Optimal replenishment cycle for perishable items facing demand uncertainty in a two-echelon inventory system

We consider a two-echelon supply chain with an upstream manufacturer and a downstream retailer for a single perishable product. The manufacturer processes raw materials into finished products, which are purchased by the retailer in each replenishment cycle. The raw materials of the manufacturer are highly perishable (i.e. perishing within hours or days), and the finished goods at the retailer face demand uncertainty and obsolescence. We model the manufacturer–retailer relationship as a Stackelberg game where the retailer is the leader and decides the replenishment cycle that minimises its mismatch cost between supply and uncertain demand. The manufacturer is the follower and decides its processing rate to minimise its unit cost for finished goods. Our results show that the raw material and finished goods lifetimes, which are interrelated through the duration of the replenishment cycle, have a significant impact on supply chain costs. Although raw material spoilage cost by itself is low, we show that short raw material lifetimes have a significant impact on the costs of both parties. Additionally, we find that while high manufacturer markups increase retailer costs, they reduce the manufacturer's costs due to large production batches.     

不同供应链合同的最优订货策略及适用性比较

针对由一个制造商和一个零售商组成的单一易逝品供应链,在随机库存问题报童模型基础上,推导了回购、收入分享和数量折扣合同下,零售商的最优订货策略、零售商和制造商的期望利润,给出了不同供应链合同的适用条件。通过一个皮衣生产、销售供应链的案例,对不同供应链合同下的最优订货策略、合同适用性及原因进行了分析、比较。为理解不同供应链合同的适用性提供了数理依据和案例解释。     

Joint pricing and inventory strategies in a supply chain subject to inventory inaccuracy

This paper focuses on pricing strategies, inventory policies for a supply chain when Radio Frequency Identification (RFID) technology is adopted to cope with inventory inaccuracy. The supply chain consists of one supplier and one retailer, in which the RFID tag price is shared between the supplier and the retailer. We present and compare the performance differences between a wholesale price contract and a consignment contract when the retailer is the Stackelberg leader and the supplier is the follower. Based on the optimal pricing and inventory decisions, an interesting observation of contract selection is that there are two critical values of inventory available rate such that when the inventory availability is less than the lower value, both the supplier and the retailer prefer a consignment contract; when the inventory availability is greater than the upper value, a wholesale price contract is their best choice; when the inventory availability is between the two values, the supplier prefers a wholesale price contract and the retailer prefers a consignment contract. Additionally, there exist threshold values of RFID tag price and sharing rate to determine the contract preference for the retailer. Furthermore, the profits of both the supplier and the retailer are independent of the RFID tag price sharing rate in a wholesale price contract, and the supplier has the incentive to invest in RFID tag cost in a consignment contract.     

The effects of inflation and the time value of money on some inventory systems

The effects of inflation and the time value of money on the optimal policies of the order-level system and the economic lot-size system are examined. Two different inflation rates, one for the internal and the other for the external costs, are assumed. The objective is to minimize the present value of the total costs per unit time.     

The impact of strategic inventory and procurement strategies on green product design in a two-period supply chain

This study analyses the impact of power structures and strategic inventory on the development-intensive and marginal-cost-intensive green product types under three procurement strategies. The results suggest that (i) in the manufacturer-Stackelberg game, the retailer retains strategic inventory to earn higher profits. The retailer's decision improves profit for the manufacturer and greening level of the product; (ii) for the marginal-cost-intensive green product, the power structures and procurement strategies cannot make any impact on the greening level and the retailer cannot build up strategic inventory under retailer-Stackelberg game; (iii) under the Nash game, the procurement decision creates conflict between the supply chain members for marginal-cost-intensive green products; (iv) if the retailer does not maintain strategic inventory or procures product in a single lot, then the manufacturer prefers to produce marginal-cost-intensive products and retailer prefers to sale development-intensive products to receive maximum profits under manufacturer-Stackelberg game. The optimal preferences are concurrent under retailer-Stackelberg game, but not under the Nash game; (v) single-period equilibrium solutions may exhibit sub-optimal characteristics, but two-period planning can lead to exemplary outcomes in the perspective of the greening level and profits of the supply chain members.     

