Contracting Under Vendor Managed Inventory Systems Using Holding Cost Subsidies

Vendor managed inventory systems are becoming increasingly popular. An important issue in implementing a vendor managed inventory scheme is the contracting terms that dictate the ownership of the inventory and the responsibility of inventory replenishment decisions. Thus the performance of a vendor managed system crucially depends on these terms and on how inventory‐related costs are shared in a supply chain. We consider a system where a manufacturer supplies a single product to a retailer who faces random demand in a competitive market. The retailer incurs a fixed cost per order, inventory holding cost, and a penalty cost for a stockout (unsatisfied demand is back‐ordered). Further, the manufacturer incurs a penalty cost when there is a stockout at the retailer and a fixed replenishment cost. We assume that the players are rational and act noncooperatively. We compare the performance of retailer managed inventory systems, where the retailer places orders and makes replenishment decisions, with vendor managed inventory systems, wherein the vendor or manufacturer makes inventory and replenishment decisions. Specifically, in the vendor managed inventory system, we propose and evaluate holding cost subsidy‐type contracts on inventories offered by the retailer to improve system performance. We evaluate this contract in the context of three widely used inventory systems—deterministic economic order quantity, continuous review (Q, r) policies, and periodic review policies—and show when such contracts may improve channel performance.     

Managing Electricity Peak Loads in Make‐To‐Stock Manufacturing Lines

In this article, we study the control of stochastic make‐to‐stock manufacturing lines in the presence of electricity costs. Electricity costs are difficult to manage because unit costs increase with the total load, that is, the amount of electricity needed by the manufacturing line at a certain point in time. We demonstrate that standard methods for controlling manufacturing lines cannot be used and that standard analytic results for stochastic manufacturing lines do not hold in the presence of electricity costs. We develop a control policy that balances electricity costs with inventory holding and backorder costs. We derive closed‐form expressions and analytic properties of the expected total cost for manufacturing lines with two workstations and demonstrate the accuracy and robustness of the policy for manufacturing lines with more than two workstations. The results indicate that avoiding electricity peak loads requires additional investment in manufacturing capacity and higher inventory and backorder costs. Our approach also applies to companies which aim at reducing their carbon emissions in addition to their operating costs.     

A Stochastic Inventory Model With Fast‐Ship Commitments

We present a multiperiod model of a retail supply chain, consisting of a single supplier and a single retailer, in which regular replenishment occurs periodically but players have the option to support fast delivery when customers experience a stockout during a replenishment period. Because expedited shipments increase the supplier's transportation cost, and possibly production/inventory costs, the supplier typically charges a markup over and above the prevailing wholesale price for fast‐shipped items. When fast shipping is not supported, items are backordered if customers are willing to wait until the start of the next replenishment period. We characterize the retailers and the supplier's optimal stocking and production policies and then utilize our analytical framework to study how the two players respond to changes in supply chain parameters. We identify a sufficient condition such that the centralized supply chain is better off with the fast‐ship option. We find a range of markups for fast‐ship orders such that the fast‐ship option is preferred by both the supplier and the retailer in a decentralized chain. However, a markup that is a win–win for both players may not exist even when offering fast‐ship option is better for the centralized chain. Our analysis also shows that depending on how the markup is determined, greater customer participation in fast‐ship orders does not necessarily imply more profits for the two players. For some predetermined markups, the retailer's profit with the fast‐ship option is higher when more customers are willing to wait. However, the retailer may not be able to benefit from the fast‐ship option because the supplier may choose not to support the fast‐ship option when fast‐ship participation increases due to the fact that the fast‐ship participation rate adversely affects the initial order size.     

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.     

Point‐of‐Use Hybrid Inventory Policy for Hospitals

Modern point‐of‐use technology at hospitals has enabled new replenishment policies for medical supplies. One of these new policies, which we call the hybrid policy, is currently in use at a large U.S. Midwest hospital. The hybrid policy combines a low‐cost periodic replenishment epoch with a high‐cost continuous replenishment option to avoid costly stockouts. We study this new hybrid policy under deterministic and stochastic demand. We develop a parameter search engine using simulation to optimize the long‐run average cost per unit time and, via a computational study, we provide insights on the benefits (reduction in cost, inventory, and number of replenishments) that hospitals may obtain by using the hybrid policy instead of the commonly used periodic policies. We also use the optimal hybrid policy parameters from the deterministic analysis to propose approximate expressions for the stochastic hybrid policy parameters that can be easily used by hospital management.      

