Managing finished-goods inventory under capacitated delayed differentiation

Delayed differentiation or postponement is widely advocated to mitigate conflicts between product diversity and inventory cost savings. Manufacturers practicing postponement often suffer from severely constrained finishing capacities and noticeable finishing lead times. Therefore, inventories are still needed for finished products. Using the concept of inventory shortfall, this paper studies base-stock inventory models with and without demand forecasting and provides a computationally efficient method to set optimal inventory targets for finished products under capacitated postponement. Computations show inventory-saving benefit quickly vanishes after the capacity reaches a certain level. The value of forecasted advance-demand information (ADI) to postponement is justified, but can easily be overstated. Finishing capacities usually force manufacturers to build ahead according to demand forecast. When capacity limitation becomes severe, intuitions often guide producers to build to forecast even more than finishing lead times ahead. Results of this research indicate that these intuitions may be invalid and build to forecast more than finishing lead times ahead may not be a good practice. Further studies reveal that under capacitated postponement the forecasted advance-demand information is useful only when the variance of demand forecast errors is less than that of demands, and show that the optimal forecast lead time can be obtained in the same way as if the capacity is unlimited.     

Optimal Dynamic Order Scheduling under Capacity Constraints Given Demand‐Forecast Evolution

We consider a manufacturer without any frozen periods in production schedules so that it can dynamically update the schedules as the demand forecast evolves over time until the realization of actual demand. The manufacturer has a fixed production capacity in each production period, which impacts the time to start production as well as the production schedules. We develop a dynamic optimization model to analyze the optimal production schedules under capacity constraint and demand‐forecast updating. To model the evolution of demand forecasts, we use both additive and multiplicative versions of the martingale model of forecast evolution. We first derive expressions for the optimal base stock levels for a single‐product model. We find that manufacturers located near their market bases can realize most of their potential profits (i.e., profit made when the capacity is unlimited) by building a very limited amount of capacity. For moderate demand uncertainty, we also show that it is almost impossible for manufacturers to compensate for the increase in supply–demand mismatches resulting from long delivery lead times by increasing capacity, making lead‐time reduction a better alternative than capacity expansion. We then extend the model to a multi‐product case and derive expressions for the optimal production quantities for each product given a shared capacity constraint. Using a two‐product model, we show that the manufacturer should utilize its capacity more in earlier periods when the demand for both products is more positively correlated.     

Managing High‐Tech Capacity Expansion via Reservation Contracts

We study capacity reservation contracts between a high‐tech manufacturer (supplier) and her OEM customer (buyer). The supplier and the buyer are partners who enter a ‘design‐win” agreement to develop the product, and who share the stochastic demand information. To encourage the supplier for more aggressive capacity expansion, the buyer reserves capacity upfront by paying a deductible fee. As capacity expansion demonstrates diseconomy of scale in this context, we assume convex capacity costs. We show that as the buyer's revenue margin decreases, the supplier faces a sequence of four profit scenarios with decreasing desirability. We examine the effects of market size and demand variability to the contract conditions. We propose two channel coordination contracts, and discuss how such contracts can be tailored for situations where the supplier has the option of not complying with the contract, and when the buyer's demand information is only partially updated during the supplier's capacity lead‐time.     

基于分层MTO订单的准入策略研究

研究按订单生产(make to order,MTO)模式下随机订单的准入策略.本文提出的准入决策方法分为两步,首先在考虑随机订单的不同属性基础上,采用TOPSIS(technique for order preference by similarity to an ideal solution)方法计算新到订单与理想订单的接近程度,以此作为订单的综合收益,从而对新订单进行分层排序;其次采用MDP(Markov decision process)模型分别计算接受和拒绝订单的期望收益,从而决定是否接受该订单.研究发现,当市场需求接近或大于产能时,企业可从订单分层中获益;反之,市场需求显著小于产能时,分层不会带来额外收益.企业分层收益随需求增加或产能减少而递增,且与生产前置期呈倒U型关系.数值模拟发现,订单分层越精细,收益越大,且分层数约为需求与企业产能的比值时,订单分层收益接近最大值.     

AN ALTERNATE MODEL FOR LEAD-TIME DEMAND: CONTINUOUS-REVIEW INVENTORY SYSTEMS

The calculation of reorder points when the distribution of lead-time demand is normal is quite complex, primarily because of having to bound it away from negative demand values. A number of researchers have sought feasible alternative forms of lead-time demand which can be calculated without undue difficulty. It is proposed here to assume a Poisson (daily) demand and an exponential lead time (days). If they are assumed independent their convolution is geometric, which is itself asymptotically exponential. This has a number of advantages: (1) The exponential lead time is appropriate where the lead time is often short (i.e., local source), occasionally longer (when the local sources stock out), and, infrequently, quite long. (2) The geometric lead-time demand is independent of changes of time scale. (3) Reorder points and lot sizes appear in simple closed form. (4) The exponential asymptote is sufficiently close that this further simplification is usually warranted.     

