooses the reorder point R. Within the VMI scenario, we explore the effect of divisions of channel power on supply chain and individual agent performance
by examining different game theoretic models. Optimal policies and analytical results, including existence and uniqueness
proofs for equilibrium solutions under VMI, are derived. Numerical results are provided to compare the effectiveness of VMI
and to analyze different channel power relationships under a variety of environmental conditions. We find that VMI can result
in considerable supply chain savings over traditional relationships and that the relative division of channel power can significantly
effect the performance of VMI. Interestingly, we find that the greatest system benefits from VMI arise in asymmetric channel
power relationships, but that individual agents lack the incentive to assume a leadership role.
This research evaluates how vendor managed inventory (VMI) affects a supply channel. Specifically, VMI always leads to a higher buyer's profit, but supplier's profit varies. In the short-term, VMI is found to reduce total costs of the channel system, but under certain cost conditions between buyer and supplier, it could decrease the purchasing price and supplier's profit. In the long-run, it could more likely increase supplier's profit than in the short-run. Finally, VMI is an effective supply chain strategy that can realize many of the benefits obtainable only in a fully integrated supply chain.
Vendor managed inventory is an integrated approach for retailer–vendor coordination, according to which the vendor decides on the appropriate inventory levels within bounds that are agreed upon in a contractual agreement between vendor and retailers. In this contract, the vendor usually incurs a penalty cost for items exceeding these bounds. The purpose of this paper is to develop a model for a supply chain with single vendor and multiple retailers under VMI mode of operation. This model explicitly includes the VMI contractual agreement between the vendor and retailers. The developed model can easily describe supply chains with capacity constraints by selecting high penalty cost. Theorems are established to alleviate the complexity of the model and render the mathematics tractable. Moreover, an efficient algorithm is devised to find the global optimal solution. This algorithm reduces the computational efforts significantly. In addition, numerical experiments are conducted to show the utility of the proposed model.
This paper deals with the joint management of operations at the supply hub for the customer and the upstream supplier. Different operating conditions are considered, namely, backordering, minimum and maximum specified inventory levels. Some analytical insights on better managing suppliers operating under a vendor managed inventory program are presented. Essentially, we show that the penalty cost imposed on over- and under-stocking, and the min–max policy for hub inventory reside in the power of the hub operator. The relationship between supply hub policy and performance measures is quite complex and non-linear in nature. We suggest a structured hierarchical approach which can help supply hub in achieving balance between various parties involved in chain. A numerical example and an algorithm are included to highlight this result.
In this paper we use policy-iteration to explore the behaviour of optimal control policies for lost sales inventory models with the constraint that not more than one replenishment order may be outstanding at any time. Continuous and periodic review, fixed and variable lead times, replenishment order sizes which are constrained to be an integral multiple of some fixed unit of transfer and service level constraint models are all considered. Demand is discrete and, for continuous review, assumed to derive from a compound Poisson process. It is demonstrated that, in general, neither the best (s, S) nor the best (r, Q) policy is optimal but that the best policy from within those classes will have a cost which is generally close to that of the optimal policy obtained by policy iteration. Finally, near-optimal computationally-efficient control procedures for finding (s, S) and (r, Q) policies are proposed and their performance illustrated.
As the implementation of JIT practice becomes increasingly popular, each echelon in a supply chain tends to carry fewer inventories, and thus the whole supply chain is made more vulnerable to lost sales and/or backorders. The purpose of this paper is to recast the inventory model to be more relevant to current situations, where the penalty cost for a shortage occurrence at a downstream stage in a supply chain is continually transmitted to the upstream stages. The supplier, in this case, at the upstream of the supply chain is responsible for all the downstream shortages due to the chain reaction of its backlog. The current paper proposes a model in which the backorder cost per unit time is a linearly increasing function of shortage time, and it claims that the optimal policy for the supplier is setting the optimal shortage time per inventory cycle to minimize its total relevant cost in a JIT environment.
We consider a continuous review (r, Q) inventory system with Poisson demands and at most one order outstanding. The replenishment lead time is either constant or exponentially distributed. Demands not covered immediately from inventory are lost. Costs include a linear order cost with a fixed cost per order, and a fixed cost per unit lost sale. As regards inventory holding costs, the cost of capital often constitutes a major part. This paper focuses on these interest-related holding costs.In the undiscounted case, holding costs are linear and inventory performance is measured by the long-run average total cost incurred per unit time. In the discounted case, the performance measure is the expected present value of the ordering and lost sales costs. The cost associated with capital tied up in inventory is accounted for by an appropriate discount rate.We formulate an exact model and design a policy-iteration algorithm for the discounted case. Results on the form of an optimal replenishment policy are derived and the model is compared to a previously derived model for the undiscounted case. Numerical experiments are used to evaluate the difference between the optimal solutions with and without discounting. The effect of a stochastic lead time on this difference is also considered by comparing solutions with constant and exponential lead times. In general, the differences seem to be fairly small but exceptional cases exist when the service level is low.