Coordination in a Single‐Supplier,Multi‐Retailer Distribution System: Supplier‐Facilitated Transshipments

We consider supplier‐facilitated transshipments for achieving supply chain coordination in a single supplier, multi‐retailer distribution system with non‐cooperative retailers. The previous transshipment literature has focused on coordination through retailer‐negotiated transshipments and thus does not consider the supplier's decision‐making. In contrast, in this study, we assume the supplier is an active participant in the system and we seek to understand how the supplier can facilitate the implementation of coordinating transshipments. We study a two‐period model with wholesale orders at the start of the first period and preventive transshipments performed at the start of the second period. Inspired by a supplier‐facilitated transshipment scheme observed in practice, we assume the supplier implements transshipments through a bi‐directional adjustment contract. Under this contract, each retailer can either buy additional inventory from, or sell back excess inventory to, the supplier. We show that coordination can be achieved through carefully designed contracts with state‐dependent adjustment prices and a wholesale price menu. We demonstrate that the supplier's role in facilitating coordinating transshipments is critical. In addition, we use our understanding of the coordinating contract form to derive some simpler and easier‐to‐implement heuristic contracts. We use a numerical study to demonstrate the value, to the supplier, of using the coordinating adjustment and wholesale prices, and to evaluate the heuristics’ performance.     

应对突发事件的库存共享策略

以包含两个销售商的库存系统为例,构建了一个描述库存共享应对突发事件的非合作博弈模型,证明了其纳什均衡解是唯一存在的。研究结果显示库存共享策略总有可能使得销售商的期望利润得以改进。另外,比较静态分析反映了转载价格和转载成本显著影响库存共享销售商的最优订货量和最优期望利润。最后,提出了一个简单的求解模型纳什均衡解的启发式算法。     

A Bayesian Inventory Model Using Real‐Time Condition Monitoring Information

Lack of coordination between machinery fault diagnosis and inventory management for spare parts can lead to increased inventory costs and disruptions in production activity. We develop a framework for incorporating real‐time condition monitoring information into inventory decisions for spare parts. We consider a manufacturer who periodically replenishes inventory for a machine part that is subject to deterioration. The deterioration is captured via condition monitoring and modeled using a Wiener process. The resulting degradation model is used to derive the life distribution of a functioning part and to estimate the demand distribution for spare parts. This estimation is periodically updated, in a Bayesian manner, as additional information on part deterioration is obtained. We develop an inventory model that incorporates this updated demand distribution and demonstrate that a dynamic base‐stock policy, in which the optimal base‐stock level is a function of some subset of the observed condition monitoring information, is optimal. We propose a myopic critical fractile policy that captures the essence of the optimal policy, but is easier to compute. Computational experiments indicate that this heuristic performs quite well relative to the optimal policy. Adaptive inventory policies such as these can help manufacturers to increase machine availability and reduce inventory costs.     

An Efficient and Robust Design for Transshipment Networks

Transshipment, the sharing of inventory among parties at the same echelon level of a supply chain, can be used to reduce costs. The effectiveness of transshipment is in part determined by the configuration of the transshipment network. We introduce chain configurations in transshipment settings, where every party is linked in one connected loop. Under simplifying assumptions we show analytically that the chain configuration is superior to configurations suggested in the literature. In addition, we demonstrate the efficiency and robustness of chain configurations for more general scenarios and provide managerial insights regarding preferred configurations for different problem parameters.     

Lateral transshipment with partial request and random switching

A large body of inventory management research has been devoted to lateral transshipment. Most of the existent models assume that the unmet local demand will automatically request transshipment, and that the unmet local demand does not seek inventory at other locations within the same echelon. In contrast, we investigate a two-store retailer’s inventory replenishment and transshipment decisions when those two assumptions do not hold. Specifically, we use a fixed request rate to model partial demand for transshipment at the shortage store and a random switch rate to model the arrival of the unmet demand at the surplus store. We characterize the optimal transshipment and inventory replenishment policies. We find that it is not always in the best interest of the retailer to satisfy as much as possible the transshipment demand. In light of the switched demand flowing to the surplus store, the retailer may benefit from saving the leftover inventory at the surplus store for the switched demand. The optimal transshipment policy follows a double-threshold structure when the prospect of the switched demand is not large enough; and a transshipment quantity of zero becomes optimal otherwise. Through an extensive numerical analysis, we examine the impact of the request rate and the switch rate, together with other parameters. We also evaluate a few simple-to-use transshipment heuristics, including one that we devise based on the structure of the optimal transshipment policy. The consistent, near-optimal performance of the devised heuristic is a confirmation of the importance of our theoretical work on the optimal policy.     