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.     

Inventory Management for Customers with Alternative Lead Times

It is common for suppliers operating in batch‐production mode to deal with patient and impatient customers. This paper considers inventory models in which a supplier provides alternative lead times to its customers: a short or a long lead time. Orders from patient customers can be taken by the supplier and included in the next production cycle, while orders from impatient customers have to be satisfied from the on‐hand inventory. We denote the action to commit one unit of on‐hand inventory to patient or impatient customers as the inventory‐commitment decision, and the initial inventory stocking as the inventory‐replenishment decision. We first characterize the optimal inventory‐commitment policy as a threshold type, and then prove that the optimal inventory‐replenishment policy is a base‐stock type. Then, we extend our analysis to models to consider cases of a multi‐cycle setting, a supply‐capacity constraint, and the on‐line charged inventory‐holding cost. We also evaluate and compare the performances of the optimal inventory‐commitment policy and the inventory‐rationing policy. Finally, to further investigate the benefits and pitfalls of introducing an alternative lead‐time choice, we use the customer‐choice model to study the demand gains and losses, known as demand‐induction and demand‐cannibalization effects, respectively.     

Benefits of Hybrid Lateral Transshipments in Multi‐Item Inventory Systems under Periodic Replenishment

Lateral transshipments are a method of responding to shortages of stock in a network of inventory‐holding locations. Conventional reactive approaches only seek to meet immediate shortages. The study proposes hybrid transshipments which exploit economies of scale by moving additional stock between locations to prevent future shortages in addition to meeting immediate ones. The setting considered is motivated by retailers who operate networks of outlets supplying car parts via a system of periodic replenishment. It is novel in allowing non‐stationary stochastic demand and general patterns of dependence between multiple item types. The generality of our work makes it widely applicable. We develop an easy‐to‐compute quasi‐myopic heuristic for determining how hybrid transshipments should be made. We obtain simple characterizations of the heuristic and demonstrate its strong cost performance in both small and large networks in an extensive numerical study.     

无人零售业态下自动售卖机联合补货策略研究

研究无人零售业态下自动售卖机的多产品联合补货问题，建立由补货成本、库存持有成本、缺货成本构成的平均补货成本模型，分析容量约束与固定补货阈值下的最优补货策略。结果表明，企业会倾向于在剩余较少产品时进行补货，剩余的产品往往是投影面积最小使得相同面积可容纳最多数量的产品；比较最优补货时间与平均补货成本发现，延长补货时间可以降低平均补货成本，在补货阈值越大、固定补货成本越低或售卖机容量越小时，最优补货时间会降低，反之，平均补货成本会增加。此外，分析不同成本变动对平均成本的影响发现，单位成本变动均会引起平均补货成本的增加，且在单位库存持有成本变动时，最优补货策略会发生转移，向单位库存持有成本降低至一定程度的产品或向投影面积最低即相同面积可容纳数量最小的产品转移。     

How Inventory Cost Influences Introduction Timing of Product Line Extensions

In the industry with radical technology push or rapidly changing customer preference, it is firms' common wisdom to introduce high‐end product first, and follow by low‐end product‐line extensions. A key decision in this “down‐market stretch” strategy is the introduction time. High inventory cost is pervasive in such industries, but its impact has long been ignored during the presale planning stage. This study takes a first step toward filling this gap. We propose an integrated inventory (supply) and diffusion (demand) framework and analyze how inventory cost influences the introduction timing of product‐line extensions, considering substitution effect among successive generations. We show that under low inventory cost or frequent replenishment ordering policy, the optimal introduction time indeed follows the well‐known “now or never” rule. However, sequential introduction becomes optimal as the inventory holding gets more substantial or the product life cycle gets shorter. The optimal introduction timing can increase or decrease with the inventory cost depending on the marketplace setting, requiring a careful analysis.     

