Some Analytical Results for a Two-Product Newsboy Problem

A recent Decision Sciences paper considered maximizing the probability of achieving a profit target in a two-product newsboy problem. Numerical solutions to this problem revealed some intriguing properties, but the authors were unable to analytically explain many of their results. This paper presents an analytical solution procedure to this problem for the case of uniformly distributed demands. The analytical structure reveals more intriguing properties and these properties are proven and explained.     

Optimal ordering and pricing decisions for a target oriented newsvendor

This paper is the first to study pricing and target oriented decision making together in the newsvendor model. Specifically, this paper studies a newsvendor who decides on order quantity and selling price to maximize the probability of achieving both profit and revenue targets simultaneously. First, it is shown that the probability of a newsvendor achieving both targets depends critically on the relative magnitudes of the profit margin and the ratio between the profit target and the revenue target. Second, the closed-form expressions of the optimal order quantity, the optimal selling price, and the maximal profit and revenue probability are obtained. It is shown that if the product has greater price elasticity, the best strategy is always to price lower and order more.     

The benefit of horizontal decentralization in durable good procurement

A conventional wisdom in industry and academia is that firms suffer from decentralized procurement. In this paper, we demonstrate an important and counter-intuitive benefit of procurement decentralization in a common setting where a firm with multiple divisions procures a durable good from a supplier. We start with a two-period model and obtain analytic equilibrium results on the supplier's wholesale prices, and the firm's procurement quantities and profits under procurement centralization and decentralization. These results show that the firm's profit will benefit from decentralization if and only if the product is durable. We further show that the profit improvement always increases in durability and the number of divisions. To generalize the basic model with two periods, we design an iterative algorithm to compute the equilibrium results for any number of periods. Our extensive numerical simulations show the robustness of our analytic results and managerial insights.     

Assortment optimisation problem: A distribution-free approach

Assortment optimisation is a critical decision that is regularly made by retailers. The decision involves a trade-off between offering a larger assortment of products but smaller inventories of each product and offering a smaller number of varieties with more inventory of each product. We propose a robust, distribution-free formulation of the assortment optimisation problem such that the assortment and inventory levels can be jointly optimised without making specific assumptions on the demand distributions of each product. We take a max-min approach to the problem that provides a guaranteed lower bound to the expected profit when only the mean and variance of the demand distribution are known. We propose and test three heuristic algorithms that provide solutions in O(nlog (n)) time and identify two cases where one of the heuristics is guaranteed to return optimal policies. Through numerical studies, we demonstrate that one of the heuristics performs extremely well, with an average optimality gap of 0.07% when simulated under varying conditions. We perform a sensitivity analysis of product and store demand attributes on the performance of the heuristic. Finally, we extend the problem by including maximum cardinality constraints on the assortment size and perform numerical studies to test the performance of the heuristics.     

A Competitive Model of Customization with Lead‐Time Effects

In this article, we study the competitive interactions between a firm producing standard products and a firm producing custom products. Consumers with heterogeneous preferences choose between n standard products, which may not meet their preferences exactly but are available immediately, and a custom product, available only after a certain lead time l. Standard products incur a variety cost that increases with n and custom products incur a lead time cost that is decreasing in the lead time l. We consider a two‐stage game wherein at stage 1, the standard product firm chooses the variety and the custom firm chooses the lead time and then both firms set prices simultaneously. We characterize the subgame‐perfect Nash equilibrium of the game. We find that both firms can coexist in equilibrium, either sharing the market as local monopolists or in a price‐competitive mode. The standard product firm may offer significant or minimal variety depending on the equilibrium outcome. We provide several interesting insights on the variety, lead time, and prices of the products offered and on the impact of problem parameters on the equilibrium outcomes. For instance, we show that the profit margin and price of the custom product are likely to be higher than that of standard products in equilibrium under certain conditions. Also, custom firms are more likely to survive and succeed in product markets with larger potential market sizes. Another interesting insight is that increased consumer sensitivity to product fit may result in lower lead time for the custom product.     

Fusion Product Planning: A Market Offering Perspective*

Devices that integrate multiple functions together are popular in consumer electronic markets. We describe these multifunction devices as fusion products as they fuse together products that traditionally stand alone in the marketplace. In this article, we investigate the manufacturer's fusion product planning decision, adopting a market offering perspective that allows us to address the design and product portfolio decisions simultaneously. The general approach adopted is to develop and analyze a profit‐maximizing model for a single firm that integrates product substitution effects in identifying an optimal market offering. In the general model, we demonstrate that the product design and portfolio decisions are analytically difficult to characterize because the number of possible portfolios can be extremely large. The managerial insight from a stylized all‐in‐one model and numerical analysis is that the manufacturer should, in most cases, select only a subset of fusion and single‐function products to satisfy the market's multidimension needs. This may explain why the function compositions available in certain product markets are limited. In particular, one of the key factors driving the product portfolio decision is the margin associated with the fusion products. If a single all‐in‐one fusion product has relatively high margins, then this product likely dominates the product portfolio. Also, the congruency of the constituent single‐function products is an important factor. When substitution effects are relatively high (i.e., the product set is more congruent), a portfolio containing a smaller number of products is more likely to be optimal.     