Joint Initial Stocking and Transshipment—Asymptotics and Bounds

A common problem faced by many firms in their supply chains can be abstracted as follows. Periodically, or at the beginning of some selling season, the firm needs to distribute finished goods to a set of stocking locations, which, in turn, supply customer demands. Over the selling season, if and when there is a supply‐demand mismatch somewhere, a re‐distribution or transshipment will be needed. Hence, there are two decisions involved: the one‐time stocking decision at the beginning of the season and the supply/transshipment decision throughout the season. Applying a stochastic dynamic programming formulation to a two‐location model with compound Poisson demand processes, we identify the optimal supply/transshipment policy and show that the optimal initial stocking quantities can be obtained via maximizing a concave function whereas the contribution of transshipment is of order square‐root‐of T. Hence, in the context of high‐volume, fast‐moving products, the initial stocking quantity decision is a much more important contributor to the overall profit. The bounds also lead to a heuristic policy, which exhibits excellent performance in our numerical study; and we further prove both the bounds and the heuristic policy are asymptotically optimal when T approaches infinity. Extension to multiple locations is also discussed.     

On the benefits of operational flexibility in a distribution network with transshipment

We consider a centralized distribution network with multiple retailers who receive replenishment inventory to satisfy customer demand of the local markets. The operational flexibility of the network is defined as the opportunity that one retailer's excess inventory can be transferred to satisfy other retailers’ unmet customer demand due to stock-outs. A general modeling framework is developed to optimize retailers’ order quantities under any possible flexibility level of a stylized two-stage distribution network. We apply the framework to formulate and solve the transshipment problem of a distribution network with three retailers. Six typical flexibility levels are investigated to make the comparison study on the firm's profit performance under three ordering quantity policies: average demand, newsvendor order quantity, and optimal order quantity. We find that the operational flexibility and system optimization are complements to the firm's performance. The ordering policy with newsvendor ordering quantity can perform fairly well with moderate flexibility level when compared with the optimized ordering policy with full flexibility.     

Dynamic Pricing and Inventory Management with Regular and Expedited Supplies

We consider a periodic‐review inventory system with regular and expedited supply modes. The expedited supply is faster than the regular supply but incurs a higher cost. Demand for the product in each period is random and sensitive to its selling price. The firm determines its order quantity from each supply in each period as well as its selling price to maximize the expected total discounted profit over a finite or an infinite planning horizon. We show that, in each period if it is optimal to order from both supplies, the optimal inventory policy is determined by two state‐independent thresholds, one for each supply mode, and a list price is set for the product; if only the regular supply is used, the optimal policy is a state‐dependent base‐stock policy, that is, the optimal base‐stock level depends on the starting inventory level, and the optimal selling price is a markdown price that decreases with the starting inventory level. We further study the operational impact of such supply diversification and show that it increases the firm's expected profit, reduces the optimal safety‐stock levels, and lowers the optimal selling price. Thus that diversification is beneficial to both the firm and its customers. Building upon these results, we conduct a numerical study to assess and compare the respective benefit of dynamic pricing and supply diversification.     

区分仓库与货架库存需求影响效应的零售商库存决策

既往有关库存水平影响需求条件下的库存问题研究中,通常对终端库存水平是否存在货架与零售商仓库库存水平的区别未作深入探讨。本文的研究认为,现实中许多零售商拥有仓库,其现有库存水平包括仓库库存和货架库存两部分,而影响需求的仅为与货架展示能力相关的库存,因此有必要对二者的需求影响效应进行区分。在明确这一区别的前提下,本文首先建立了供应商管理库存情况下库存水平影响需求问题的一般库存模型,给出零售商的最优订货策略;并考虑货架的容量限制,给出零售商启用仓库的判断条件。由于仓库库存仅在能够影响货架展示能力的条件下才能够影响消费需求,本文还进一步讨论了在零售商拥有仓库时,区分货架与仓库的库存水平影响需求条件下的最优库存与订货决策。这对于经营不同特征商品的零售商在进行是否需要拥有仓库,以及拥有仓库条件下的库存决策具有很好的参考价值。     

Decentralised bilevel model for shared inventory management

In this study, we consider the case of a large corporation that owns a warehouse and two concurrent chains. The company opted for shared inventory policy. The warehouse is looking into minimising its inventory cost and at the same time reducing the fluctuation of the personnel. The chains, independently, are trying to minimise their inventory costs. The warehouse plays the role of a leader in optimising its objectives and, as followers, the two chains try to satisfy their objectives. The problem is formulated into a decentralised nonlinear bilevel programming problem. We also consider the fuzziness of some parameters due to the imprecise available information. We propose the mathematical model and we solve it for our specific case.     

