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.     

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。     

Single‐Period Two‐Product Assemble‐to‐Order Systems with a Common Component and Uncertain Demand Patterns

We consider a single‐period assemble‐to‐order system that produces two types of end products to satisfy two independent and stochastic customer orders. Each type of product is used to fulfill a particular customer order and these two products share a common component. Furthermore, one customer may confirm her order before the other one, and the manufacturer needs to make a commitment immediately upon the receipt of each customer order on how many products to be delivered. We propose a model for optimizing the inventory and production decisions under the above ATO environment. We also extend our model to the situation where the manufacturer can fulfill the unsatisfied low‐priority demand using the left‐over inventories after fulfilling the high‐priority demand, in case the low‐priority customer arrives first. Numerical experiments are conducted, which provide some interesting insights on the impact of uncertain demand pattern.     

A Single‐Period Assortment Optimization Model

This paper studies a single‐period assortment optimization problem with unequal cost parameters. The consumer choice process is characterized by a Multinomial Logit (MNL) model. When the store traffic is a continuous random variable, we explicitly derive the structure of the optimal assortment. Our approach is to use a comprehensive measure–profit rate to evaluate the profitability of each variant and then determine which product should be offered. We demonstrate that the optimal assortment contains the few items that have the highest profit rate. When the store traffic is discrete, the optimal solution is difficult to obtain. We propose a “profit rate” heuristic, which is inspired by the result for the case of continuous store traffic. In a special case with equal cost parameters and normal demand distribution, the profit rate heuristic is indeed optimal. Using randomly generated data, we test the effectiveness of the heuristic and find that the average percentage error is less than 0.1% and that the hit rate is above 90%. Our research provides managerial insights on assortment planning and accentuates the importance of measuring the profitability of each product when the demand is random and cannibalization among different products exists.     

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.     

A free gift card alternative to price discounts in the newsvendor problem

In this paper, we develop a newsvendor model in which the retailer gives “free” gift cards to consumers who purchase a regularly priced product at the end of the selling season instead of discounting the product. The model is developed for a market with patient consumers. We derive the sufficient optimality condition for the retailer's stocking level in the first period and the optimal gift card value in the second period. We also investigate the conditions under which giving gift cards results in higher expected profits than discounting the product. We find that five factors determine the effectiveness of gift cards. The first three factors are consumers' valuation per $1 of gift card, gift card redemption rates, and the average gross margin of the retailer. The last two factors are the degree to which consumers use gift cards to pay for products which they would have purchased from the retailer in the future with cash, and the additional spending above the gift card value consumers make when they redeem the card. The last two factors have a strong interaction. We also find that gift cards can be profitable when patient consumers consistently value each $1 by their redemption probability, even with 100% redemption. Numerical analysis shows that in the presence of patient consumers, increases in the redemption rate may lead to an increase in the expected profit. Similar counter-intuitive behavior of the expected profit occurs with changes in other problem parameters. The analysis also shows that gift cards' profit advantage over discounting increases with the variability of demand. The analysis also indicates that gift cards are most effective for low to medium priced products sold by high margin retailers.     

基于无缺陷退货的网上销售易逝品供应链协调模型

本文针对网上在线销售易逝品的无缺陷退货现象,考虑了供应链的最优订购协调问题。利用一个两阶段动态规划来描述动态市场环境下网上销售商的两次订购行为,在假定在两个销售阶段都发生无缺陷退货现象的前提下,分别建立了集中和分散决策模型,同时设计了价格保护契约以实现供应链的协调运作。最后,利用数值仿真得出了一些重要的管理启示。通过研究发现：（1）当不确定性较大时,网上销售商需要在第1阶段多订购产品以应对需求风险,因此导致了较低的系统期望利润。并且,需求的不确定性越大,供应链协调越有价值。（2）当第1阶段或第2阶段退货率或两阶段退货率都增加时,两个阶段的最优订购量均减小。（3）对于需求波动性较高的产品,顾客的退货率越小或者可服务退货率越大,价值越高（即对供应链系统期望利润的提高越显著）。     

Pricing and ordering decisions in a supply chain with downward substitution and imperfect process yield

We consider a manufacturer sourcing from two suppliers of asymmetric component quality and producing a quality-differentiated product, namely a low- and high-quality version, with each having deterministic demand. The manufacturer adopts the existing process to produce low-quality products with components from the supplier with low component quality, and develops a new process to produce high-quality products with components from the supplier with high component quality. The new process has imperfect yield, and products that do not meet the specifications for high-quality products can substitute for low-quality products produced with the existing process. We investigate the suppliers’ price decisions and the manufacturer’s ordering and production decisions in a game-theoretical model under dual sourcing. Our analyses reveal that increasing product differentiation or higher yield of high-quality products do not necessarily translate to a higher profit for the manufacturer. In light of the manufacturer’s sourcing strategies, we show that sourcing from a single supplier with high- and low-quality components yields a lower profit than sourcing from one supplier with high component quality and the other with low component quality. Finally, we investigate the manufacturer’s decision-making with endogenous yield rate of high-quality products. Our analyses demonstrate that the manufacturer benefits from setting the yield rate of high-quality products ahead of the suppliers’ price decisions.     

