A joint model for cash and inventory management for a retailer under delay in payments

As retail companies continue to navigate through the economy downturn, it becomes critical to find innovative cost reduction methods. Cash management is a cost-intensive process for retailers, who are currently focusing on effective cash management, such as deciding on the maximum cash level to keep in their business accounts and how much to borrow to finance inventories and pay suppliers. In this paper, we consider the problem of finding the optimal operational (how much to order and when to pay the supplier) and financial decisions (maximum cash level and loan amount) by integrating the cash management and inventory lot sizing problems. We consider a supplier offering a retailer an interest-free credit period for settling the payment. Beyond this period, the supplier charges interest on the outstanding balance. Whenever the cash exceeds a certain limit, it will be invested in purchasing financial securities. At the time when the retailer pays the supplier for the received order, cash is withdrawn from the account, incuring various financial costs. If the cash level becomes zero or not sufficient, the retailer obtains an asset-based loan at interest. We model this problem as a nonlinear program and propose a solution procedure for finding the optimal solution. We perform a numerical study to analyze the impact of optimal cash management on the inventory decisions. The results indicate that the optimal order quantity decreases as the retailer’s return on cash increases. We compare our model to a model that ignores financial considerations of cash management, and show numerically that our model lowers the retailer’s cost. Also, we illustrate the effect of changing various model parameters on the optimal solution and obtain managerial insights.     

Contracting for vendor‐managed inventory with a time‐dependent stockout penalty

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.     

基于购买行为的随机生命周期易逝品库存策略

研究需求和商品生命周期均为随机的零售商库存管理问题,提出按照购买行为特征对需求进行分类,在不同类型的客户之间进行库存分配并允许缺货的库存策略.通过构建动态规划模型,求解出零售商最优库存策略,包括补货策略和库存分配策略.与先到先服务策略相比,该策略能显著提升零售商的利润,减少商品损坏的损失.     

A local search method for periodic inventory routing problem

Inventory routing problem considers inventory allocation and routing problems simultaneously, in which the replenishment policies and routing arrangement are determined by the supplier under the vendor managed inventory mode. What we consider here is a periodic inventory routing problem that once the delivery time, quantity and routing are determined, they will remain the same in the following periods. The problem is modeled concisely, and then it is decomposed into two subproblems, inventory problem and vehicle routing problem. The inventory problem is solved by proposing a local search method, which is achieved by four operators on delivery quantity and retailer’s demand. Insertion operator aims to insert a new replenishment point of a retailer while removal operator is to remove a replenishment point. Besides, addition operator is adopted as an assistant tool, and crossover operator is proposed for some special cases. We also propose a tabu search method to solve the routing problem. Finally, the computational results show that the method is efficient and stable.     

The joint replenishment problem involving multiple suppliers offering quantity discounts

In this article, we deal with the problem of determining the economic operating policy when a number of items are to be procured from a number of suppliers offering different quantity discounts schedules. In such inventory problems, a fixed cost is incurred with each replenishment order, independent of the suppliers as well as the items involved in the order. Further, the item involves a minor fixed cost. In such a system, it includes the supplier selection problem when considering the quantity discounts as well as the general joint replenishment problem. We develop a hybrid genetic algorithm for this NP-hard decision problem and extend it to systems with resource restrictions.     

Joint shipment consolidation and inventory decisions in a two-stage distribution system

This study is motivated by a problem that an industrial distributorship faced while distributing automotive spare parts to service and repair centers. Considering the problem encountered, we present an analytical model for joint inventory and shipment consolidation decisions in a two-stage distribution system with a single distribution center, multiple non-identical retailers, and an outside supplier. The retailers face stochastic end-customer demand and use continuous review to replenish inventories. On the other hand, the distribution center uses a periodic review policy and employs a time-based shipment consolidation policy to dispatch retailers’ accumulated orders at the end of each consolidation cycle. We present an exact optimization technique to compute the optimal replenishment quantity at the distribution center, order-up-to level at retailers, and a shipment consolidation cycle length to measure the effects of inventory at retailers on the overall performance. Finally, we perform numerical experiments to measure the impact of various parameters on the overall distribution system.     

