A mixed inventory model with variable lead time and random supplier capacity

In this paper, we have studied analytically the implication of a controllable lead-time and a random supplier capacity on the continuous review inventory policy, in which the order quantity, reorder point and lead-time are decision variables. Two models are considered: the normal lead-time demand and lead-time demand is distributed free. For both cases, after formulating the general model, some properties of the optimal ordering policy have been developed. Particularly, we have shown that the expected annual total cost is a unimodal function and quasi-convex in the order quantity. When the variable capacity distribution is exponential, we develop effective procedures for finding the optimal solutions. Furthermore, the effects of parameters are also performed.     

Coordinating operational policy with financial hedging for risk-averse firms

A risk-averse firm׳s financial hedging activity can impact the decision making in its daily operations. We introduce a CE-based approach that can help the firm to simplify the procedure in making hedging-consistent decisions. A key feature of this new approach is that it allows for the existence of nonfinancial random factors, which give rise to the risk exposure that cannot be hedged in the financial market. By using a CE operator, we show that the optimal operational policy can be obtained by maximizing the CE-based value function. Although the CE operator may bring additional nonlinearity to the value function, we find that the commonly desired base-stock policy can remain optimal under specific conditions. We hope that this new approach can help pave the way for future investigation on joint operations management and financial hedging problems in dynamic settings.     

Production and changeover control policies of a class of failure prone buffered flow-shops

This article deals with a stochastic optimal control problem for a class of buffered multi-parts flow-shops manufacturing system. The involved machines are subject to random breakdowns and repairs. The flow-shop under consideration is not completely flexible and hence requires setup time and cost in order to switch the production from a part type to another, this changeover is carried on the whole line. Our objective is to find the production plan and the sequence of setups that minimise the cost function, which penalises inventories/backlogs and setups. A continuous dynamic programming formulation of the problem is presented. Then, a numerical scheme is adopted to solve the obtained optimality conditions equations for a two buffered serial machines two parts case. A complete heuristic policy, based on the numerical observations which describe the optimal policies in system states, is developed. It will be shown that the obtained policy is a combination of a KANBAN/CONWIP and a modified hedging corridor policy. Moreover, based on our observations and existent research studies extension to cover more complex flow-shops is henceforth possible. The robustness of such a policy is illustrated through sensitivity analysis.     

Capacity Planning with Financial and Operational Hedging in Low‐Cost Countries

The authors of this article outline a capacity planning problem in which a risk‐averse firm reserves capacities with potential suppliers that are located in multiple low‐cost countries. While demand is uncertain, the firm also faces multi‐country foreign currency exposures. This study develops a mean‐variance model that maximizes the firm's optimal utility and derives optimal utility and optimal decisions in capacity and financial hedging size. The authors show that when demand and exchange rate risks are perfectly correlated, a risk‐averse firm, by using financial hedging, will achieve the same optimal utility as a risk‐neutral firm. In this study as well, a special case is examined regarding two suppliers in China and Vietnam. The results show that if a single supplier is contracted, financial hedging most benefits the highly risk‐averse firm when the demand and exchange rate are highly negatively related. When only one hedge is used, financial hedging dominates operational hedging only when the firm is very risk averse and the correlation between the two exchange rates have become positive. With both theoretical and numerical results, this study concludes that the two hedges are strategic tools and interact each other to maximize the optimal utility.     

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.     

THE VALUE OF SKU RATIONALIZATION IN PRACTICE (THE POOLING EFFECT UNDER SUBOPTIMAL INVENTORY POLICIES AND NONNORMAL DEMAND)

Several approaches to the widely recognized challenge of managing product variety rely on the pooling effect. Pooling can be accomplished through the reduction of the number of products or stock‐keeping units (SKUs), through postponement of differentiation, or in other ways. These approaches are well known and becoming widely applied in practice. However, theoretical analyses of the pooling effect assume an optimal inventory policy before pooling and after pooling, and, in most cases, that demand is normally distributed. In this article, we address the effect of nonoptimal inventory policies and the effect of nonnormally distributed demand on the value of pooling. First, we show that there is always a range of current inventory levels within which pooling is better and beyond which optimizing inventory policy is better. We also find that the value of pooling may be negative when the inventory policy in use is suboptimal. Second, we use extensive Monte Carlo simulation to examine the value of pooling for nonnormal demand distributions. We find that the value of pooling varies relatively little across the distributions we used, but that it varies considerably with the concentration of uncertainty. We also find that the ranges within which pooling is preferred over optimizing inventory policy generally are quite wide but vary considerably across distributions. Together, this indicates that the value of pooling under an optimal inventory policy is robust across distributions, but that its sensitivity to suboptimal policies is not. Third, we use a set of real (and highly erratic) demand data to analyze the benefits of pooling under optimal and suboptimal policies and nonnormal demand with a high number of SKUs. With our specific but highly nonnormal demand data, we find that pooling is beneficial and robust to suboptimal policies. Altogether, this study provides deeper theoretical, numerical, and empirical understanding of the value of pooling.     

