Experimental Results Indicating Lattice‐Dependent Policies May Be Optimal for General Assemble‐To‐Order Systems

We consider an assemble‐to‐order (ATO) system with multiple products, multiple components which may be demanded in different quantities by different products, possible batch ordering of components, random lead times, and lost sales. We model the system as an infinite‐horizon Markov decision process under the average cost criterion. A control policy specifies when a batch of components should be produced, and whether an arriving demand for each product should be satisfied. Previous work has shown that a lattice‐dependent base‐stock and lattice‐dependent rationing (LBLR) policy is an optimal stationary policy for a special case of the ATO model presented here (the generalized M‐system). In this study, we conduct numerical experiments to evaluate the use of an LBLR policy for our general ATO model as a heuristic, comparing it to two other heuristics from the literature: a state‐dependent base‐stock and state‐dependent rationing (SBSR) policy, and a fixed base‐stock and fixed rationing (FBFR) policy. Remarkably, LBLR yields the globally optimal cost in each of more than 22,500 instances of the general problem, outperforming SBSR and FBFR with respect to both objective value (by up to 2.6% and 4.8%, respectively) and computation time (by up to three orders and one order of magnitude, respectively) in 350 of these instances (those on which we compare the heuristics). LBLR and SBSR perform significantly better than FBFR when replenishment batch sizes imperfectly match the component requirements of the most valuable or most highly demanded product. In addition, LBLR substantially outperforms SBSR if it is crucial to hold a significant amount of inventory that must be rationed.     

Product Positioning in a Two‐Dimensional Market Space

This paper examines the optimal product portfolio positioning for a monopolist firm in a market where consumers exhibit vertical differentiation for product performance and horizontal differentiation for product feature. Our key results are as follows: (i) Variable costs drive vertical differentiation. In the presence of significant volume‐dependent manufacturing costs, the optimal portfolio contains a mix of vertically and horizontally differentiated products and an increase in the variable cost makes adding vertically differentiated products relatively more profitable; if fixed volume‐independent design costs dominate, the portfolio exhibits solely horizontal differentiation. (ii) Horizontal differentiation is the main profit lever, and vertical differentiation brings only a marginal benefit; this is true even when most of the consumers exhibit low willingness to pay for performance, which is often used as an excuse to offer low‐end products. (iii) There are more low‐quality products than high‐quality ones, and market coverage increases when the willingness to pay for performance increases. In summary, the model shows how portfolio composition decisions depend on the product cost structure and the consumer preferences.     

When to Offer Lower Quality or Remanufactured Versions of a Product

We investigate the profitability of adding a lower quality or remanufactured product to the product portfolio of a monopoly firm, both in single‐period and steady‐state settings. Consumer behavior is characterized by a deterministic utility function for the original product and a nonlinear relative utility function for the lower quality product. We find a threshold for the cost of the low‐quality product below which it is optimal to add it to the firm's portfolio, and show that while a cost advantage is necessary to make the lower quality offering profitable under linear or convex relative utility functions, market segmentation alone can justify the addition of the lower quality product under concave relative utility functions. In particular, we characterize (i) the new product cost under which it is optimal to offer a lower quality version of the product even if it is as costly to produce as the original product; and (ii) the weighted average of new and remanufactured product costs in the steady state under which it becomes cost effective to offer new products under the remanufactured label. Finally, we also identify the maximum possible profits from customer segmentation and the form of the relative utility function that achieves them. We discuss the implications for the common marketing practices of branding and generics.     

PRODUCT MARKET REGULATION,FIRM SELECTION,AND UNEMPLOYMENT

This paper analyzes the effect of product market regulation (PMR) on unemployment in a search model with heterogeneous multiple‐worker firms. In our setup, PMR modifies the distribution of firm productivities, thereby affecting the equilibrium rate of unemployment. We distinguish between PMR related to entry costs and PMR that generates recurrent fixed costs. We find that: (i) higher entry costs raise the rate of unemployment mainly through our novel selection effect, (ii) higher fixed costs decrease unemployment through the selection effect and increase it through the competition effect analyzed in Blanchard and Giavazzi (2003, Quarterly Journal of Economics, 118, 879–907). Firm heterogeneity magnifies the impact of both types of regulatory costs. We propose econometric evidence consistent with the unemployment effects of sunk versus recurring costs.     