考虑激励模式的动态回收闭环供应链最优决策与协调研究

考虑由单一的制造商和零售商组成的闭环供应链,制造商不仅通过正向供应链销售新产品,还通过激励措施从消费者那里回收旧产品,且将动态回收过程、HJB阶段控制纳入到供应链中。除探讨不同情形下均衡决策外,还设计激励成本分担契约来促进废旧产品的回收。研究表明:集中决策较分散决策供应链系统利润更高,产品回收率更高,回收激励强度更高;产品的销售价格、批发价格、零售商收益、制造商收益与回收率呈正相关,回收激励强度与回收率呈负相关;激励成本分担契约下,制造商的回收强度、回收率达到集中决策的水平,有趣的是激励成本分担契约下,产品的批发价格、销售价格均略高于分散决策的水平,制造商的收益实现帕累托改进,零售商的收益只有在一定情形下才会实现帕累托改进,供应链系统的整体收益实现帕累托改进。此外,还探讨了激励成本分担情形下零售商不出现破产的条件。最后给出算例分析验证了相关结论。     

资金约束时零售商融资与订货决策及价值分析

针对供应链中存在资金约束的情形,建立了包含制造商（M）、零售商（R）双层结构、不考虑残次品率、库存成本和融资周期长短的简洁供应链决策模型。研究了当市场需求不确定和零售商资金不足情形下,零售商选择是否融资这两种情况下,其订货决策的变化,以及零售商和制造商的收益变化。通过有无融资条件下零售商不同数量自有资金时订货量和期望收益对比和零售商自有资本一定时订货量随周期变化的数值分析,证明了零售商的融资决策与订货量决策会随着其自有资金及市场需求的变化而变化;验证了融资可以提高零售商和供应链的收益,而且能够使得供应链的总产品尽快达到最佳产量,有效满足消费者需求。     

Warehouse location and two-echelon inventory management with concave operating cost

In this paper, we study a location–inventory network design problem which jointly optimises the warehouse location, the warehouse–retailer assignments, the warehouse–retailer echelon inventory replenishment and the safety stock-level decisions over an infinite planning horizon. The consideration of the facility operating cost, the safety stock cost and the two-echelon inventory cost results in an MIP model with several nonlinear terms. Due to the complex trade-offs among the various costs and multiple nonlinear terms in the model, traditional solution approaches no longer work for this problem. We outline a polymatroid cutting-plane approach based on the submodular property of the cost terms to address this problem. Computational results demonstrate that the cutting-plane method based on polymatroid inequalities can efficiently solve randomly generated instances with moderate sizes.     

Multi-item inventory model with variable backorder and price discount under trade credit policy in stochastic demand

In this paper, a two echelon supply chain with one manufacturer and one retailer is developed for multi products. The retailer faced with the uncertain demand for all products which follows a normal distribution. The production process is assumed to be imperfect, and the defectiveness is assumed to follow a beta distribution. The manufacturer produces and delivers the products in a number of equal-sized batches to the manufacturer's warehouse, and thereby it is delivers in a number of equal batches to the retailer's warehouse. Shortages are allowed to occur, at the retailer side, and it is backordered partially. The retailer offers a price discount for backordered items to his customers. Both the lead time crashing cost and the partial backorder ratio are considered as the inverse function of lead time. Under these assumptions, there are three inventory models proposed in this paper, one with non-integrated approach, the other with an integrated approach without trade credit and finally an integrated approach with trade credit. A new iterative algorithmic procedure has been developed to minimise the total cost. Finally, numerical examples are given to illustrate the models and the sensitivity analysis is conducted over various model parameters.     

Ordering policies under one time only discount and price sensitive demand

Purchase price reductions, even on a one-time-only basis, allow retailers the opportunity to lower their own selling prices, albeit temporarily, in an effort to increase sales. This results in not only additional revenues but also in extra inventory costs. The model presented in this paper examines such a cost/revenue tradeoff, through simultaneous determination of the most profitable: (i) stock level to be purchased by the retailer; (ii) discount level to be passed on to the customers; (iii) stock level qualifying for the retailer's discount; and (iv) time to initiate the discount. Numerical examples are included throughout to illustrate the main features of the model.     

