Dynamic Pricing,Production, and Channel Coordination with Stochastic Learning

We consider a decentralized two‐period supply chain in which a manufacturer produces a product with benefits of cost learning, and sells it through a retailer facing a price‐dependent demand. The manufacturer's second‐period production cost declines linearly in the first‐period production, but with a random learning rate. The manufacturer may or may not have the inventory carryover option. We formulate the resulting problems as two‐period Stackelberg games and obtain their feedback equilibrium solutions explicitly. We then examine the impact of mean learning rate and learning rate variability on the pricing strategies of the channel members, on the manufacturer's production decisions, and on the retailer's procurement decisions. We show that as the mean learning rate or the learning rate variability increases, the traditional double marginalization problem becomes more severe, leading to greater efficiency loss in the channel. We obtain revenue sharing contracts that can coordinate the dynamic supply chain. In particular, when the manufacturer may hold inventory, we identify two major drivers for inventory carryover: market growth and learning rate variability. Finally, we demonstrate the robustness of our results by examining a model in which cost learning takes place continuously.     

一种考虑原材料库存成本的变质物品EPQ模型

在库存管理研究中,单独实现产成品或原材料库存成本最小,往往无法获得整个库存系统的最优控制策略.本文提出了一种同时考虑产成品和原材料库存成本的变质物品EPQ集成模型.运用迭代寻优法得到模型最优解,得出计划期内最优原材料订购次数,原材料订购周期内的最优生产次数和最优服务水平,并对主要参数进行了灵敏度分析,为生产制造企业的库存管理提供了决策依据.     

SETUP REDUCTION AND MACHINE AVAILABILITY

This paper is an extension of Billington, who used the framework of the economic production quantity (EPQ) to model setup cost reduction. In the present paper, we use the EPQ model as a starting point to investigate the nature of setup costs and the effect of setup time reduction on the increase in available capacity. Reducing setup is vital to a company's success because a lengthy changeover of machinery is expensive: it demands long production runs to justify its cost, and these, in turn, lead to excessive inventory and to a slow response to customer needs. As in Billington, setup reduction is modeled as a function of an annual amortized investment. The paper examines the behavior of the setup time, the inventory cost, the lot size, and the freeing up of machine time in the face of a capacity constraint. A solution algorithm is provided to find setup times that minimize the sum of setup and holding cost, subject to a constraint on machine availability. The analysis sheds light on the true nature of setup cost and on the opportunity cost of not reducing setups. In the constrained optimization, the Lagrangian multiplier gives an estimate of the marginal value of adding one time unit of machine capacity, or, alternatively, of reducing one unit of setup time.     

CONFORMANCE QUALITY AND REPLACEMENT COSTS UNDER WARRANTY

In this paper, I investigate the impact of the conformance quality of a durable product on manufacturer's and user's replacement costs while the product is under warranty. I first relate conformance quality to reliability and then examine its effects on warranty costs to manufacturer and customer under both pro-rata and free-replacement warranties. In particular, I show that the reduction in customer's cost is generally contingent on more stringent quality improvement than the reduction in manufacturer's costs. I also discuss the value of inspection, and I present an application based on real data.     

信息共享下库存量牛鞭效应的影响因素研究

目前的研究多从供应链上游角度出发考虑传统牛鞭效应,而本文从供应链下游的角度研究库存量牛鞭效应得到了不一样的管理学启示.在需求函数方面,建立的需求模型包括市场规模、价格敏感性系数等更有现实意义的要素.在此,本文建立了包括一个零售商和一个制造商的简单两级供应链,得出了制造商在采用补充至订货点策略和最小均方差预测技术,在两种不同的信息共享模式下的库存量牛鞭效应表达式,并对他们的影响因素进行了分析.而且通过数值分析对模型进行了验证并得到新的结果.通过研究发现,信息共享能够显著降低制造商的库存量牛鞭效应;零售商和制造商的库存量牛鞭效应都不受市场规模的影响;零售商的库存量牛鞭效应在一定条件下不存在;相比于零售商提前期,制造商提前期对制造商的库存量牛鞭效应影响更大.同时,价格敏感性系数、价格自相关系数等因素对制造商库存量牛鞭效应也有不同程度的影响.     