Inventory Rationing for Multiple Class Demand under Continuous Review

We consider how a firm should ration inventory to multiple classes in a stochastic demand environment with partial, class‐dependent backlogging where the firm incurs a fixed setup cost when ordering from its supplier. We present an infinite‐horizon, average cost criterion Markov decision problem formulation for the case with zero lead times. We provide an algorithm that determines the optimal rationing policy, and show how to find the optimal base‐stock reorder policy. Numerical studies indicate that the optimal policy is similar to that given by the equivalent deterministic problem and relies on tracking both the current inventory and the rate that backorder costs are accumulating. Our study of the case of non‐zero lead time shows that a heuristic combining the optimal, zero lead time policy with an allocation policy based on a single‐period profit management problem is effective.     

Managing Slow‐Moving Perishables in the Grocery Industry

We address the value of information and value of centralized control in the context of a two‐echelon, serial supply chain with one retailer and one supplier that provide a single perishable product to consumers. Our analysis is relevant for managing slow‐moving perishable products with fixed lot sizes and expiration dates of a week or less. We evaluate two supply chain structures. In the first structure, referred to as decentralized information sharing, the retailer shares its demand, inventory, and ordering policy with the supplier, yet both facilities make their own profit‐maximizing replenishment decisions. In the second structure, centralized control, incentives are aligned and the replenishment decisions are coordinated. The latter supply chain structure corresponds to the industry practices of company‐owned stores or vendor‐managed inventory. We measure the value of information and value of centralized control as the marginal improvement in expected profits that a supply chain achieves relative to the case when no information is shared and decision making is decentralized. Key assumptions of our model include stochastic demand, lost sales, and fixed order quantities. We establish the importance of information sharing and centralized control in the supply chain and identify conditions under which benefits are realized. As opposed to previous work on the value of information, the major benefit in our setting is driven by the supplier's ability to provide the retailer with fresher product. By isolating the benefit by firm, we show that sharing information is not always Pareto‐improving for both supply chain partners in the decentralized setting.     

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。     

Inventory Commitment and Prioritized Backlogging Clearance with Alternative Delivery Lead Times

We propose a model where customers are classified into two groups: short lead‐time customers who require the product immediately and long lead‐time customers to whom the supplier may deliver either immediately or in the next cycle. Unmet orders are backlogged with associated costs. Specifically, the supplier faces two problems: how the on‐hand inventories should be allocated between the two classes of customers and how the backlogged orders should be cleared when replenishments arrive. We treat the former as an inventory commitment problem and handle the latter with priority rules. We characterize and compare the inventory commitment policies with three priority rules in clearing backlogs. We also explore the optimal inventory replenishment decision and evaluate the performance of each priority rule.     

Grocery Perishables Management

In this article, we study the joint pricing and inventory control problem for perishables when a retailer does not sell new and old inventory at the same time. At the beginning of a period, the retailer makes replenishment and pricing decisions, and at the end of a period, the retailer decides whether to dispose of ending inventory or carry it forward to the next period. The objective of the retailer is to maximize the long‐run average profit. Assuming zero lead time, we propose an efficient solution approach to the problem, which is also generalized to solve three extensions to the basic model. A feature of the present study is that we consider explicitly the influence of perishability on the demand. Among the insights gathered from the numerical analysis, we find that dynamic pricing aids extending shelf life and when disposal incurs a lower cost, or even a positive salvage value, the retailer is induced to dispose earlier since the benefit of selling new inventory offsets the loss due to disposal. We also observe that the faster the perceived rate of deterioration, the lower the threshold of the ending inventory for disposal. Perhaps a bit counter‐intuitive, maximizing profits does not mean eliminating disposals or expirations.     