Integrated supply chain model for a deteriorating item with procurement cost dependent credit period

This study develops an integrated production inventory model of supplier and retailer where a delay in payment is offered by supplier to retailer for a constant deteriorating item. Here shortages are not allowed. In this model retailer’s procurement cost linearly depends on the credit period and supplier’s process cost also is a linear function of the amount of quantity purchased by retailer. In this model, the objective is to decide the position of the credit period and number of replenishment of retailer in finite time horizon in such a way that the integrated system gets the optimum cost. The model is explained with the help of numerical examples and the sensitivity analysis of some parameters are also carried out.     

Stochastic models for the coordinated production and shipment problem in a supply chain

In this study, we consider the coordination of transportation and production policies between a single supplier and a single retailer in a stochastic environment. The supplier controls the production, holds inventory and ships the products to the retailer to satisfy the external demand. We model the system as a Markov decision process, and show that the optimal production and transportation decisions are complex and non-monotonic. Therefore, we analyze two widely-used shipment policies in the industry as well, namely time-based and quantity-based shipment policies in addition to a hybrid time-and-quantity based shipment policy. We numerically compare the performances of these policies with respect to the optimal policy and analyze the effects of the parameters in the system.     

Coordinating a three-level supply chain with delay in payments and a discounted interest rate

Both researchers and practitioners recognize the importance of the interactions between financial and inventory decisions in the development of cost effective supply chains. Moreover, achieving effective coordination among the supply chain players has become a pertinent research issue. This paper considers a three-level supply chain, consisting of a capital-constrained supplier, a retailer, and a financial intermediary (bank), coordinating their decisions to minimize the total supply chain costs. Specifically, we consider a retailer managing its cash through the supplier’s bank, in return for permissible delay in payments from the supplier. The bank, benefiting from increasing its cash holdings with the retailer’s cash deposits, offers the supplier a discount on its borrowing rate. We show that the proposed coordination mechanism achieves significant cost reduction, by up to 26.2%, when compared to the non-coordinated model. We also find that, with coordination, the retailer orders in larger quantities than its economic order quantity, and that a higher return on cash for the retailer leads to a higher order quantity. Furthermore, we empirically validate our proposed coordination mechanism, by showing that banks, retailers, and suppliers have much to gain through collaboration. Thus, using COMPUSTAT datasets for the years 1950 through 2012, we determine the most important factors that affect the behavior of the retailers and suppliers in granting and receiving trade credit. Our results indicate that engaging into such a coordination mechanism is a win–win situation to all parties involved.     

Situation reactive approach to Vendor Managed Inventory problem

In this research, we deal with VMI (Vendor Managed Inventory) problem where one supplier is responsible for managing a retailer’s inventory under unstable customer demand situation. To cope with the nonstationary demand situation, we develop a retrospective action-reward learning model, a kind of reinforcement learning techniques, which is faster in learning than conventional action-reward learning and more suitable to apply to the control domain where rewards for actions vary over time. The learning model enables the inventory control to become situation reactive in the sense that replenishment quantity for the retailer is automatically adjusted at each period by adapting to the change in customer demand. The replenishment quantity is a function of compensation factor that has an effect of increasing or decreasing the replenishment amount. At each replenishment period, a cost-minimizing compensation factor value is chosen in the candidate set. A simulation based experiment gave us encouraging results for the new approach.     

基于LA型供应商的易逝品供应链价格补贴契约

针对由单个损失厌恶型供应商和单个风险中性型零售商组成的供应链系统,在前景理论框架下,研究了存在缺货损失下的基于批发价格契约和价格补贴契约的易逝品供应链协调问题。首先分析了分散化供应链系统在批发价格契约下供应商和零售商的最优决策,并将供应商的最优生产量与集中化供应链系统下的最优生产量进行了比较;从理论上严格证明了当供应商的最优生产量小于集中化供应链系统下的最优生产量时,供应商不能通过批发价格契约使得自己的生产量为集中化供应链的生产量。然后分析了在缔结政府提供的价格补贴契约下供应商和零售商的最优决策。研究结果表明,损失厌恶型供应商在批发价格契约下的最优生产量可能偏离系统最优生产量,这时政府可以通过价格补贴契约来协调整个供应链。     