Value of Sharing Production Yield Information in a Serial Supply Chain

New developments in corporate information technology such as enterprise resource planning systems have significantly increased the flow of information among members of supply chains. However, the benefits of sharing information can vary depending on the supply chain structure and its operational characteristics. Most of the existing research has studied the impact of sharing downstream information (e.g., a manufacturer sharing information with its suppliers). We evaluate the benefits of sharing upstream yield information (e.g., a supplier sharing information with the manufacturer) in a two‐stage serial supply chain in which the supplier has multiple internal processes and is faced with uncertain output due to yield losses. We are interested in determining when the sharing of the supplier's information is most beneficial to the manufacturer. After proposing an order‐up‐to type heuristic policy, we perform a detailed computational study and observe that this information is most beneficial when the supplier's yield variance is high and when end‐customer demand variance is low. We also find that the manufacturer's backorder‐to‐holding cost ratio has little, if any, impact on the usefulness of information.     

TIME‐BASED PRICING AND LEADTIME POLICIES FOR A BUILD‐TO‐ORDER MANUFACTURER

We studied time‐based policies on pricing and leadtime for a build‐to‐order and direct sales manufacturer. It is assumed that the utility of the product varies among potential customers and decreases over time, and that a potential customer will place an order if his or her utility is higher than the manufacturer's posted price. Once an order is placed, it will be delivered to the customer after a length of time called “leadtime.” Because of the decrease in a customer's utility during leadtime, a customer will cancel the order if the utility falls below the ordering price before the order is received. The manufacturer may choose to offer discounted prices to customers who would otherwise cancel their orders. We discuss two price policies: common discounted price and customized discounted price. In the common discounted price policy, the manufacturer offers a single lower price to the customers; in the customized discounted price policy, the manufacturer offers the customers separately for individual new prices. Our analytical and numerical studies show that the discounted price policies results in higher revenue and that the customized discounted price policy significantly outperforms the common discounted price policy when product utility decreases rapidly. We also study two leadtime policies when production cost decreases over time. The first uses a fixed leadtime, and the second allows the leadtime to vary dynamically over time. We find that the dynamic leadtime policy significantly outperforms the fixed leadtime policy when the product cost decreases rapidly.     

OPTIMAL ORDERING IN A DUAL‐SUPPLIER SYSTEM WITH DEMAND FORECAST UPDATES

We study how an updated demand forecast affects a manufacturer's choice in ordering raw materials. With demand forecast updates, we develop a model where raw materials are ordered from two suppliers—one fast but expensive and the other cheap but slow—and further provide an explicit solution to the resulting dynamic optimization problem. Under some mild conditions, we demonstrate that the cost function is convex and twice‐differentiable with respect to order quantity. With this model, we are able to evaluate the benefit of demand information updating which leads to the identification of directions for further improvement. We further demonstrate that the model applies to multiple‐period problems provided that some demand regularity conditions are satisfied. Data collected from a manufacturer support the structure and conclusion of the model. Although the model is described in the context of in‐bound logistics, it can be applied to production and out‐bound logistics decisions as well.     

How Inventory Cost Influences Introduction Timing of Product Line Extensions

In the industry with radical technology push or rapidly changing customer preference, it is firms' common wisdom to introduce high‐end product first, and follow by low‐end product‐line extensions. A key decision in this “down‐market stretch” strategy is the introduction time. High inventory cost is pervasive in such industries, but its impact has long been ignored during the presale planning stage. This study takes a first step toward filling this gap. We propose an integrated inventory (supply) and diffusion (demand) framework and analyze how inventory cost influences the introduction timing of product‐line extensions, considering substitution effect among successive generations. We show that under low inventory cost or frequent replenishment ordering policy, the optimal introduction time indeed follows the well‐known “now or never” rule. However, sequential introduction becomes optimal as the inventory holding gets more substantial or the product life cycle gets shorter. The optimal introduction timing can increase or decrease with the inventory cost depending on the marketplace setting, requiring a careful analysis.     

Quantity Discount‐Based Inventory Coordination: Effectiveness and Critical Environmental Factors

It is understood that quantity discounts provide a practical foundation for coordinating inventory decisions in supply chains. The primary objective of this research is to test, under a variety of environmental conditions, the effectiveness of quantity discounts as an inventory coordination mechanism between a buyer and a supplier. A comprehensive simulation experiment with anova has been designed to investigate the impacts of (1) choice of quantity discount‐based inventory coordination policies, (2) magnitude of demand variation, (3) buyer's and supplier's relative inventory cost structure, and (4) buyer's economic time‐between‐orders on the effectiveness of supply chain inventory coordination. The analytical results confirm that the quantity discount policies have managerial properties as a mediator for inventory coordination. The results also show that the performance of quantity discount‐based inventory coordination policies is influenced significantly by environmental factors, such as the magnitude of demand variation, the buyer's and the supplier's inventory cost structure, and the buyer's economic time‐between‐orders.     