Decentralized inventory control in a two-stage capacitated supply chain

This paper investigates a two-stage supply chain consisting of a capacitated supplier and a retailer that faces a stationary random demand. Both the supplier and the retailer employ base stock policies for inventory replenishment. All unsatisfied demand is backlogged and the customer backorder cost is shared between the supplier and the retailer. We investigate the determination of decentralized inventory decisions when the two parties optimize their individual inventory-related costs in a noncooperative manner. We explicitly characterize the Nash equilibrium inventory strategies and identify the causes of inefficiency in the decentralized operation. We then study a set of simple linear contracts to see whether these inefficiencies can be overcome. Finally, we investigate Stackelberg games where one of the parties is assumed to be dominating.     

On the inventory performance of multi-criteria classification methods: empirical investigation

A number of multi-criteria inventory classification (MCIC) methods have been proposed in the academic literature. However, most of this literature focuses on the development and the comparison of ranking methods of stock keeping units (SKUs) in an inventory system without any interest in the original and most important goal of this exercise which is the combined service-cost inventory performance. Moreover, to the best of our knowledge these MCIC methods have never been compared in an empirical study. Such an investigation constitutes the objective of this paper. We first present the inventory performance evaluation method that we illustrate based on an example commonly used in the relevant literature which consists of 47 SKUs. Then, we present the empirical investigation that is conducted by means of a large data-set consisting of more than 9086 SKUs and coming from a retailer in the Netherlands that sells do-it-yourself products. The results of the empirical investigation show that the MCIC methods that impose a descending ranking of the criteria, with a dominance of the annual dollar usage and the unit cost criteria, have the lowest combined cost-service performance efficiency.     

A periodic review inventory model with loss-averse retailer,random supply capacity and demand

This paper studies a periodic review inventory model with random supply capacity and demand, where the retailer is loss-averse. For the single-period problem, it is shown that the retailer will not order unless the initial inventory level is less than a critical value, and the order-up-to level is generally not a constant. Moreover, the critical value and optimal order quantity are only dependent on the random demand and independent on the random capacity. We also investigate the impacts of loss aversion, price and cost on the optimal order quantity and maximum expected utility. Then a dynamic programming approach is used to analyse the retailer’s ordering policy in the multi-period case. In each period, if the initial inventory level is above a given value, an order will not be placed. Otherwise, the upper bound on the optimal order quantity is given. The numerical experiments are conducted to illustrate the optimal ordering policies.     

Consumer search,transshipment, and bargaining power in a supply chain

We study a decentralised supply chain with one manufacturer and two symmetric retailers who could transship their excess inventory between each other. Without transshipment, the retailer’s unsatisfied customers search and buy the product at the other retailer with some probability. With transshipment, the retailer can transship the other retailer’s excess inventory to fulfil its own unmet demand. However, a transshipment price is often charged by one retailer for transshipping goods to another. We show the retailer’s profit is unimodal in the transshipment price, and the manufacturer’s profit increases in the customer search probability. Although the retailer’s preference over transshipment depends on the magnitude of search probability and transshipment price, the retailer may always prefer the transshipment no matter their magnitude. We then study the effect of bargaining power over the transshipment decision (whether to transship between retailers and at what transshipment price). Our analysis suggests that the manufacturer always prefers to control the transshipment price rather than to control whether to transship, while the retailer can prefer both. We also find that increasing bargaining power always benefits the manufacturer but could hurt the retailer. We finally check the robustness of our results by investigating the case with asymmetric retailers     

Analyzing the effects of inventory cost setting rules in a disassembly and recovery environment

In this study we consider a disassembly and recovery facility receiving end-of-life products and facing demand for a specific part that is disassembled from the product and then recovered. The disassembly and recovery operations can be either performed before hand, or upon customer arrival. In the latter case, a discount on the selling price is applied to compensate the customer for waiting for the completion of the disassembly and recovery operations. One of the difficulties faced in planning for such a system is the determination of the opportunity cost associated with carrying recovered parts inventory. The difficulty arises in seeking the value added to the part given the costs incurred for maintaining the product return, disassembly and recovery costs and revenue earned from the hulk, that is the remaining product after the disassembly of the part. The main objective of the study is to investigate the effect of different rules to determine this opportunity cost on the performance of the system. Six rules are considered in the study. The performance of the rules is assessed by a computational study under an approximate inventory control policy.     