A Production–Inventory Model for a Push–Pull Manufacturing System with Capacity and Service Level Constraints

We study a hybrid push–pull production system with a two‐stage manufacturing process, which builds and stocks tested components for just‐in‐time configuration of the final product when a specific customer order is received. The first production stage (fabrication) is a push process where parts are replenished, tested, and assembled into components according to product‐level build plans. The component inventory is kept in stock ready for the final assembly of the end products. The second production stage (fulfillment) is a pull‐based assemble‐to‐order process where the final assembly process is initiated when a customer order is received and no finished goods inventory is kept for end products. One important planning issue is to find the right trade‐off between capacity utilization and inventory cost reduction that strives to meet the quarter‐end peak demand. We present a nonlinear optimization model to minimize the total inventory cost subject to the service level constraints and the production capacity constraints. This results in a convex program with linear constraints. An efficient algorithm using decomposition is developed for solving the nonlinear optimization problem. Numerical results are presented to show the performance improvements achieved by the optimized solutions along with managerial insights provided.     

The Timing of Capacity Investment with Lead Times: When Do Firms Act in Unison?

We study competitive capacity investment for the emergence of a new market. Firms may invest either in capacity leading demand or in capacity lagging demand at different costs. We show how the lead time and other operational factors including volume flexibility, existing capacity, and demand uncertainty impact equilibrium outcomes. Our results indicate that a type of bandwagon behavior is the most likely equilibrium outcome: if both firms are going to invest, then they are most likely to act in unison. Contrary to much received wisdom, we show that leader–follower behavior is very uncommon in equilibrium where firms do not have volume flexibility, and will not occur at all if lead times are sufficiently short. On the other hand, if there is volume flexibility in production, then the likelihood of this sequential investment behavior increases. Our findings underscore the importance of operational characteristics in determining the competitive dynamics of capacity investment timing.     

寡头发电商投资阈值与容量选择模型及其分析

发电容量投资不足或过剩都将带来巨大经济与社会损失.论文针对不确定需求下的电力市场,在分析了容量约束下的寡头发电商竞价策略基础上,运用实物期权和博弈论思想,构建了寡头发电投资阈值与容量选择模型,并通过数值仿真给出了投资商的投资阈值与最优投资容量,分析结果表明:1)随投资商数量的增加,投资阈值下降,但最优的投资容量也随之下降;若需求不确定性增大,投资阈值与最优容量则随之增大;2)就整个电力市场而言,在发电商数量比较少时,电力市场效率较低,但电力供给充裕;而在发电商数量较多时,市场效率较高,但电力供给却较为紧张.     

Sizing Inventory When Lead Time and Demand are Correlated

Determining appropriate inventory levels has been a subject of interest for both researchers and practitioners. Standard practice is to treat lead time demand as a random sum of random numbers and rely on established probability theory to calculate both reorder point and safety stock levels. A key assumption in these calculations, however, is that lead time and demand are not correlated. In this paper, we first explore situations where this assumption is untrue and then develop equations to determine the reorder point and the safety stock when lead time and demand are correlated. More specifically, we (1) derive formulas for the average and variance of the demand in a lead time, which can then be used to calculate the reorder point and the safety stock, (2) apply these formulas to two distributions for which there is a closed‐form solution: normal and Poisson, and (3) examine the effect of correlation on safety stock requirements under the normal distribution.     

产能和需求不确定情形下ATO系统最优库存和生产决策研究

通过将产成品的最终组装环节延迟到观察到实际需求以后进行,按订单组装(Assemble-to-Order,ATO)策略能够有效避免按库存生产(Make-to-Stock)策略下因为生产过剩而带来的损失和风险。然而,在未来产能有限的情形下,生产商必须提前组装部分产成品,以最大化自身收益。本文考虑一个未来需求和组装产能同时具有不确定性的单周期ATO系统:在观察到实际需求以前,生产商必须准备好所有的零部件库存,并组装适量的产成品;观察到实际需求和实际可用组装能力以后,则根据需要进一步追加产成品产量,以尽可能满足客户需求,从而最大化自身利益。通过构建一个两阶段规划模型,我们研究了生产商的最优零部件库存和最优生产决策;并进一步考察了生产商可以通过紧急外包来获取额外组装产能时的最优决策。研究结果为随机环境下生产商合理采购零部件库存和合理安排生产提供了有益的管理启示。     