Managing stochastic demand in an Inventory Routing Problem with transportation procurement

We study an Inventory Routing Problem in which the supplier has a limited production capacity and the stochastic demand of the retailers is satisfied with procurement of transportation services. The aim is to minimize the total expected cost over a planning horizon, given by the sum of the inventory cost at the supplier, the inventory cost at the retailers, the penalty cost for stock-out at the retailers and the transportation cost. First, we show that a policy based just on the average demand can have a total expected cost infinitely worse than the one obtained by taking into account the overall probability distribution of the demand in the decision process. Therefore, we introduce a stochastic dynamic programming formulation of the problem that allows us to find an optimal policy in small size instances. Finally, we design and implement a matheuristic approach, integrating a rollout algorithm and an optimal solution of mixed-integer linear programming models, which is able to solve realistic size problem instances. Computational results allow us to provide managerial insights concerning the management of stochastic demand.     

Hedging through index-based price contracts in commodity-based supply chains

This paper studies the optimal hedging strategy of risk-neutral firms in supply chain settings. We model a retailer procuring goods through index-based price contracts from two commodity processors. The processors’ input commodity prices are random and correlated. The retailer faces price-sensitive demand curves; therefore, it controls product demand through retail pricing in the final product market. We characterize the optimal contracting terms for the processors and show that they prefer to hedge part of their exposure to the commodity price risk. The optimal contract for processor comprises a processing margin independent of the commodity price volatility and a hedge ratio that is a function of the commodity price volatility and the products substitution factor. We uncover a new rationale for hedging in settings where downstream firms have pricing power; both processors and the retailer benefit from the retailer’s pricing power when their margins are linked to input prices; an index-based price contract is a means to link the processors’ and the retailer’s margins. We further investigate how different market parameters affect the optimal hedge ratios and extend our model to settings with random market sizes and asymmetric substitution for final products.     

Sourcing from Multiple Suppliers for Price‐Dependent Demands

We analyze a model that integrates demand shaping via dynamic pricing and risk mitigation via supply diversification. The firm under consideration replenishes a certain product from a set of capacitated suppliers for a price‐dependent demand in each period. Under deterministic capacities, we derive a multilevel base stock list price policy and establish the optimality of cost‐based supplier selection, that is, ordering from a cheaper source before more expensive ones. With general random capacities, however, neither result holds. While it is optimal to price low for a high inventory level, the optimal order quantities are not monotone with respect to the inventory level. In general, a near reorder‐point policy should be followed. Specifically, there is a reorder point for each supplier such that no order is issued to him when the inventory level is above this point and a positive order is placed almost everywhere when the inventory level is below this point. Under this policy, it may be profitable to order exclusively from the most expensive source. We characterize conditions under which a strict reorder‐point policy and a cost‐based supplier‐selection criterion become optimal. Moreover, we quantify the benefit from dynamic pricing, as opposed to static pricing, and the benefit from multiple sourcing, as opposed to single sourcing. We show that these two strategies exhibit a substitutable relationship. Dynamic pricing is less effective under multiple sourcing than under single sourcing, and supplier diversification is less valuable with price adjustments than without. Under limited supply, dynamic pricing yields a robust, long‐term profit improvement. The value of supply diversification, in contrast, mainly comes from added capacities and is most significant in the short run.     

Location and reliability problems on a line: Impact of objectives and correlated failures on optimal location patterns

In this paper we study a class of locations models where facilities are not perfectly reliable and failures may be correlated. We analyze problems with Median and Center objectives under complete and incomplete customer information regarding the state of facilities. The goal is to understand how failure probabilities, correlations, availability of information, and problem objective affect the optimal location patterns. In particular, we want to find analytical confirmations for location patterns observed in numerical experiments with network location models. To derive closed-form analytical results the analysis is restricted to a simple (yet classic) setting: a 2-facility problem on a unit segment, with customer demand distributed uniformly over the segment (results can be extended to other demand distributions as well). We derive explicit expressions for facility trajectories as functions of model parameters, obtaining a number of managerial insights. In addition we provide the decomposition of the optimal cost into the closed form components corresponding to the cost of travel, the cost of facility unreliability and the cost of incomplete information. Most of the theoretical insights are confirmed via numerical experiments for models with larger (3–5) number of facilities.     