Building Supply Chain Resilience through Virtual Stockpile Pooling

Stockpiling inventory is an essential strategy for building supply chain resilience. It enables firms to continue operating while finding a solution to an unexpected event that causes a supply disruption or demand surge. While extremely valuable when actually deployed, stockpiles incur large holding costs and usually provide no benefits until such a time. To help to reduce this cost, this study presents a new approach for managing stockpiles. We show that if leveraged intelligently, stockpiles can also help an organization better meet its own regular demand by enabling a type of virtual pooling we call virtual stockpile pooling (VSP). The idea of VSP is to first integrate the stockpile into several locations’ regular inventory buffers and then dynamically reallocate the stockpile among these locations in reaction to the demand realizations to achieve a kind of virtual transshipment. To study how to execute VSP and determine when it can provide the most value, we formulate a stylized multi‐location stochastic inventory model and solve for the optimal stockpile allocation and inventory order policies. We show that VSP can provide significant cost savings: in some cases nearly the full holding cost of the stockpile (i.e., VSP effectively maintains the stockpile for free), in other cases nearly the savings of traditional physical inventory pooling. Last, our results prescribe implementing VSP with many locations for large stockpiles, but only a few locations for small stockpiles.     

Note on solving inventory models from operational research view

In this article, we will show that an optimal solution can be derived without complicated mathematical derivation, an improvement on the paper [Yang, G.K., et al., 2011. Note on inventory models with Weibull distribution deterioration. Production Planning & Control, 22 (4), 437–444] that was recently published in Production Planning & Control. We extend their inventory model with a generalised deterioration and backlog rates. Our findings will allow researchers to consider inventory models directly from the view of operational research instead of complex analysis.     

The Effect of Distribution Processes on Replenishment Lead Time and Inventory

We investigate the interrelationship of distribution center picking policies and supply chain inventory performance. In particular, we show how the picking sequence in the upstream supply chain link affects the inventory levels of items being replenished to a downstream link for a common “ship‐when‐full” trailer dispatching policy. Perturbing the picking sequence affects items’ inventory levels asymmetrically which causes the aggregate system inventory to vary. We separate the items in replenishment into those units in transit and those awaiting shipment from the upstream distribution step: we call the latter the residual replenishment. We show that the process governing aggregate residual replenishment is Markov and has a stationary distribution that is discrete uniform. Computing the item‐level residual distribution is intractable and so we develop analytical models from which we derive hypotheses for the effectiveness of stable vs. random picking sequences, how item residual replenishment varies with stable picking sequences, and how the aggregate inventory level changes with picking sequence. These suggest a heuristic sequencing algorithm for minimizing inventory, which performs well in simulation tests over a large testbed of parameter sets.     

Coordinated Logistics: Joint Replenishment with Capacitated Transportation for a Supply Chain

In this study, we consider the integrated inventory replenishment and transportation operations in a supply chain where the orders placed by the downstream retailer are dispatched by the upstream warehouse via an in‐house fleet of limited size. We first consider the single‐item single‐echelon case where the retailer operates with a quantity based replenishment policy, (r,Q), and the warehouse is an ample supplier. We model the transportation operations as a queueing system and derive the operating characteristics of the system in exact terms. We extend this basic model to a two‐echelon supply chain where the warehouse employs a base‐stock policy. The departure process of the warehouse is characterized in distribution, which is then approximated by an Erlang arrival process by matching the first two moments for the analysis of the transportation queueing system. The operating characteristics and the expected cost rate are derived. An extension of this system to multiple retailers is also discussed. Numerical results are presented to illustrate the performance and the sensitivity of the models and the value of coordinating inventory and transportation operations.     

Optimal Inventory Control with Dual‐Sourcing,Heterogeneous Ordering Costs and Order Size Constraints

We consider a dual‐sourcing inventory system, where procuring from one supplier involves a high variable cost but negligible fixed cost whereas procuring from the other supplier involves a low variable cost but high fixed cost, as well as an order size constraint. We show that the problem can be reduced to an equivalent single‐sourcing problem. However, the corresponding ordering cost is neither concave nor convex. Using the notion of quasi‐convexity, we partially characterize the structure of the optimal policy and show that it can be specified by multiple thresholds which determine when to order from each supplier and how much. In contrast to previous research, which does not consider order size constraints, we show that it is optimal to simultaneously source from both suppliers when the beginning inventory level is sufficiently low. We also show that the decision to source from the low‐cost supplier is not monotonic in the inventory level. Our results require that the variable costs satisfy a certain condition which guarantees quasi‐convexity. However, extensive numerical results suggest that our policy is almost always optimal when the condition is not satisfied. We also show how the results can be extended to systems with multiple capacitated suppliers.     