Portfolio rebalancing with an investment horizon and transaction costs

In this paper we consider the problem of rebalancing an existing financial portfolio, where transaction costs have to be paid if we change the amount held of any asset. These transaction costs can be fixed (so paid irrespective of the amount traded provided a trade occurs) and/or variable (related to the amount traded). We indicate the importance of the investment horizon when rebalancing such a portfolio and illustrate the nature of the efficient frontier that results when we have transaction costs. We model the problem as a mixed-integer quadratic programme with an explicit constraint on the amount that can be paid in transaction cost. Our model incorporates the interplay between optimal portfolio allocation, transaction costs and investment horizon. We indicate how to extend our model to include cardinality constraints and present a number of enhancements to the model to improve computational performance. Results are presented for the solution of publicly available test problems involving up to 1317 assets.     

Myopic Analysis for Multi‐Echelon Inventory Systems with Batch Ordering and Nonstationary/Time‐Correlated Demands

We provide an exact myopic analysis for an N‐stage serial inventory system with batch ordering, linear ordering costs, and nonstationary demands under a finite planning horizon. We characterize the optimality conditions of the myopic nested batching newsvendor (NBN) policy and the myopic independent batching newsvendor (IBN) policy, which is a single‐stage approximation. We show that echelon reorder levels under the NBN policy are upper bounds of the counterparts under both the optimal policy and the IBN policy. In particular, we find that the IBN policy has bounded deviations from the optimal policy. We further extend our results to systems with martingale model of forecast evolution (MMFE) and advance demand information. Moreover, we provide a recursive computing procedure and optimality conditions for both heuristics which dramatically reduces computational complexity. We also find that the NBN problem under the MMFE faced by one stage has one more dimension for the forecast demand than the one faced by its downstream stage and that the NBN policy is optimal for systems with advance demand information and stationary problem data. Numerical studies demonstrate that the IBN policy outperforms on average the NBN policy over all tested instances when their optimality conditions are violated.     

供应链中基于信息更新的订货时间及价格联合决策研究

文章考虑在信息可更新的情况下,由一个制造商和一个零售商组成的供应链中订货时间及价格的联合决策问题.在模型中,制造商为零售商提供多次订货时间选择及相应的订货价格,而零售商可以在销售季节开始前自由选择订货时间并享受相应的价格.文章以不同订货时间对信息更新程度的影响为着眼点,将订货时间作为内生决策变量,突破了已有文献中仅限于两次订货时间选择的局限,分别从集中决策和分散决策两个角度建立供应链节点企业的利润模型,并在分散决策情况下引入收益共享契约,寻找帕累托改进.最后通过数值试验证明了该模型的有效性.     

Sourcing Decisions with Competitive Suppliers and Imperfect Information

Manufacturers often must choose between outsourcing and producing internally. This choice is complex and influenced by a variety of factors, including the costs and capabilities of the potential suppliers. In addition, if the manufacturer outsources, he must design the sourcing process. We study the manufacturer's outsourcing decision, with a focus on the impact of the sourcing process on that decision. We consider a setting in which the manufacturer has imperfect information regarding the suppliers' costs and capabilities, and we assume that the manufacturer uses a two‐stage sourcing process. The first stage is the qualification stage, in which the manufacturer seeks to reduce the uncertainty regarding the suppliers' capabilities. The second stage is the supplier selection stage, in which the manufacturer selects among the qualified suppliers on the basis of price. We first characterize the optimal design of the two‐stage process, and then consider the outsourcing decision. We demonstrate several trade‐offs. Vertical integration enables the manufacturer to reduce uncertainty and extract all of the profits of production. However, outsourcing enables the manufacturer to take advantage of the (potentially) lower costs and higher capabilities of the suppliers, particularly if competition between suppliers can be encouraged. We find that the manufacturer is more likely to vertically integrate when the warranty cost and the cost of exerting effort during qualification are large, and when there is significant uncertainty regarding the suppliers' capabilities. The manufacturer is more likely to outsource when the suppliers' costs (capabilities) are low (high), and when the number of suppliers is large.     

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.     

Policy Incentives for Dangerous (But Necessary) Operations

In industries where firms perform dangerous (but necessary) operations, liability costs—due to potential harm to third parties—can be significant. Firms may therefore find it optimal to exit the market, and this may lead to an inefficiently low number of incumbents. A social planner can discourage exit by offering appropriately designed subsidies. Ex ante subsidies defray the costs associated with making operations safer (e.g., funds to subsidize the purchase of safety equipment). Ex post subsidies mitigate the financial damages caused by an accident (e.g., funds to defray the cost of cleaning up a toxic spill). We consider a model where (i) firms have private information about their ability to improve reliability and (ii) reliability investments are unobservable. We demonstrate that when the social value of reliability outweighs the benefit of increased competition, it is optimal to offer ex ante subsidies alone (i.e., to subsidize the cost of making operations safer). Conversely, when the benefits of competition outweigh the benefits of reliability, a combination of ex ante and ex post subsidies is optimal (i.e., not only to subsidize safer operations, but also to share the costs of a potential accident).     