An improved ordering policy for continuous review inventory systems with arbitrary inter-demand time distributions

In this paper, we revisit the optimality of (s,S) policies in continuous review inventory models where demand forms a renewal process. We explain why when orders are placed at demand epochs, (s,S) policies are not optimal in general, and propose a simple but practical ordering policy by introducing a delay in order placement as a policy parameter. Under our proposed policy, the operating characteristics of such systems can be evaluated using the existing results in the literature. In order to demonstrate the effectiveness of our policy, we restrict our analysis to a special class of inventory systems where demand follows a counting process, fixed ordering costs are negligible and leadtimes are constant. We derive expressions for the operating characteristics of such systems under our policy and present insights on the behavior of the policy parameters which minimize the average total cost rate under our policy. Using these results, we develop an efficient heuristic for computing the policy parameters. Finally, we investigate the effectiveness of our policy in comparison to policies which place orders only at demand epochs. The results of our numerical experiment indicate that our policy can result in a significant savings.     

The bullwhip effect on inventory under different information sharing settings based on price-sensitive demand

Information sharing (IS) is proved to be a valid method to counter demand variability amplification along the supply chain, or bullwhip effect (BWE). Different from the traditional way of measuring the BWE based on order quantity, we measure the BWE on inventory in different IS settings and try to find the best IS approach. In this paper, the retailer will face the market demand which is price-sensitive, and the price follows a first-order autoregressive process. This demand model includes some indexes that can provide more useful managerial insights than previously studied parameters. Our study identifies the best IS setting under any conditions, and clarifies that the benefits of IS will be evident when the overall market product pricing process is highly correlated over time, the demand shocks to the retailer are high, the price sensitivity coefficient is small, the overall market shocks are low, the retailer’s lead-time is long and the manufacturer’s lead-time is short.     

Two-echelon spare parts inventory system subject to a service constraint

In this paper, we consider a spare parts inventory problem faced by a manufacturer of electronic machines with expensive parts that are located at various customer locations. The parts fail infrequently according to a Poisson process. To serve customers when a failure occurs, the manufacturer operates a central warehouse and many field depots that stock spare parts. The central warehouse acts as a repair facility and replenishes stock at the field depots. There is a centralized decision-maker who manages the inventory in both the central warehouse and the field depots. We develop a continuous review, base stock policy for this two-echelon, multi-item spare parts inventory system. We formulate a model to minimize the system-wide inventory cost subject to a response time constraint at each field depot. We present an efficient heuristic algorithm and study its computational effectiveness.     

多供应商、多销售商的两级供应链库存模型研究

研究多个供应商、多个销售商组成的两级供应链的库存系统,在具有价格弹性的市场需求、允许供应商和销售商产生缺货的条件下,针对有无价格折扣的两种情况,分别建立了供应商、销售商各自的库存模型;结合满足供应商和销售商Pareto有效性,建立了含价格折扣的供应链系统整体盈利最大的库存模型.     

Sequencing mixed-model assembly lines to minimize part inventory cost

A mixed-model assembly line enables the joint production of different models of a common base product in intermixed model sequence (lot size one). Previous approaches for the short-term planning task of model sequencing either aim at minimizing work overload (mixed-model sequencing and car sequencing) or leveling part usages (level scheduling). However, at many manufacturers parts are consolidated by a third party logistics provider, who stocks Just-in-Time delivered parts in a consignment warehouse adjacent to the line. The manufacturer issues a complete cargo carrier (e.g. a euro-pallet) whenever his own intermediate storage of parts is depleted. Thus, the manufacturer aims at a model sequence which minimizes his own inventory costs. This paper formalizes this novel model sequencing problem and describes different heuristic and exact procedures. Furthermore, the solutions yielded by these approaches are compared to the traditional level scheduling.