Design of Stochastic Distribution Networks Using Lagrangian Relaxation

This paper addresses the design of single commodity stochastic distribution networks. The distribution network under consideration consists of a single supplier serving a set of retailers through a set of distribution centers (DCs). The number and location of DCs are decision variables and they are chosen from the set of retailer locations. To manage inventory at DCs, the economic order quantity (EOQ) policy is used by each DC, and a safety stock level is kept to ensure a given retailer service level. Each retailer faces a random demand of a single commodity and the supply lead time from the supplier to each DC is random. The goal is to minimize the total location, shipment, and inventory costs, while ensuring a given retailer service level. The introduction of inventory costs and safety stock costs leads to a nonlinear NP-hard optimization problem. A Lagrangian relaxation approach is proposed. Computational results are presented and analyzed showing the effectiveness of the proposed approach.     

带有订单转保理的供应链金融的收益共享博弈模型

当作为供应商的中小企业出现了严重的财务困境问题时,急需有效融资工具和创新管理模式加以解决.订单转保理可以令资质良好的零售商为资金短缺的供应商提供融资担保,有效解决供应商的订单减少和融资难的问题.然而,分散决策的订单转保理融资模式,使得做担保的零售商的收益降低,不能明显改善供应链效率.针对此问题,研究订单转保理模式下的供应链协调模型,并重点研究由供应商与零售商组成的二级供应链的订单转保理收益共享模型.研究发现:收益共享决策模型供应链总收益小于集中决策供应链总收益,大于分散决策的供应链总收益,表明供应链成员相互合作程度越高,越有利于供应链发展,从而表明协调在供应链中发挥重要作用.然而,集中决策模型只能得到供应链最优总收益,无法得到供应商和零售商的最优收益.收益共享模型不仅能够提高产品订货量,降低产品批发价格,增加供应商和零售商的收益,而且通过最优的收益共享系数可以得到供应商和零售商的最优收益.收益共享机制能够为供应商和零售商共赢协调发展提供新的运作管理模式.     

损失厌恶下考虑参照利润效应的供应链决策模型

针对由一个风险中性供应商和一个损失厌恶零售商构成的二级供应链,研究随机需求下考虑零售商参照利润效应的供应链决策问题.在回购政策下,建立以供应商为主方、零售商为从方的Stackelberg主从博弈模型.结合参照依赖偏好模型分别得到集中和分散供应链决策,分析供应链最优决策与损失厌恶程度、参照利润强度和零售商乐观水平之间的关系,并进一步设计能够实现供应链完美协调的回购契约机制.研究结果表明,在集中和分散供应链决策下,零售商订货量均随着损失厌恶和乐观程度的增加而减少.而当零售商损失厌恶程度较低时,订货量随参照利润强度的增加而增加;反之,亦成立.对于批发价格决策,则存在一个阈值,当高于该阈值时,批发价格随着零售商损失厌恶、乐观程度和参照利润强度的增大而增加;低于该阈值时,批发价格随着损失厌恶、乐观程度和参照利润强度的增大而降低.     

Impacts of supply disruptions and customer differentiation on a partial-backordering inventory system

In this paper, we study a single-product inventory system which involves a supplier, a retailer, and differentiated customers. The supplier provides products to the retailer which in turn sells products to its customers. The supplier is unreliable and is subject to random disruptions. The retailer adopts a periodic-review inventory policy, under which the retailer reviews its inventory position every a fixed period of time and decides whether a replenishment is needed or not. Partial backordering is applied when a stockout occurs. That is, under the situations of stockouts, customers can choose either to backorder products or to abandon the purchase. Customers are segmented into two classes according to their backordering probabilities. The customer class with high backordering probability is provided with high priority to receive backorders. In this paper we allow more than one outstanding orders to exist, which is not the case in the previous literature. We develop a simulation model for such an inventory system and investigate the impacts of supply disruptions and customer differentiation on this inventory system.     