Multiple In‐Cycle Transshipments with Positive Delivery Times

We study a centralized inventory sharing system of two retailers that are replenished periodically. Between two replenishments, a unit can be transshipped to a stocked‐out retailer from the other. It arrives a transshipment time later, during which the stocked‐out retailer incurs backorder cost. Without transshipment, backorder cost is incurred until the next replenishment. Since the transshipment time is shorter than the time between two replenishments, transshipments can reduce the backorder cost at the stocked‐out retailer and the holding costs at the other retailer. The system is directed by a centralized inventory manager, who minimizes the long‐run average cost consisting of replenishment, holding, backorder, and transshipment costs. The transshipment policy is characterized by hold‐back inventory levels, which are nonincreasing in the remaining time until the next replenishment. The transshipment policy differs from those in the literature because we allow for multiple transshipments between replenishments, positive transshipment times, and backorder costs. We also discuss the challenges associated with positive replenishment time and develop upper and lower bounds of average cost in this case. Bounds are numerically shown to have an average gap of 1.1%. A heuristic solution is based on the upper bound and differs from the optimal cost by at most this gap.     

Managing Retail Shelf and Backroom Inventories When Demand Depends on the Shelf‐Stock Level

Inventory displayed on the retail sales floor not only performs the classical supply function but also plays a role in affecting consumers’ buying behavior and hence the total demand. Empirical evidence from the retail industry shows that for some types of products, higher levels of on‐shelf inventory have a demand‐increasing effect (“billboard effect”) while for some other types of products, higher levels of on‐shelf inventory have a demand‐decreasing effect (“scarcity effect”). This suggests that retailers may use the amount of shelf stock on display as a tool to influence demand and operate a store backroom to hold the inventory of items not displayed on the shelves, introducing the need for efficient management of the backroom and on‐shelf inventories. The purpose of this study is to address such an issue by considering a periodic‐review inventory system in which demand in each period is stochastic and depends on the amount of inventory displayed on the shelf. We first analyze the problem in a finite‐horizon setting and show under a general demand model that the system inventory is optimally replenished by a base‐stock policy and the shelf stock is controlled by two critical points representing the target levels to raise up/drop down the on‐shelf inventory level. In the infinite‐horizon setting, we find that the optimal policies simplify to stationary base‐stock type policies. Under the billboard effect, we further show that the optimal policy is monotone in the system states. Numerical experiments illustrate the value of smart backroom management strategy and show that significant profit gains can be obtained by jointly managing the backroom and on‐shelf inventories.     

Dynamic Pricing and Inventory Management with Dual Suppliers of Different Lead Times and Disruption Risks

It is common for a firm to make use of multiple suppliers of different delivery lead times, reliabilities, and costs. In this study, we are concerned with the joint pricing and inventory control problem for such a firm that has a quick‐response supplier and a regular supplier that both suffer random disruptions, and faces price‐sensitive random demands. We aim at characterizing the optimal ordering and pricing policies in each period over a planning horizon, and analyzing the impacts of supply source diversification. We show that, when both suppliers are unreliable, the optimal inventory policy in each period is a reorder point policy and the optimal price is decreasing in the starting inventory level in that period. In addition, we show that having supply source diversification or higher supplier reliability increases the firm's optimal profit and lowers the optimal selling price. We also demonstrate that, with the selling price as a decision, a supplier may receive even more orders from the firm after an additional supplier is introduced. For the special case where the quick‐response supplier is perfectly reliable, we further show that the optimal inventory policy is of a base‐stock type and the optimal pricing policy is a list‐price policy with markdowns.     

Information‐Sensitive Replenishment when Inventory Records Are Inaccurate

Inspired by recent empirical work on inventory record inaccuracy, we consider a periodic review inventory system with imperfect inventory records and unobserved lost sales. Record inaccuracies are assumed to arrive via an error process that perturbs physical inventory but is unobserved by the inventory manager. The inventory manager maintains a probability distribution around the physical inventory level that he updates based on sales observations using Bayes Theorem. The focus of this study is on understanding, approximating, and evaluating optimal forward‐looking replenishment in this environment. By analyzing one‐ and two‐period versions of the problem, we demonstrate several mechanisms by which the error process and associated record inaccuracy can impact optimal replenishment. Record inaccuracy generally brings an incentive for a myopic manager to increase stock to buffer the added uncertainty. On the other hand, a forward‐looking manager will stock less than a myopic manager, in part to improve information content for future decisions. Using an approximate partially observed dynamic programming policy and associated bound, we numerically corroborate our analytical findings and measure the effectiveness of an intelligent myopic heuristic. We find that the myopic heuristic is likely sufficiently good in practical settings targeting high service levels.