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.     

Assortment Planning for Vertically Differentiated Products

We consider the problem of a retailer managing a category of vertically differentiated products. The retailer has to pay a fixed cost for each product included in the assortment and a variable cost per product sold. Quality levels, fixed, and variable costs are exogenously determined. Customers differ in their valuation of quality and choose the product (if any) that maximizes their utility. First, we consider a setting in which the selling prices are also fixed. We find that the optimal set of products to offer depends on the distribution of customer valuations and might include dominated products, that is, products which are less attractive than at least one other product, on every possible dimension. We develop an efficient algorithm to identify an optimal assortment. Second, we consider a setting in which the retailer also determines the selling prices. We show that in this case the optimal assortment does not include any dominated product and does not vary with the distribution of customer valuations when there is no fixed cost. We develop several efficient algorithms to identify an optimal assortment and optimally price the products. We also test the applicability of our methods with realistic data for two product categories.     

The Effect of Competition on the Efficient–Responsive Choice

In determining their operations strategy, a firm chooses whether to be responsive or efficient. For firms competing in a market with uncertain demand and varying intensity of substitutability for the competitor's product, we characterize the responsive or efficient choice in equilibrium. To focus first on the competitive implications, we study a model where a firm can choose to be responsive at no additional fixed or marginal cost. We find that competing firms will choose the same configuration (responsive or efficient), and responsiveness tends to be favorable when demand uncertainty is high or when product competition is not too strong. Intense competition can drive firms to choose to be efficient rather than responsive even when there is no additional cost of being responsive. In such a case, both firms would be better off by choosing to be responsive but cannot credibly commit. We extend the basic model to study the impact of endogenized production timing, multiple productions and product holdback (or, equivalently, postponed production). For all these settings, we find structurally similar results; firms choose the same configuration, and the firms may miss Pareto‐improvements. Furthermore, through extensions to the basic model, we find that greater operational flexibility can make responsiveness look less attractive in the presence of product competition. In contrast to our basic model and other extensions, we find it is possible for one firm to be responsive while the other is efficient when there is either a fixed cost or variable cost premium associated with responsive delivery.     

Optimal Procurement Design of an Assembly Supply Chain with Information Asymmetry

We study a decentralized assembly supply chain in which an assembler (she) assembles a set of n components, each produced by a different supplier (he), into a final product to satisfy an uncertain market demand. Each supplier holds private cost information to himself, for which the assembler only has a subjective estimate. Furthermore, the assembler believes that the suppliers' costs follow a joint discrete probability distribution. The assembler aims to design an optimal menu of contracts to maximize her own expected profit. The assembler's problem is a complex multi‐dimensional constrained optimization problem. We prove that there exists a unique optimal menu of contracts for the assembler, and we further develop an efficient algorithm with a complexity of O(n) to compute the optimal contract. In addition, we conduct a comprehensive sensitivity analysis to analyze how environmental parameters affect individual firm's performance and the value of information to the assembler, to each supplier, and to the supply chain. Our results suggest that each supplier's private cost information becomes more valuable to the assembler and each supplier when the average market demand increases or when the final product unit revenue increases. Surprisingly, when a supplier's cost volatility increases and its mean remains the same, the value of information to the assembler or to each supplier does not necessarily increase. Furthermore, we show that when the suppliers' cost distributions become more positively correlated, the suppliers are always worse off, but the assembler is better off. However, the value of information for the assembler might increase or decrease.     

Real option games with R&D and learning spillovers

We demonstrate to decision makers how to optimally make costly strategic pre-investment R&D decisions in the presence of spillover effects in an option pricing framework with analytic tractability. Decisions are modeled as impulse-type controls with random outcome. Two firms face two decisions that are solved interdependently in a two-stage game. The first-stage decision is: What is the optimal level of coordination (optimal policy/technology choice)? The second-stage decision is: What is the optimal effort for a given level of the spillover effects and the cost of information acquisition? The framework is extended to a two-period closed-loop stochastic game with (path-dependency inducing) switching costs that make strategy revisions harder. When conditions of learning-by-doing exist, we find that strategy shifts are easier to observe in market environments of high growth and high volatility.     