Optimal Policies for Selling New and Remanufactured Products

Because of environmental and economic reasons, an increasing number of original equipment manufacturers (OEMs) nowadays sell both new and remanufactured products. When both products are available, customers will buy the one that gives them a higher (and non‐negative) utility. Thus, if the firm does not price the products properly, then product cannibalization may arise and its revenue may be adversely impacted. In this paper, we study the pricing problem of a firm that sells both new and remanufactured products over a finite planning horizon. Customer demand processes for both new and remanufactured products are random and price‐sensitive, and product returns (also called cores) are random and remanufactured upon receipt. We characterize the optimal pricing and manufacturing policies that maximize the expected total discounted profit. If new products are made‐to‐order (MTO), we show that when the inventory level of remanufactured product increases, the optimal price of remanufactured product decreases while the price difference between new and remanufactured products increases; however, the optimal selling price of new product may increase or decrease. If new products are made to stock (MTS), then the optimal manufacturing policy is of a base‐stock policy with the base‐stock level decreasing in the remanufactured product inventory level. To understand the potential benefit in implementing an MTO system, we study the difference between the value functions of the MTO and MTS systems, and develop lower and upper bounds for it. Finally, we study several extensions of the base model and show that most of our results extend to those more general settings.     

Managing Supply Risk for Vertically Differentiated Co‐Products

The manufacturing complexity of many high‐tech products results in a substantial variation in the quality of the units produced. After manufacturing, the units are classified into vertically differentiated products. These products are typically obtained in uncontrollable fractions, leading to mismatches between their demand and supply. We focus on product stockouts due to the supply–demand mismatches. Existing literature suggests that when faced with product stockouts, firms should satisfy all unmet demand of a low‐end product by downgrading excess units of a high‐end product (downward substitution). However, this policy may be suboptimal if it is likely that low‐end customers will substitute with a higher quality product and pay the higher price (upward substitution). In this study, we investigate whether and how much downward substitution firms should perform. We also investigate whether and how much low‐end inventory firms should withhold to strategically divert some low‐end demand to the high‐end product. We first establish the existence of regions of co‐production technology and willingness of customers to substitute upward where firms adopt different substitution/withholding strategies. Then, we develop a managerial framework to determine the optimal selling strategy during the life cycle of technology products as profit margins shrink, manufacturing technology improves, and more capacity becomes available. Consistent trends exist for exogenous and endogenous prices.     

Revenue Management in Order‐Driven Production Systems

This article investigates the effectiveness of a tactical demand‐capacity management policy to guide operational decisions in order‐driven production systems. The policy is implemented via a heuristic that attempts to maximize revenue by selectively accepting or rejecting customer orders for multiple product classes when demand exceeds capacity constantly over the short term. The performance of the heuristic is evaluated in terms of its ability to generate a higher profit compared to a first‐come‐first‐served (FCFS) policy. The policies are compared over a wide range of conditions characterized by variations in both internal (firm) and external (market) factors. The heuristic, when used with a Whole Lot order‐processing approach, produces higher profit compared to FCFS when profit margins of products are substantially different from each other and demand exceeds capacity by a large amount. In other cases it is better to use the heuristic in conjunction with the Split Lot order‐processing approach.     

A Profit‐Maximizing Approach to Disposition Decisions for Product Returns*

Motivated by the asset recovery process at IBM, we analyze the optimal disposition decision for product returns in electronic products industries. Returns may be either remanufactured for reselling or dismantled for spare parts. Reselling a remanufactured unit typically yields higher unit margins. However, demand is uncertain. A common policy in many firms is to rank disposition alternatives by unit margins. We propose a profit‐maximization approach that considers demand uncertainty. We develop single period and multiperiod stochastic optimization models for the disposition problem. Analyzing these models, we show that the optimal allocation balances expected marginal profits across the disposition alternatives. A detailed numerical study reveals that our approach to the disposition problem outperforms the current practice of focusing exclusively on high‐margin options, and we identify conditions under which this improvement is the highest. In addition, we show that a simple myopic heuristic in the multiperiod problem performs well.     