爱尔朗型按订单装配系统最优生产——库存控制策略研究

本文研究具有复杂装配结构的爱尔朗型按订单装配(ATO)系统的组件生产与库存优化控制问题。系统涉及多种组件,一个最终产品和多类客户需求。在此系统中,各种组件的生产时间服从爱尔朗分布,各类客户的需求为泊松到达过程。针对不同客户需求类型:产品需求与独立组件需求且同为销售损失型,建立基于马尔可夫决策过程(MDP)的平均总成本模型,应用动态规划方法求解最优策略。仿真模拟方法实现最优策略,并通过数值实验分析多生产阶段和系统参数对最优策略的影响。研究结果表明,爱尔朗型生产时间ATO系统的最优策略为状态依赖型策略,即组件的生产与库存分配由动态基础库存水平值和动态库存配给水平值控制。对于任一组件,其基础库存水平值和库存配给水平值均随着生产阶段的增加而降低,且生产阶段对基础库存水平值和平均总成本的影响较显著。     

End‐of‐Life Inventory Decisions for Consumer Electronics Service Parts

We consider a consumer electronics manufacturer's problem of controlling the inventory of spare parts in the final phase of the service life cycle. The final phase starts when the part production is terminated and continues until the last service contract or warranty period expires. Placing final orders for service parts is considered to be a popular tactic to satisfy demand during this period and to mitigate the effect of part obsolescence at the end of the service life cycle. Previous research focuses on repairing defective products by replacing the defective parts with properly functioning spare ones. However, for consumer electronic products there typically is considerable price erosion while repair costs stay steady over time. As a consequence, there might be a point in time at which the unit price of the product drops below the repair costs. If so, it is more cost effective to adopt an alternative policy to meet service demands toward the end of the final phase, such as offering customers a new product of the similar type or a discount on a next generation product. This study examines the cost trade‐offs of implementing alternative policies for the repair policy and develops an exact expression for the expected total cost function. Using this expression, the optimal final order quantity and switching time from repair to an alternative policy can be determined simultaneously. Numerical analysis of a real world case sheds light on the cost benefits of these policies and also yields insights into the quantitative importance of the various cost parameters.     

Enabling Opportunism: Revenue Sharing when Sales Revenues are Unobservable

We consider a supply chain with a supplier that sells to a retailer under a revenue‐sharing arrangement. Demand is uncertain and unobservable to the supplier. We assume that the retailer is rational, that is, the retailer behaves opportunistically and underreports sales revenues to the supplier whenever such underreporting is profitable. Assuming the supplier has the ability to audit the retailer and learn about the actual sales revenues, we show that the supplier will never find it optimal to audit to the point that ensures truthful reporting for all demand realizations. By committing to an auditing policy, the supplier can exploit retailer opportunism and derive profits that at times even exceed those that could be obtained when dealing with a retailer that always strictly adheres to the agreed‐upon contract terms. We also show that the retailer's opportunistic behavior can increase total supply chain profits.     

Production lot sizing with process deterioration and machine breakdown under inspection schedule

The paper develops integrated production, inventory and maintenance models for a deteriorating production system in which the production facility may not only shift from an ‘in-control’ state to an ‘out-of-control’ state but also may break down at any random point in time during a production run. In case of machine breakdown, production of the interrupted lot is aborted and a new production lot is started when the on-hand inventory is depleted after corrective repair. The process is inspected during each production run to examine the state of the production process. If it is found in the ‘in-control’ state then either (a) no action is taken except at the time of last inspection where preventive maintenance is done (inspection policy-I) or (b) preventive maintenance is performed (inspection policy-II). If, however, the process is found to be in the ‘out-of-control’ state at any inspection then restoration is done. The proposed models are formulated under general shift, breakdown and repair time distributions. As it is, in general, difficult to find the optimal production policy under inspection policy-I, a suboptimal production policy is derived. Numerical examples are taken to determine numerically the optimal/suboptimal production policies of the proposed models, to examine the sensitivity of important model parameters and to compare the performance of inspection and no inspection policies.     