Modeling the manager's match-or-wait dilemma in a make-to-forecast production situation

The make-to-forecast manufacturing environment is characterized by the manufacture of individual, expensive-to-store units which come in alternative configurations or models. Since the production lead times are longer than customers are willing to wait, production is started in anticipation of orders for particular models and then modified while in production, if economically desirable, to match the actual customer orders. Ideally, no finished goods inventory occurs in this process. Occasionally, however, such unsold finished items (called “orphans” here) are generated. Since their holding cost is substantial, especially if they are physically large and hard to store, the orphans become a serious managerial problem. The dilemma management faces with an orphan is: should the orphan be modified (to the specifications of a new order) to dispose of it now, perhaps even at a loss, or should it be held another period (thereby incurring the substantial holding cost) for a possibly better matching order with a more tolerable modification cost?     

Supplier Encroachment and Investment Spillovers

It is conventional wisdom that a manufacturer's encroachment into retail space will likely hurt an existing retailer. In contrast to this conventional belief, current research indicates that a retailer may welcome a manufacturer's encroachment despite the new competition in the final market. The encroachment may help the manufacturer have some “skin in the game” at the retail level, which will cause the manufacturer to make a selfish cost‐reducing investment that spills over to the retailer as a lower wholesale price. Such a spillover effect enhances the retailer's profit as long as the encroachment does not result in extreme retail competition by a certain degree of product differentiation, and ultimately generates Pareto gains in the supply chain. The spillover effect is so robust that the retailer's benefit from the encroachment remains even after considering potential mitigating factors such as selling costs, a nonlinear form of cost reduction, decentralized encroachment, additional retail competition, price competition, and a negotiation between the manufacturer and the retailer.     

Unsold Versus Unbought Commitment: Minimum Total Commitment Contracts with Nonzero Setup Costs

We study a minimum total commitment (MTC) contract embedded in a finite‐horizon periodic‐review inventory system. Under this contract, the buyer commits to purchase a minimum quantity of a single product from the supplier over the entire planning horizon. We consider nonstationary demand and per‐unit cost, discount factor, and nonzero setup cost. Because the formulations used in existing literature are unable to handle our setting, we develop a new formulation based on a state transformation technique using unsold commitment instead of unbought commitment as state variable. We first revisit the zero setup cost case and show that the optimal ordering policy is an unsold‐commitment‐dependent base‐stock policy. We also provide a simpler proof of the optimality of the dual base‐stock policy. We then study the nonzero setup cost case and prove a new result, that the optimal solution is an unsold‐commitment‐dependent (s, S) policy. We further propose two heuristic policies, which numerical tests show to perform very well. We also discuss two extensions to show the generality of our method's effectiveness. Finally, we use our results to examine the effect of different contract terms such as duration, lead time, and commitment on buyer's cost. We also compare total supply chain profits under periodic commitment, MTC, and no commitment.     

Supply Chain Scheduling: Distribution Systems

We study conflict and cooperation issues arising in a supply chain where a manufacturer makes products which are shipped to customers by a distributor. The manufacturer and the distributor each has an ideal schedule, determined by cost and capacity considerations. However, these two schedules are in general not well coordinated, which leads to poor overall performance. In this context, we study two practical problems. In both problems, the manufacturer focuses on minimizing unproductive time. The distributor minimizes customer cost measures in the first problem and minimizes inventory holding cost in the second problem. We first evaluate each party's conflict, which is the relative increase in cost that results from using the other party's optimal schedule. Since this conflict is often significant, we consider several practical scenarios about the level of cooperation between the manufacturer and the distributor. These scenarios define various scheduling problems for the manufacturer, the distributor, and the overall system. For each of these scheduling problems, we provide an algorithm. We demonstrate that the cost saving provided by cooperation between the decision makers is usually significant. Finally, we discuss the implications of our work for how manufacturers and distributors negotiate, coordinate, and implement their supply chain schedules in practice.     