Dynamic Pricing and Lead‐Time Policies for Make‐to‐Order Systems*

Make‐to‐order firms use different approaches for managing their lead‐times and pricing in the face of changing market conditions. A particular firm's approach may be largely dictated by environmental constraints. For example, it makes little sense to carefully manage lead‐time if its effect on demand is muted, as it can be in situations where leadtime is difficult for the market to gauge or requires investment to estimate. Similarly, it can be impractical to change capacity and price. However, environmental constraints are likely to become less of an issue in the future with the expanding e‐business infrastructure, and this trend raises questions into how to manage effectively the marketing mix of price and lead‐time in a more “friction‐free” setting. We study a simple model of a make‐to‐order firm, and we examine policies for adjusting price and capacity in response to periodic and unpredictable shifts in how the market values price and lead‐time. Our analysis suggests that maintaining a fixed capacity while using lead‐time and/or price to absorb changes in the market will be most attractive when stability in throughput and profit are highly valued, but in volatile markets, this stability comes at a cost of low profits. From a pure profit maximization perspective, it is best to strive for a short and consistent lead‐times by adjusting both capacity and price in response to market changes.     

Coordinating Service‐Sensitive Demand and Capacity by Adaptive Decision Making: An Application of Case‐Based Decision Theory*

The subject of this article is the simultaneous choice of product price and manufacturing capacity if demand is stochastic and service‐level sensitive. In this setting, capacity as well as price have an impact on demand because several aspects of service level depend on capacity. For example, delivery time will be reduced if capacity is increased given a constant demand rate. We illustrate the relationship between service level, capacity, and demand reaction by a stylized application problem from the after‐sales services industry. The reaction of customers to variations in service level and price is represented by a kinked price‐demand‐rate function. We first derive the optimal price‐capacity combination for the resulting decision problem under full information. Subsequently, we focus on a decision maker (DM) who lacks complete knowledge of the demand function. Hence the DM is unable to anticipate the service level and consequently cannot identify the optimal solution. However, the DM will acquire additional information during the sales process and use it in subsequent revisions of the price‐capacity decision. Thus, this decision making is adaptive and based on experience. In contrast to the literature, which assumes certain repetitive procedures somewhat ad hoc, we develop an adaptive decision process based on case‐based decision theory (CBDT) for the price‐capacity problem. Finally, we show that a CBDT DM in our setting eventually finds the optimal solution, if the DM sets the price based on absorption costs and adequately adjusts the capacity with respect to the observed demand.     

A SIMULATION GAME FOR TEACHING SERVICE‐ORIENTED SUPPLY CHAIN MANAGEMENT: DOES INFORMATION SHARING HELP MANAGERS WITH SERVICE CAPACITY DECISIONS?*

For decades, the Beer Game has taught complex principles of supply chain management in a finished good inventory supply chain. However, services typically cannot hold inventory and can only manage backlogs through capacity adjustments. We propose a simulation game designed to teach service‐oriented supply chain management principles and to test whether managers use them effectively. For example, using a sample of typical student results, we determine that student managers can effectively use end‐user demand information to reduce backlog and capacity adjustment costs. The game can also demonstrate the impact of demand variability and reduced capacity adjustment time and lead times.     

Supply Performance in Multi‐Echelon Inventory Systems with Intermediate Product Demand: A Perspective on Allocation

In this article, we study the performance of multi‐echelon inventory systems with intermediate, external product demand in one or more upper echelons. This type of problem is of general interest in inventory theory and of particular importance in supply chain systems with both end‐product demand and spare parts (subassemblies) demand. The multi‐echelon inventory system considered here is a combination of assembly and serial stages with direct demand from more than one node. The aspect of multiple sources of demands leads to interesting inventory allocation problems. The demand and capacity at each node are considered stochastic in nature. A fixed supply and manufacturing lead time is used between the stages. We develop mathematical models for these multi‐echelon systems, which describe the inventory dynamics and allow simulation of the system. A simulation‐based inventory optimization approach is developed to search for the best base‐stock levels for these systems. The gradient estimation technique of perturbation analysis is used to derive sample‐path estimators. We consider four allocation schemes: lexicographic with priority to intermediate demand, lexiographic with priority to downstream demand, predetermined proportional allocation, and proportional allocation. Based on the numerical results we find that no single allocation policy is appropriate under all conditions. Depending on the combinations of variability and utilization we identify conditions under which use of certain allocation polices across the supply chain result in lower costs. Further, we determine how selection of an inappropriate allocation policy in the presence of scarce on‐hand inventory could result in downstream nodes facing acute shortages. Consequently we provide insight on why good allocation policies work well under differing sets of operating conditions.     