Structuring Work Distribution for Global Product Development Organizations

This study describes (through an application) a novel approach toward organizing work distribution across globally distributed design and development centers of a product development (PD) organization. While there exist several studies (and modeling applications) for work distribution and allocation for manufacturing and supply chain networks, those related to product development organizations are limited to qualitative suggestions such as offshoring of modular tasks. However, most PD efforts are characterized by significant complexity in information sharing and information dependency among PD tasks (represented by coupling in the system architecture of the firm), thus preventing the identification of modular tasks. Also, redesigning the architecture to introduce modularity has associated risks of costs and product integrity. We demonstrate a methodology to organize work distribution globally in an industrial setting, utilizing the design structure matrix to quantify the system architecture of the firm. Our optimization results show significant cost savings through a restructured PD organization. On analysis of the results, we make two significant observations: (a) while offshoring based on modularity is generally appropriate, it is not the whole answer, as there exists a trade‐off between the efficiency of performing specific PD tasks at the offshore location and the modularity of the task; and (b) firms should successively increase work allocation to the offshore location, benefiting from capability improvements through learning effects.     

The supplier selection problem with quantity discounts and truckload shipping

To minimize procurement expenditures both purchasing and transportation costs need to be considered. We study a procurement setting in which a company needs to purchase a number of products from a set of suppliers to satisfy customer demand. The suppliers offer total quantity discounts and transportation costs are based on truckload shipping rates. The goal is to select a set of suppliers so as to satisfy product demand at minimal total costs. The resulting optimization problem is strongly NP-hard. We develop integer programming based heuristics to solve the problem. Extensive computational experiments demonstrate the efficacy of the proposed heuristics and provide insight into the impact of instance characteristics on effective procurement strategies.     

OEM product design in a price competition with remanufactured product

An original equipment manufacturer (OEM) produces new products and often faces a dilemma when determining the level of interchangeability in its product design. The interchangeability is considered as a degree to which the product can be disassembled without force, and thus an increasing degree of interchangeability would decrease the OEM's production cost, but it would also lower a remanufacturer's cost in cannibalizing used items. Decreasing the level of interchangeability to deter the remanufacturer, on the other hand, would simultaneously increase the production costs of the OEM. We thus formulate a two-period supply chain model consisting of two chain members, an OEM and a remanufacturer, to investigate the product design decision of the OEM and both chain members' competitive pricing strategies. We then characterize the equilibrium decisions and profits with regard to costs and consumers' preference for the remanufactured product. We also evaluate a strategic game in which the OEM chooses the degree of interchangeability, and the remanufacturer determines its collection strategy. We find that the product-design strategy is effective for the OEM in competing with the remanufacturer, but it is not necessarily harmful to the remanufacturer.     

BAYESIAN MODELS FOR NEW PRODUCT PRICING

This paper develops an information decision system for new product pricing based on Bayesian updating of prior estimates of demand distribution parameter values and on optimization by dynamic programming. The model considers the interaction of production and pricing decisions and emphasizes the simultaneous making of both decisions. After presentation of the basic model, approximate techniques are introduced which obtain most of the benefit of the approach while requiring only a fraction of the computer cost and input data. Numerical examples using growing demand and price sensitivity are given to demonstrate the high computer cost of the first model and the relative performance (on a profit basis) of the approximate techniques.     

Overcoming Learning Aversion in Evaluating and Managing Uncertain Risks

Decision biases can distort cost‐benefit evaluations of uncertain risks, leading to risk management policy decisions with predictably high retrospective regret. We argue that well‐documented decision biases encourage learning aversion, or predictably suboptimal learning and premature decision making in the face of high uncertainty about the costs, risks, and benefits of proposed changes. Biases such as narrow framing, overconfidence, confirmation bias, optimism bias, ambiguity aversion, and hyperbolic discounting of the immediate costs and delayed benefits of learning, contribute to deficient individual and group learning, avoidance of information seeking, underestimation of the value of further information, and hence needlessly inaccurate risk‐cost‐benefit estimates and suboptimal risk management decisions. In practice, such biases can create predictable regret in selection of potential risk‐reducing regulations. Low‐regret learning strategies based on computational reinforcement learning models can potentially overcome some of these suboptimal decision processes by replacing aversion to uncertain probabilities with actions calculated to balance exploration (deliberate experimentation and uncertainty reduction) and exploitation (taking actions to maximize the sum of expected immediate reward, expected discounted future reward, and value of information). We discuss the proposed framework for understanding and overcoming learning aversion and for implementing low‐regret learning strategies using regulation of air pollutants with uncertain health effects as an example.