Optimal inventory policy with noninstantaneous receipt under trade credit

In the last two decades, the models for inventory replenishment policies under trade credit have been widely studied by several researchers. However, the extant papers only consider the effects of permissible delay in payments in the inventory systems. In some situations, the supplier also may offer a cash discount to encourage retailer to pay for his purchases quickly. On the other hand, an inventory model with instantaneous receipt is not a common feature in actual practice. For generality, this study develops an inventory model with noninstantaneous receipt under trade credit, in which the supplier provides not only a permissible delay but also a cash discount to the retailer. We then characterize the optimal solution and provide an easy-to-use criterion to find the optimal order strategies. Finally, several numerical examples are presented to illustrate the theoretical results.     

A multi-item supply chain with credit periods and weight freight cost discounts

It is possible to realize considerable savings by aggregating the replenishment of a variety of items in a multi-item supply chain. This joint multi-item replenishment policy has already been widely applied in a variety of industries. This type of policy may make it possible for the retailer to take advantage of transport economies of scale by the utilization of freight discounts for greater weight. In addition, a supplier will often extend forward financing to a retailer. In this paper, a multi-item supply chain with a credit period and weight freight cost discounts is considered. The retailer bears the freight costs, but the freight carrier provides freight-transport discounts that are positively related to the weight of the cargo transported. From both the individual and the channel perspectives, we deal with the dual problems of determining the ideal supplier credit period, and of the best way for the retailer to make multi-item replenishment and pricing decisions, while still maximizing profits. We outline the optimal properties and develop algorithms for solving the problems described, as well as discuss the impact of the freight cost discounts, the inventory holding cost, and the interest rate on the behavior of both parties.     

Dynamic supply chain coordination under consignment and vendor-managed inventory in retailer-centric B2B electronic markets

This study examines the dynamic performance of vertically decentralized two-echelon channel coordination for deteriorating goods under consignment and vendor-managed inventory (VMI) contracts with revenue sharing from retailer-centric business-to-business transactions in both traditional markets and electronic markets (EMs). The research presents the profit-maximization problem and devises a method for making cross-enterprise dynamic joint decisions by combining calculus with dynamic programming for a retailer-led Stackelberg supply chain under cooperative and non-cooperative game settings over a multi-period planning horizon. The applicability of the proposed model is assessed using a case study involving a highly perishable product, sliced raw fish, in a supply chain comprising a regional seafood supplier and a local store belonging to a large national retail chain. The analytical results show that, in a cooperative setting, the EM with a consigned revenue-sharing VMI contract tends to achieve lower retail prices, larger stock quantity, improved channel efficiency, and increases in both retailer and supplier profits through an additional one-part tariff. Additionally, consumers benefit from lower retail prices and society benefits from increased overall channel profits in the cooperative channel and EM.     

基于收益共享的供应链中断协调研究

本文假定市场需求不确定和供给存在中断危机，同时考虑订货过剩损失和缺货成本，研究了由零售商、主供应商和备份供应商组成的供应链网络，构建了收益共享合同协调模型，通过相关参数的设定达到供应链协调。供应链协调时的供货量及整体利润均大于分散模型；备份供应商的供货量及利润随着中断危机的增大而增加，零售商利润也随之增加。     

Replenish-up-to inventory control policy with random replenishment intervals

The multi period inventory problems have been studied under two main assumptions. Continuous review assumption where an order can be made at any time depending on inventory position and periodic review assumption where an order can be initiated only at discrete time epochs. In this study, we analyze a multi period inventory problem that falls under neither of these two assumptions. In the case we consider, there are periodic replenishments but the replenishment intervals are taken to be i.i.d. random variables. This setting represents the real life cases where a supplier visits a retailer with random inter arrival times and the retailer replenishes his inventories based on a replenish-up-to-level inventory control policy. We also assume that only a certain fraction of unmet demand is backordered and the rest of it is lost.In this setting under general distribution between replenishment epochs, we show the concavity of the expected profit function and give the condition that must hold for the optimal replenish-up-to-level. We also present the specific solutions and analysis under two different distributions, namely, uniform and exponential distributions, together with some numerical examples.     