需求时间不确定下的多供应商配套供货模型研究

本文在基于Supply Hub的运作模式下,研究了N个配套供应商对单个制造商的单周期准时供货模型。当制造商的需求时间不确定时,供应商需要依据预期成本最小化来确定各自最优的供货时间。通过找到各个供应商在信息封闭和信息共享这两种模式下的最优供货时间决策,并且对比不同模式下供应商成本和制造商服务水平,证明了配套供应商之间通过一定程度的信息共享能够有效降低成本和提高服务水平。最后提出一种基于Supply Hub主导的多供应商准时供货策略,从而实现了系统整体绩效的优化。     

Joint modified block replacement and production/inventory control policy for a failure-prone manufacturing cell

This paper considers a joint preventive maintenance (PM) and production/inventory control policy of an unreliable single machine, mono-product manufacturing cell with stochastic non-negligible corrective and preventive delays. The production/inventory control policy, which is based on the hedging point policy (HPP), consists in building and maintaining a safety stock of finished products in order to respond to demand and to avoid shortages during maintenance actions. Without considering the impact of preventive and corrective actions on the overall performance of the production system, most authors working in the reliability and maintainability domains confirm that the age-based preventive maintenance policy (ARP) outperforms the classical block-replacement policy (BRP). In order to reduce wastage incurred by the classical BRP, we consider a modified block replacement policy (MBRP), which consists in canceling a preventive maintenance action if the time elapsed since the last maintenance action exceeds a specified time threshold. The main objective of this paper is to determine the joint optimal policy that minimizes the overall cost, which is composed of corrective and preventive maintenance costs as well as inventory holding and backlog costs. A simulation model mimicking the dynamic and stochastic behavior of the manufacturing cell, based on more realistic considerations of the real behavior of industrial manufacturing cells, is proposed. Based on simulation results, the joint optimal MBRP/HPP parameters are obtained through a numerical approach that combines design of experiment, analysis of variance and response surface methodologies. The joint optimal MBRP/HPP policy is compared to classical joint ARP/HPP and BRP/HPP optimal policies, and the results show that the proposed MBRP/HPP outperforms the latter. Sensitivity analyses are also carried out in order to confirm the superiority of the proposed MBRP/HPP, and it is observed that for practitioners, the proposed joint MBRP/HPP offers not only cost savings, but is also easy to manage, as compared to the ARP/HPP policy.     

OPTIMAL AND NEAR OPTIMAL CONTROL OF A TWO-PART-TYPE STOCHASTIC MANUFACTURING SYSTEM WITH DYNAMIC SETUPS

This paper deals with a manufacturing system consisting of a single machine subject to random failures and repairs. The machine can produce two types of parts. When the production is switched from one part type to the other, a random setup time is incurred at a constant cost rate. The objective is to track the demand, while keeping the work-in-process as close as possible to zero for both products. The problem is formulated as an optimal stochastic control problem. The optimal policy is obtained numerically by discretizing the continuous time continuous state opti-mality conditions using a Markov chain approximation technique. The discretized optimality conditions are shown to correspond to an infinite horizon, discrete time, discrete state dynamic programming problem. The optimal setup policy is shown to have two different structures depending on the parameters of the system. A heuristic policy is proposed to approximate the optimal setup policy. Simulation results show that the heuristic policy is a very good approximation for sufficiently reliable systems.     

具有多元马氏需求的多产品多阶段库存优化模型

本文研究一类新的多产品库存控制策略,即具有多元马氏需求特征的多产品多阶段的订货点订货量(Q, R, SS)策略,该策略考虑市场需求在不同产品之间具有多元马氏转移特征,并考虑缺货因素设置安全库存。论文首先建立了多产品多阶段的多元马氏需求预测模型,并通过该模型确定了各种产品需求之间的关系。同时,在该模型的理论基础上,提出了多产品多阶段的总期望成本模型及其最优(Q, R, SS)策略,进而结合算例给出模型的最优策略的数值解。     

Combined Pricing and Portfolio Option Procurement

In this paper, we study a single‐product periodic‐review inventory system that faces random and price‐dependent demand. The firm can purchase the product either from option contracts or from the spot market. Different option contracts are offered by a set of suppliers with a two‐part fee structure: a unit reservation cost and a unit exercising cost. The spot market price is random and its realization may affect the subsequent option contract prices. The firm decides the reservation quantity from each supplier and the product selling price at the beginning of each period and the number of options to exercise (inventory replenishment) at the end of the period to maximize the total expected profit over its planning horizon. We show that the optimal inventory replenishment policy is order‐up‐to type with a sequence of decreasing thresholds. We also investigate the optimal option‐reservation policy and the optimal pricing strategy. The optimal reservation quantities and selling price are shown to be both decreasing in the starting inventory level when demand function is additive. Building upon the analytical results, we conduct a numerical study to unveil additional managerial insights. Among other things, we quantify the values of the option contracts and dynamic pricing to the firm and show that they are more significant when the market demand becomes more volatile.     

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.