Product Portfolio Strategies: The Case of Multifunction Products

Motivated by the proliferation of multifunction products, we investigate product portfolio decisions of a single firm by analyzing the impact of three major factors. First, because multifunction products provide complete or partial functionalities of single‐function products, we incorporate substitution or cannibalization effects between the potential products. Second, we explicitly model the variable costs of manufacturing the single‐function and multifunction products. Third, we examine the firm's pricing decisions because of their impact on the degree of cannibalization between the multifunction product and one or more single‐function products. Using an economic model, we first characterize the firm's optimal product portfolio (through a quantity‐based decision), which in turn determines the market equilibrium prices for each product in its portfolio. Some of the unique insights stemming from our analysis are: (a) the optimal product portfolio choice is driven primarily by maximum profit margins for the single‐function products weighted by the demand substitution effects; and (b) from a product design perspective, the complete functionality of the base single‐function product is always included in the optimal product offering, but this is not necessarily the case with the complete functionality of the nonbase single‐function product.     

A Model for Partial Product Complementarity and Strategic Production Decisions under Demand Uncertainty

This paper considers a general industrial setting where multiple manufacturers each produce a different product and sell it to the markets. These products are partially complementary in the sense that there is a common demand stream that requests all these products as complementary sets and there are streams of individual demands each requesting only one of the products. All demands are uncertain and may follow any general, joint distributions. Facing demand uncertainties, the manufacturers each choose a production quantity for its product with an objective to maximize its own expected profit. We formulate the problem as a non‐cooperative game to study the strategic interactions of such firms and their implications to supply chain performance. We show that such a game may have numerous equilibria. Among all the possible equilibria, however, we prove that there always exists a unique one that maximizes each and every manufacturer's profit, and we derive an explicit solution for this Pareto‐optimal equilibrium point. We further study the optimal solution for a centralized system and compare it with the decentralized solution. Managerial insights are drawn as to how system parameters and control mechanisms affect firms' decisions and performance.     

基于好评返现和差评偏好的体验型产品两阶段定价决策研究

假定产品存在发布试销期与正式销售期,在销售商不采取好评返现与采取好评返现两种情形下分别建立考虑消费者差评偏好的两阶段定价决策模型,用KT方法得到相应的最优决策和利润,给出了销售商实施好评返现的条件。基于导函数分析方法与数值仿真技术,分析了好评返现与差评偏好对产品定价、销售商利润和消费者效用的影响,证实了好评返现下消费者重视差评信息的合理性,并针对消费者、平台和销售商提出了对策。研究表明:只有产品质量中等的销售商才会采取好评返现策略,其利润随产品质量的提升而先递增后递减;好评返现提高了销售商第二阶段的市场份额和售价,导致消费者效用损失;消费者越重视差评信息,实施好评返现的高(低)质量产品销售商越多(少),且销售商利润将下降;好评返现扭曲了评价信息的真实性,降低了消费者对在线评价系统的信任度。     

Bertrand寡占市场企业交叉持股时定价策略和最优持股的研究

本文首先研究了公司间交叉持股的利益分配问题,导出了n个公司间交叉持股的利润分配公式。以此为基础,导出了Bertrand寡占市场公司间交叉持股时价格反应函数和均衡价格的一般表达式。通过构建一个两阶段动态博弈,着重研究了Bertrand双寡头市场两厂商交叉持股时的均衡策略问题,给出了厂商间均衡定价与最优持股,分析了均衡策略对厂商经济行为及市场绩效的影响。研究结果表明,可替代品市场的两厂商间交叉持股具有反竞争、促合作的效应。较之非交叉持股,均衡交叉持股提高了均衡价格水平,降低了两厂商各自的产量水平,使各自在较低产量水平下获得较高的利润,从而实现了两厂商间双赢的局面。然而,交叉持股将导致消费者剩余减少,社会经济福利降低。     

考虑企业竞争的产品线延伸策略研究

越来越多的企业延伸其产品线以满足消费者不同需求,本文采用博弈论探讨了企业产品线延伸策略的有效性。在竞争情形下,两个企业均有机会进行产品线延伸抢夺市场份额。通过消费者效用理论构建了两个企业的需求函数,并得到了均衡解及其利润。研究发现：Nash博弈下,当延伸成本较高时,竞争性企业会放弃产品线延伸;当延伸成本适中时,进行产品线延伸的企业将获得更多利润,而不进行产品线延伸的竞争对手将遭受损失;当延伸成本较低时,虽然企业最优的选择是延伸其产品线,但是两个企业会陷入“囚徒困境”——产品线延伸非但没有获得更多利润反而使利润减少了;另外,当两企业进行Stackelberg博弈时,本文核心结论依然成立,但两企业陷入囚徒困境的可能性增大。     