Inter-temporal inventory competition and the effects of capacity constraints

This paper addresses an intertemporal inventory competition between a supplier (a provider, manufacturer) and a retailer engaged in a supply chain. The paper's focus is on the effect of capacity constraints on both parties when demands are seasonal. The paper provides a comparative study of two solution approaches, one is based on supply chain competition and the other is based on system wide optimization. Our results demonstrate that with dynamic inventory competition, the retailer reduces inventory costs by reducing the response period to higher demands while increasing the supply requests compared to the system-wide optimal approach. As a result, the supplier's inventory costs increase. An example illustrating these particular facets of the problem and its application is presented and discussed in light of the supplier and the retailer coordinating policies.     

Inventory ordering policies of delayed deteriorating items under permissible delay in payments

The existing literature on inventory of deteriorating items considers deterioration to begin as soon as the items are stocked. However, there are several deteriorating items that do not start deteriorating immediately they are held in stock. Some farm produce like potatoes, yams and even some fruits and vegetables have this property. Depletion of these items as soon as they are stocked will depend on demand, and when deterioration begins, it will depend on both demand and deterioration. In this paper, we develop a mathematical model on the inventory of deteriorating items that do not start deteriorating immediately they are stocked. The model also takes into cognizance the fact that in business activities nowadays customers are given some allowed period within which to settle for the goods supplied to them. They can use the accrued money from sales of the supplied goods to earn interest within the allowed period. They are charged interest only when they fail to settle the amount they owe the supplier at the end of the allowed period.     

Retailer policy, uncertainty reduction, and supply chain performance

We investigate how the retailer’s inventory policy affects the total cost of a serial supply chain. When the retailer uses the locally optimal (s,S) policy, there is randomness in order time and order quantity to the supplier whereas the supplier sees randomness only in order quantity for the suboptimal (R,T) policy and only in order time for another suboptimal (Q,r) policy. Using an extensive computational study, we find that the suboptimal policies perform better from the total supply chain perspective. The benefit of policy changes is magnified when the retailer costs are low, when the supplier costs are high, and when there is information sharing.     

Myopic optimal policy for a multi-period, two-delivery-lead-times, stochastic inventory problem with minimum cumulative commitment and capacity

This paper studies a single-product, multi-period, stochastic inventory problem that imposes the lower and upper bounds on the cumulative order quantity during a planning horizon and allows two delivery lead times. This model includes three features. The first one is that a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer’s total cumulative order quantity during the planning horizon is constrained with the capacity. The second one is that the buyer agrees to purchase the product at least a certain percentage of the purchased capacity during the planning horizon. The third one is that the supplier allows the buyer to order the product with two-delivery-lead-times. We identify conditions under which a myopic ordering policy is optimal. We also develop an algorithm to calculate the optimal capacity when the minimum cumulative order quantity commitment is a certain percentage of the capacity. We then use the algorithm to evaluate the effect of the various parameters on the buyer’s minimum expected total cost during the planning horizon. Our computation shows that the buyer would benefit from the commitments and two-delivery-lead-times.     

Managing inventory with two suppliers under yield uncertainty and risk aversion

In this paper, we consider a single-product single-period inventory model in which the retailer can source from two suppliers. The primary supplier is cheaper but unreliable in the sense that it generates supply yield uncertainty, whereas the secondary supplier is perfectly reliable but more expensive. The reliable supplier's capacity is fixed and the retailer cannot order more than the quantity reserved in advance. We study the problem in the context of a risk-averse retailer who has to determine the optimal order quantity from the primary supplier and the optimal reserved quantity from the secondary supplier. We develop the model in the perspective of a low risk averse retailer and quantify the risk via an exponential utility function. We show by numerical experiments how the resulting dual sourcing strategies differ from those obtained in the risk-neutral analysis. We also examine the sensitivity of some model-parameters on the optimal decisions.     

Inventory management in supply chains: A bargaining problem

This paper is focused on supply chain management from the perspective of inventory management. The coordination of order and production policies between buyers and suppliers in supply chains is of particular interest. When a buyer of an item decides independently, he will place orders based on his economic order quantity (EOQ). However, the buyer's EOQ may not lead to a favorable policy for the supplier. A cooperative order and production policy can reduce total cost significantly. Should the buyer have the dominant position to impose his EOQ on the supplier, then consequently no incentive exists for him to deviate from his EOQ in order to choose a cooperative policy. To induce the buyer to order in quantities more favorable to the supplier, the supplier could offer a cooperative policy associated by a side payment to the buyer. The research presented in this paper provides several bargaining models depending on alternative production policies of the supplier. With these bargaining models the offered cooperative policy and the offered side payment can be derived.     