Dynamic ordering and pricing for a perishable goods supply chain

The paper studies the combined problem of pricing and ordering for a perishable product supply chain with one supplier and one retailer in a finite horizon. The lifetime of the product is two periods and demand in each period is random and price-sensitive. In each period, the supplier determines first a wholesale price and then the retailer decides an order quantity and retail prices. We show that the optimal pricing strategy for the non-fresh product depends only on its inventory, and the optimal pricing strategy and the optimal order quantity for the fresh product depend only on the wholesale price and they have a constant relation. Moreover, the game between the retailer and the supplier for finite horizon is equivalent to a one period game with only one order. Thus, the optimal policies are identical at each period. For the additive and multiplicative demands, we further obtain equations to compute the optimal strategies. All of above results are extended into the infinite horizon case and longer lifetime products. Finally, a numerical analysis is given.     

Inventory control model for a supply chain system with multiple types of items and minimum order size requirements

This paper considers a replenishment problem for a single buyer who orders multiple types of items from two or more heterogeneous suppliers in order to sell to end customers. The buyer periodically orders each type of item from the suppliers according to a select inventory control policy. Processing the order, each supplier enforces the policy that an order from the buyer must meet a predetermined minimum order quantity (MOQ). Therefore, the buyer must decide how much to order from each supplier considering the current inventory level, demand forecast, and MOQ requirement. The buyer's problem is formulated as an integer programming model and an efficient implementation strategy is suggested to apply the model to real problems. Numerical experiments are performed to test the validity of the proposed model as well as the efficiency of the implementation strategy. The experimental results show that this model combined with the implementation method yields a considerable cost reduction compared to the most efficient policy currently available.     

Capacity-constrained supplier selection model with lost sales under stochastic demand behaviour

In today’s market conditions, volume of demand is quite uncertain and thus it is hard to estimate. In many cases, buyer is prone to use supply chain flexibility rather than inventory holding strategy to withstand demand uncertainty. We assume that the buyer releases a replenishment order to the supplier for each cycle (or period) under the contract which is mainly composed of four parameters: (1) supply cost per unit, (2) minimum order quantity, (3) order quantity reduction penalty and (4) maximum capacity of the supplier. Based on these parameters, there are two flexibility options that buyer should evaluate in the order of cycle (1) issue an order smaller than the minimum order quantity and pay the related penalty and (2) place no order and lose the sales. Hence, Q _lost emerges as a critical buyer decision, the order quantity, below which no order is placed. Total expected supply cost plus lost sales, as a function of Q _lost is presented. We derive the optimal Q _lost that minimises the total cost function. Since capacity of each supplier is finite, we then develop a supplier selection model with total cost minimisation over the suppliers subject to capacity constraint that has a stochastic nature stemming from demand behaviour. Linearisation on the model is performed using chance-constrained programming approach. From a given set of supply bids from the potential supply chain partners, the buyer is able to make a quantifiable choice.     

Optimal replenishment decision in an EPQ model with defective items under supply chain trade credit policy

The traditional inventory of the economic order quantity model assumes perfect items in an ordered lot and an infinite replenishment rate. However, such conditions are rare in actual production environments. Additionally, most studies of this problem have only considered suppliers offering the wholesaler a grace period. In practice, wholesalers often extend a fixed credit period to downstream customers as well. This study therefore proposes a production model for a lot-size inventory system with finite production rate and defective quality under the condition of two-level trade credit policy and the condition that defective items involve both imperfect quality and scrap items. Thus, optimal wholesaler replenishment decisions can be determined for defective items under two-level trade credit policy in the EPQ framework. Four theorems for determining the optimal cycle time and the results in this study can be deduced as a special case of earlier models. Finally, illustrative examples are provided to verify the theoretical results.     

The value of information sharing in a supply chain with a seasonal demand process

This paper considers a two echelon seasonal supply chain model that consists of one supplier and one retailer, with the assumption that external demand from the customer follows a seasonal autoregressive moving average (SARMA) process, including marketing actions that cannot be deduced from the other parameters of the demand process. In our model, the supplier and the retailer employ order-up-to policy to replenish their inventory. In order to evaluate the value of information sharing in a two echelon seasonal supply chain, three levels of information sharing proposed by Yu, Yan, and Cheng (2002) are used. The results for optimal inventory policies under these three levels of information sharing are derived. We show that the seasonal effect has an important impact on optimal inventory policies of the supplier under the three levels of information sharing. Our findings also demonstrate that the replenishment of lead time must be less than the seasonal period in order to benefit from information sharing. Thus, this result provides managers with managerial insights to improve supply chain performance through information sharing integration partnerships.