Designing Supply Contracts Considering Profit Targets and Risk

Managers at all stages of a supply chain are concerned about meeting profit targets. We study contract design for a buyer–supplier supply chain, with each party maximizing expected profit subject to a chance constraint on meeting his respective profit target. We derive the optimal contract form (across all contract types) with randomized and deterministic payments. The best contract has the property that, if the chance constraints are binding, at most one party fails to satisfy his profit target for any given demand realization. This implies that “least risk sharing,”that is, minimizing the probability of outcomes for which both parties fail to achieve their profit targets, is optimal, contrary to the usual expectations of “risk sharing.” We show that an optimal contract can possess only two of the following three properties simultaneously: (i) supply chain coordination, (ii) truth‐telling, and (iii) non‐randomized payments. We discuss methods to mitigate the consequent implementation challenges. We also derive the optimal contract form when chance constraints are incorporated into several simpler and easier‐to‐implement contracts. From a numerical study, we find that an incremental returns contract (in which the marginal rebate rate depends on the return quantity) performs quite well across a relatively broad range of conditions.     

Food packaging 1974–1984

The author argues that it is clear that the manufacturers of most food products now have a bewildering array of alternative forms of packaging from which to choose. Due to pressure on profit margins, they will look for those systems that will be the cheapest having regard to many technical, commercial, legal and ecological factors. There will often be many different answers to any one packaging problem and all will be right to some extent! And not one is likely to satisfy every need!     

The Effect of Competition on Recovery Strategies

Manufacturers often face a choice of whether to recover the value in their end‐of‐life products through remanufacturing. In many cases, firms choose not to remanufacture, as they are (rightly) concerned that the remanufactured product will cannibalize sales of the higher‐margin new product. However, such a strategy may backfire for manufacturers operating in industries where their end‐of‐life products (cell phones, tires, computers, automotive parts, etc.) are attractive to third‐party remanufacturers, who may seriously cannibalize sales of the original manufacturer. In this paper, we develop models to support a manufacturer's recovery strategy in the face of a competitive threat on the remanufactured product market. We first analyze the competition between new and remanufactured products produced by a monopolist manufacturer and identify conditions under which the firm would choose not to remanufacture its products. We then characterize the potential profit loss due to external remanufacturing competition and analyze two entry‐deterrent strategies: remanufacturing and preemptive collection. We find that a firm may choose to remanufacture or preemptively collect its used products to deter entry, even when the firm would not have chosen to do so under a pure monopoly environment. Finally, we discuss conditions under which each strategy is more beneficial.     

An Auction Mechanism for Pricing and Capacity Allocation with Multiple Products

We consider a pricing and short‐term capacity allocation problem in the presence of buyers with orders for bundles of products. The supplier's objective is to maximize her net profit, computed as the difference between the revenue generated through sales of products and the production and inventory holding costs. The objective of each buyer is similarly profit maximization, where a buyer's profit is computed as the difference between the time‐dependent utility of the product bundle he plans to buy, expressed in monetary terms, and the price of the bundle. We assume that bundles' utilities are buyers' private information and address the problem of allocating the facility's output. We directly consider the products that constitute the supplier's output as market goods. We study the case where the supplier follows an anonymous and linear pricing strategy, with extensions that include quantity discounts and time‐dependent product and delivery prices. In this setting, the winner determination problem integrates the capacity allocation and scheduling decisions. We propose an iterative auction mechanism with non‐decreasing prices to solve this complex problem, and present a computational analysis to investigate the efficiency of the proposed method under supplier's different pricing strategies. Our analysis shows that the problem with private information can be effectively solved with the proposed auction mechanism. Furthermore, the results indicate that the auction mechanism achieves more than 80% of the system's profit, and the supplier receives a higher percentage of profit especially when the ratio of demand to available capacity is high.     

消费者低碳偏好下的供应链收益共享契约研究

在消费者对低碳产品存在偏好并且企业自愿减排的假定下,探讨了在由单个供应商与单个零售商构成的两级供应链中零售商确定最佳订货水平和供应商选择减少碳排放水平的决策问题。研究发现单位产品碳排放过大时,供应商不会选择减排;当单位排放较低时,选择减排战略会改善供应商和零售商的收益状况,可以实现供应链成员收益的帕累托改进;而当单位排放处于两者之间时,选择减排战略会使供应商的收益状况变差,使零售商的收益和供应链总体收益增加,虽然存在着改善供应链渠道收益状况的空间,但供应商没有减排动力,减排无法实施。针对这一问题,本文设计了收益共享契约来协调两者之间的关系,实现了帕累托改进。最后,利用Rubinstein讨价还价模型来分析分成比例在给定区间确定问题。