Supply contract with options

The purpose of this paper is to analyze the impact of an option contract for two companies of a supply chain: retailer and supplier. With an option contract the retailer orders a quantity of units and has the right to modify his order if necessary. A model to calculate the performance of an option contract in terms of contract value for the two companies engaged is presented. The two considered cases are multiple suppliers and one retailer, and one supplier and one retailer. The performance improvement obtained using this kind of contract is compared by simulation.     

考虑质押物损耗的存货质押融资决策模型

质押物的完整性是关系存货质押融资业务能否顺利开展的重要问题,质押物损耗长期困扰各参与方,阻碍了存货质押融资业务的顺利开展。考虑质押物损耗和第三方物流企业对质押物监管所带来的损耗节约的基础上,研究了存货质押融资最优决策。研究表明:当零售商的初始现金余额很低时,零售商的最优订购数量随着初始现金余额的增加而减少,之后零售商最优订货量保持不变,直到初始现金余额大于某一水平时,零售商的最优订货量开始增加;在零售商贷款且不存在破产风险时,银行的收益随着零售商初始现金余额增加而减少;当风险估值是需求的增函数时,零售商的最优订货量随利率减少。     

Economic lot-sizing and dynamic quantity competition

We study a problem of dynamic quantity competition in continuous time with two competing retailers facing different replenishment cost structures. Retailer 1 faces fixed ordering costs and variable procurement costs and all inventory kept in stock is subject to holding costs. Retailer 2 only faces variable procurement costs. Both retailers are allowed to change their sales quantities dynamically over time. Following the structure of the economic order quantity (EOQ) model, retailer 1 places replenishment orders in batches and retailer 2 follows a just-in-time (JIT) policy. The objective of both retailers is to maximize their individual average profit anticipating the competitor's replenishment and output decisions. The problem is solved by a two-stage hierarchical optimization approach using backwards induction. The second-stage model is a differential game in output quantities between the two retailers for a given cycle length. At the first stage, the replenishment policy is determined. We prove the existence of a unique optimal solution and derive an open-loop Nash equilibrium. We show that both retailers follow contrary output strategies over the order cycle. The EOQ retailer, driven by inventory holding costs, decreases his market share whereas the output of the JIT retailer increases. Moreover, depending on the cost structure, the EOQ retailer might partially be a monopolist. At the first stage, the EOQ retailer determines the cycle length, anticipating the optimal output trajectories at the second stage.     

An inventory model with deteriorating items under inflation when a delay in payment is permissible

This study develops an inventory model for initial-stock-dependent consumption rate when a delay in payment is permissible. In the inventory model, shortages are not allowed. The effect of the inflation rate, deterioration rate, initial-stock-dependent consumption rate and delay in payment are discussed. In the study, mathematical models are also derived under two different circumstances, i.e., Case I: The credit period is less than or equal to the cycle time for settling the account; and Case II: The credit period is greater than the cycle time for settling the account. Besides, expressions for an inventory system's total cost are derived for these two cases. Moreover, a computational procedure and GINO (Lasdon et al., ACM Transactions Mathematical Software 4 (1978) 34–50) are proposed to obtain the optimal order size and cycle time. The results can help managers determine the optimal total cost. Finally, a numerical example demonstrates the applicability of the proposed model.     