Supply Chain Sourcing Under Asymmetric Information

We study a supply chain with two suppliers competing over a contract to supply components to a manufacturer. One of the suppliers is a big company for whom the manufacturer's business constitutes a small part of his business. The other supplier is a small company for whom the manufacturer's business constitutes a large portion of his business. We analyze the problem from the perspective of the big supplier and address the following questions: What is the optimal contracting strategy that the big supplier should follow? How does the information about the small supplier's production cost affect the profits and contracting decision? How does the existence of the small supplier affect profits? By studying various information scenarios regarding the small supplier's and the manufacturer's production cost, we show, for example, that the big supplier benefits when the small supplier keeps its production cost private. We quantify the value of information for the big supplier and the manufacturer. We also quantify the cost (value) of the alternative‐sourcing option for the big supplier (the manufacturer). We determine when an alternative‐sourcing option has more impact on profits than information. We conclude with extensions and numerical examples to shed light on how system parameters affect this supply chain.     

THE EMPIRICAL DETERMINANTS OF INVENTORY LEVELS IN HIGH-VOLUME MANUFACTURING

This study uses survey data on several hundred automotive suppliers in North America to evaluate the determinants of inventory levels in high-volume discrete parts manufacturing. We assess the magnitude of raw materials, work-in-process, and finished goods inventories held at automotive supply plants. Inventories are shown to be jointly determined by technological and managerial factors in a manner roughly consistent with classical inventory theory. Several categories of managerial practices are found to be important. Low inventories are linked to employee problem solving and frequent communication with customers. More unexpectedly, we find the absence of inventory differences between U.S.-owned and Japanese-owned plants in North America. This contrasts with substantial differences in inventory holding between US plants and those in Japan.     

WIP inventories in the simultaneous determination of optimal production and purchase lot sizes

This paper studies an integrated production and purchasing lot sizing model with work-in-process WIP inventory. In this model, the single product is made in a multiprocess manufacturing system. The raw materials are procured from outside sources and are converted gradually into the product. A solution procedure is developed to simultaneously find the optimal lot sizes for the product and its raw materials and the corresponding total relevant cost. It is shown that if the cost of WIP inventory is considered in the production lot size computation, the optimal lot sizes of the product as well as those of the raw materials could be altered significantly.     

Just-in-time in ATO vehicle manufacturing: The Minivan-Piaggio V.E. case study

The system adopted by Piaggio V.E. to run the production of 'Minivan' aims at conciliating the manufacturing philosophy 'just-in-time' JIT with the creation of a wide range of end-product codes. Some general assumptions for a JIT production, with small lot sizes, are described together with their implementation in the operationorganizing system adopted by Piaggio V.E. for the 'Minivan' assembly line. The strategy pursued by Piaggio V.E. for the Minivan focuses on the quality of the product and the level of service in the form of fast order cycle and a high number of options offered on catalogue. According to the logic of an ATO production system, the customer orders a customized product and the manufacturer does not keep any finished inventory, but aims at effective management of the information flows.     

Value of and Interaction between Production Postponement and Information Sharing Strategies for Supply Chain Firms

We analyze the value of and interaction between production postponement and information sharing, which are two distinct strategies to reduce manufacturers’ uncertainty about demand. In both single‐level and two‐level supply chains, from the manufacturer's perspective, while information sharing is always valuable, production postponement can sometimes be detrimental. Furthermore, the value of production postponement is not merely driven by savings in inventory holding cost as postponement enables the manufacturer to avoid both excess and shortfall in production. We find that production postponement and information sharing strategies may substitute, complement, or conflict with each other, depending on the extent of the increase in the unit production cost when production is postponed. In a two‐level supply chain, from the retailer's perspective, information sharing and production postponement can be beneficial or detrimental. When information sharing is beneficial to the retailer, the retailer always shares her demand information with the manufacturer voluntarily. In addition, this voluntary information sharing is truthful because inflated or deflated demand information hurts the retailer through a higher wholesale price or a stock‐out. However, the retailer never shares her demand information voluntarily if the manufacturer has already adopted production postponement because production postponement and information sharing strategies always conflict with each other. Even when the retailer does not benefit from information sharing, we show that the manufacturer can always design an incentive mechanism to induce the retailer to share the demand information, irrespective of whether the manufacturer has already implemented production postponement or not. The above findings underscore the need for a careful assessment of demand uncertainty‐reduction strategies before the supply chain players embark upon them.