Inventory‐Based Dynamic Pricing with Costly Price Adjustment

We study an average‐cost stochastic inventory control problem in which the firm can replenish inventory and adjust the price at anytime. We establish the optimality to change the price from low to high in each replenishment cycle as inventory is depleted. With costly price adjustment, scale economies of inventory replenishment are reflected in the cycle time instead of lot size—An increased fixed ordering cost leads to an extended replenishment cycle but does not necessarily increase the order quantity. A reduced marginal cost of ordering calls for an increased order quantity, as well as speeding up product selling within a cycle. We derive useful properties of the profit function that allows for reducing computational complexity of the problem. For systems requiring short replenishment cycles, the optimal solution can be easily computed by applying these properties. For systems requiring long replenishment cycles, we further consider a relaxed problem that is computational tractable. Under this relaxation, the sum of fixed ordering cost and price adjustment cost is equal to (greater than, less than) the total inventory holding cost within a replenishment cycle when the inventory holding cost is linear (convex, concave) in the stock level. Moreover, under the optimal solution, the time‐average profit is the same across all price segments when the inventory holding cost is accounted properly. Through a numerical study, we demonstrate that inventory‐based dynamic pricing can lead to significant profit improvement compared with static pricing and limited price adjustment can yield a benefit that is close to unlimited price adjustment. To be able to enjoy the benefit of dynamic pricing, however, it is important to appropriately choose inventory levels at which the price is revised.     

考虑多种安全库存策略的选址-库存问题研究

考虑多种安全设置策略的物流网络的选址-库存问题,不仅是选址、订货、运输和库存的集成优化,还需要考虑多种不同的安全库存设置和转运策略。因此,本文深入讨论了二级物流网络中的六种安全库存设置策略,构建了六种考虑不同安全库存设置的选址-库存模型。在考虑集中设置安全库存时,集中安全库存需要通过转载运输实现,因此需要将转载运输成本引入选址-库存模型之中,使新的选址-库存模型更加科学合理。另外,针对六种新的选址-库存模型,提出了基于个体成本差异分配的遗传算法,迭代搜索选址、分配、库存设置策略的优化组合。最后,通过数据实验验证了模型的有效性：（1）安全库存与转载运输之间存在此消彼长的背反关系;（2）安全库存设置和转载运输策略对总成本的影响取决于两种费率权重情况。本文的研究可以为二级物流网络的选址、订货和安全库存策略集成优化决策提供参考依据。     

Order Progress Information: Improved Dynamic Emergency Ordering Policies

Technologies such as radio‐frequency identification and global positioning systems can provide improved real‐time tracking information for products and replenishment orders along the supply chain. We call this type of visibility order progress information. In this paper, we investigate how order progress information can be used to improve inventory replenishment decisions. To this end, we examine a retailer facing a stochastic lead time for order fulfillment. We characterize a replenishment policy that is based on the classical (Q, R) policy and that allows for releasing emergency orders in response to the order progress information. We show that the optimal structure of this policy is given by a sequence of threshold values dependent on order progress information. In a numerical study we evaluate the cost savings due to this improved replenishment policy.     

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.     

STOCK LEVELS AND DELIVERY RATES IN VENDORMANAGED INVENTORY PROGRAMS

Using the latest information technology, powerful retailers like Wal‐Mart have taken the lead in forging shorter replenishment‐cycles, automated supply systems with suppliers. With the objective to reduce cost, these retailers are directing suppliers to take full responsibility for managing stocks and deliveries. Suppliers' performance is measured according to how often inventory is shipped to the retailer, and how often customers are unable to purchase the product because it is out of stock. This emerging trend also implies that suppliers are absorbing a large part of the inventory and delivery costs and, therefore, must plan delivery programs including delivery frequency to ensure that the inherent costs are minimized. With the idea to incorporate this shift in focus, this paper looks at the problem facing the supplier who wants quicker replenishment at lower cost. In particular, we present a model that seeks the best trade‐off among inventory investment, delivery rates, and permitting shortages to occur, given some random demand pattern for the product. The process generating demand consists of two components: one is deterministic and the other is random. The random part is assumed to follow a compound Poisson process. Furthermore, we assume that the supplier may fail to meet uniform shipping schedules, and, therefore, uncertainty is present in delivery times. The solution to this transportationinventory problem requires determining jointly delivery rates and stock levels that will minimize transportation, inventory, and shortage costs. Several numerical results are presented to give a feel of the optimal policy's general behavior.