Optimal ordering policies in response to a discount offer

Sometimes supplier offers a temporary price discount to increase cash flow or decrease the inventory level of certain items. Thus, the manufacturer may be able to improve the effectiveness of his inventory system by ordering a special quantity at this sale period. In this paper, economic order quantity (EOQ) models with a discounted price are developed to obtain the optimal ordering policy during the sale period for five different cases: (a) coincidence of sale period with replenishment time, (b) non-coincidence of sale period with replenishment time, (c) sale period is longer than a cycle, (d) discounted price as a function of the special ordering quantity, and (e) incremental discount. Each case has its own characteristics of the sale period and the discounted price. The objective is to take the maximum possible advantage from the discounted price by ordering a special quantity during the sale period. The optimal ordering policy is obtained by maximizing the difference between the two costs: Regular EOQ cost and special quantity cost during the sale period. Moreover, a comparison of different discount scenarios is developed to sense the effect of different parameters on the ordering policies. The annual gain obtained is linearly related to the discount and the on-hand remnant inventory. Numerical analyses are provided to illustrate and testify the values of the optimal special quantity. The analysis showed an impressive improvement in the effectiveness of the inventory system when a special order is placed during the sale period. The optimal special quantity is driven for each case to visualize real-life problems. Sensitivity analysis is also initiated to study the change in the total savings with respect to the variation of the special optimal quantity.     

Multi-item dynamic lot-sizing with delayed transportation policy

We optimize ordering and inbound shipment decisions for a manufacturer that sources multiple items from a single supplier. The objective is to satisfy the requirements in the production plan with minimum transportation and inventory holding costs over a multi-period planning horizon. Transportation costs are charged to the manufacturer on a per truck shipment basis. We investigate the option of delaying a less-than-full truckload shipment to the next period, by utilizing the safety stocks as needed. We analyze the impact of delaying shipments on both cost and service levels in stochastic environments through experiments with data from a bus manufacturer. The results indicate that the proposed policy reduces both holding and transportation costs without creating much stock-out risk.     

Optimal inventory and pricing policies for remanufacturable leased products

In this paper we consider a company which leases new products and also sells remanufactured versions of the new product that become available at the end of their lease periods. When the amount of end-of-lease items in stock is not sufficient to meet the demand for remanufactured products, the firm may purchase additional cores from a third-party supplier. We develop a dynamic programming formulation for determining the optimal price of remanufactured products, and optimal payment structure for the leased products. Our objective is to maximize the discounted system-wide profit over a finite horizon. The profit function consists of revenues that are obtained from remanufactured product sales and leasing, remanufacturing and manufacturing costs, inventory holding and shortage costs. We consider a consumer choice based demand model for mapping a potential customer into one of the product segments (a remanufactured product customer or a customer for a leased product with a particular lease period) for a given price/lease payment vector. We explore several properties of the discounted profit function and provide insight on the behavior of pricing and inventory policies. We also investigate the effect of key product characteristics such as deterioration in age, cost of shortage in remanufacturable product inventory, and key market characteristics such as relative willingness-to-pay for buying a remanufactured product and relative willingness-to-pay for leasing a new product on optimal pricing policies through a computational study.     

Using System Dynamics to assess the impact of RFID technology on retail operations

The application of item-level radio frequency identification (RFID) technology in retail supply chains creates cost savings and promises large potential benefits from revenue growth. However, the economic assessment of the impact on improved store operations, labor utilization, and increased sales is still not fully explored. We propose to use System Dynamics as a structural modeling and simulation approach to integrate conventional return on investment evaluations. Building on previous research about RFID technology in retail supply chains, we developed a model based on the case exploration of a leading Italian apparel retailer. Simulations show that RFID implementations are profitable whenever they contribute to increase sales, especially when a fashion retailer is focused on clerk-assisted sales strategies. Sales growth results from the dynamic and integrated impacts of RFID technology on better inventory control, faster inventory turnover, and longer time available for store personnel to assist consumers as an effect of more efficient backroom operations.     

VMCI 下基于批发价决策权转移的供应链效率改进研究

本文在VMCI 模式下,考虑销售努力水平对市场需求的影响,研究批发价决策权由供应商转移至零售商的两级供应链效率改进问题。假定零售商决策批发价和销售努力水平,供应商决策寄售量,建立了零售商主导的Stackelberg 博弈模型,证明了集中决策下的最优解和分散决策下的均衡解均存在且唯一,集中决策下的寄售因子大于分散决策下的对应值。随后,引入收入共享与销售努力成本共担契约,论证了系统中寄售因子保持不变、批发价降低,且当契约参数满足一定条件时,可实现帕累托改进,实现供应链的效率改进。最后,分析了契约参数对于系统决策变量及利润的影响。