Trade-off between quoted lead time and price

In a make-to-order environment, lead time and price can play a crucial role in determining the financial success of a firm. Their importance increases when demand is sensitive to the quoted lead time and price. A model is presented which uses the quoted lead time and price as a mechanism to determine the optimal demand level. The relationships between the model parameters and their impacts on the firm's profit is also analysed. In addition, the effect of the number of job requests, and the mean processing time are examined. Based on the results presented in this paper, there is clear indication that the firm's profit is sensitive to the inventory holding rate, and that the inventory holding cost component is redundant in the presence of a tardiness cost component.     

Decision support for lead time and demand variability reduction

Companies undertaking operations improvement in supply chains face many alternatives. This work seeks to assist practitioners to prioritize improvement actions by developing analytical expressions for the marginal values of three parameters – (i) lead time mean, (ii) lead time variance, and (iii) demand variance – which measure the marginal cost of an incremental change in a parameter. The relative effectiveness of reducing lead time mean versus lead time variance is captured by the ratio of the marginal value of lead time mean to that of lead time variance. We find that this ratio strongly depends on whether the lead time mean and variance are independent or correlated. We illustrate the application of the results with a numerical example from an industrial setting. The insights can help managers determine the optimal investment decision to modify demand and supply characteristics in their supply chain, e.g., by switching suppliers, factory layout, or investing in information systems.     

考虑需求异常扰动和管理者损失厌恶行为的能力结构投资模型

本文在需求异常扰动的情境下,研究了运作系统专有和柔性能力结构的投资决策模型,并在数理上证明和比较了管理者两种不同风险感知情况下的能力结构比率决策问题。研究表明:在需求异常扰动发生概率、扰动分布参数以及柔性扩张系数影响下,风险中性和存在损失厌恶行为的管理者在柔性能力投资决策上存在明显的差异,依据缺货损失程度采取的补贴或惩罚机制可以改善损失厌恶管理者的柔性能力投资决策偏差。     

Demand and Production Management with Uniform Guaranteed Lead Time

Recently, innovation‐oriented firms have been competing along dimensions other than price, lead time being one such dimension. Increasingly, customers are favoring lead time guarantees as a means to hedge supply chain risks. For a make‐to‐order environment, we explicitly model the impact of a lead time guarantee on customer demands and production planning. We study how a firm can integrate demand and production decisions to optimize expected profits by quoting a uniform guaranteed maximum lead time to all customers. Our analysis highlights the increasing importance of lead time for customers, as well as the tradeoffs in achieving a proper balance between revenue and cost drivers associated with lead‐time guarantees. We show that the optimal lead time has a closed‐form solution with a newsvendor‐like structure. We prove comparative statics results for the change in optimal lead time with changes in capacity and cost parameters and illustrate the insights using numerical experimentation.     

Incentive Schemes for Semiconductor Capacity Allocation: A Game Theoretic Analysis

We study incentive issues that arise in semiconductor capacity planning and allocation. Motivated by our experience at a major U. S. semiconductor manufacturer, we model the capacity‐allocation problem in a game‐theoretic setting as follows: each product manager (PM) is responsible for a certain product line, while privately owning demand information through regular interaction with the customers. Capacity‐allocation is carried out by the corporate headquarters (HQ), which allocates manufacturing capacity to product lines based on demand information reported by the PMs. We show that PMs have an incentive to manipulate demand information to increase their expected allocation, and that a carefully designed coordination mechanism is essential for HQ to implement the optimal allocation. To this end, we design an incentive scheme through bonus payments and participation charges that elicits private demand information from the PMs. We show that the mechanism achieves budget‐balance and voluntary‐participation requirements simultaneously. The results provide important insights into the treatment of misaligned incentives in the context of semiconductor capacity‐allocation.     

THE HERMITE DISTRIBUTION AS A MODEL OF DEMAND DURING LEAD TIME FOR SLOW-MOVING ITEMS

Heretofore, the Poisson and the Laplace distributions have been used to model demand during lead time for slow-moving items. In this paper, we present a Poisson-like distribution called the Hermite. The advantage of the Hermite is that it is as simple to use as the Poisson and the Laplace are. Moreover, the Hermite is the exact distribution of demand during lead time when unit demand is Poisson, P(Λ), and lead time is normally distributed, N(μ, σ²), so long as (μ/σ²)≥Λ. Thus, the Hermite can enhance the accuracy of analysis as well as add to the tools available to the analyst.