Dynamic Pricing to Minimize Maximum Regret

We consider a dynamic pricing problem that involves selling a given inventory of a single product over a short, two‐period selling season. There is insufficient time to replenish inventory during this season, hence sales are made entirely from inventory. The demand for the product is a stochastic, nonincreasing function of price. We assume interval uncertainty for demand, that is, knowledge of upper and lower bounds but not a probability distribution, with no correlation between the two periods. We minimize the maximum total regret over the two periods that results from the pricing decisions. We consider a dynamic model where the decision maker chooses the price for each period contingent on the remaining inventory at the beginning of the period, and a static model where the decision maker chooses the prices for both periods at the beginning of the first period. Both models can be solved by a polynomial time algorithm that solves systems of linear inequalities. Our computational study demonstrates that the prices generated by both our models are insensitive to errors in estimating the demand intervals. Our dynamic model outperforms our static model and two classical approaches that do not use demand probability distributions, when evaluated by maximum regret, average relative regret, variability, and risk measures. Further, our dynamic model generates a total expected revenue which closely approximates that of a maximum expected revenue approach which requires demand probability distributions.     

短生命周期产品的三种库存模型的比较

讨论短生命周期产品库存模型,考虑无形变质因素,并假定无形变质率与需求率成反比关系.在线性需求和常数生产率的条件下,假设,若需求率为1,则视作产品的市场生命周期结束.并且,在产品生命周期的前期不存在缺货的情况下,给出了短生命周期产品分别在理想状态、允许缺货以及价格折扣导致需求率变化等3种状态下的库存模型,最后在相同参数条件下对这3种模型进行比较,找出了单位时间内平均总成本最小的最优库存模型,厂商可以根据自身的情况选择合适的库存策略.     

Value of Information in Closed Loop Supply Chains

We explore the value of information (VOI) in the context of a firm that faces uncertainty with respect to demand, product return, and product recovery (yield). The operational decision of interest in matching supply with demand is the quantity of new product to order. Our objective is to evaluate the VOI from reducing one or more types of uncertainties, where value is measured by the reduction in total expected holding and shortage costs. We start with a single period model with normally distributed demands and returns, and restrict the analysis to the value of full information (VOFI) on one or more types of uncertainty. We develop estimators that are predictive of the value and sensitivity of (combinations of) different information types. We find that there is no dominance in value amongst the different types of information, and that there is an additional pay‐off from investing in more than one type. We then extend our analysis to the multi‐period case, where returns in a period are correlated with demands in the previous period, and study the value of partial information (VOPI) as well as full information. We demonstrate that our results from the single period model (adapted for VOPI) carry‐over exactly. Furthermore, a comparison with uniformly distributed demand and return show that these results are robust with respect to distributional assumptions.     

The Design and Introduction of Product Lines When Consumer Valuations are Uncertain

This article presents a model of the design and introduction of a product line when the firm is uncertain about consumer valuations for the products. We find that product line introduction strategy depends on this uncertainty. Specifically, under low levels of uncertainty the firm introduces both models during the first period; under higher levels of uncertainty, the firm prefers sequential introduction and delays design of the second product until the second period. Under intermediate levels of uncertainty the firm's first product should be of lower quality than one produced by a myopic firm that does not take product line effects into consideration. We find that when the firm introduces a product sequentially, the strategy might depend on realized demand. For example, if realized demand is high, the firm's second product should be a higher‐end model; if demand turns out to be low, the firm's second product should be a lower‐end model or replace the first product with a lower‐end model.     

焕新计划下考虑消费者细分的产品定价策略

焕新计划是生产商为提升自身竞争优势而推出的一种促销手段，加入焕新计划的消费者在第一阶段可以享受全方位服务，在第二阶段可以享受以旧换新抵扣优惠。消费者将权衡加入焕新计划的费用、服务水平以及抵扣力度等因素决策是否在第一阶段加入焕新计划。本文假设时尚型消费者每阶段都会购买最新产品，而节俭型消费者第一阶段购买产品后在第二阶段继续使用，针对这两类消费者在实施焕新计划和不实施焕新计划两种情况下，构建两阶段模型以决策产品的最优定价；运用解析方法分析了产品的生产成本等参数对最优定价的影响；运用解析方法和数值算例方法对两模型进行对比。     

INVENTORY RATIONING AND SHIPMENT FLEXIBILITY ALTERNATIVES FOR DIRECT MARKET FIRMS

This paper investigates inventory‐rationing policies of interest to firms operating in a direct market channel. We model a single product with two demand classes, where one class requests a lower order fulfillment lead time but pays a higher price. Demand for each class follows a Poisson process. Inventory is fed by a production system with exponentially distributed build times. We study rationing policies in which the firm either blocks or backlogs orders for the lower priority customers when inventory drops below a certain level. We compare the performance of these rationing policies with a pure first‐come, first‐serve policy under various scenarios for customer response to delay: lost sales, backlog, and a combination of lost sales and backlog.     

Inventory Planning for a Modular Product Family

This paper is motivated by observing that an increasing number of firms are offering modular products assembled with multiple option choices for the consumer. Starting with the PC offerings by Dell which allowed (and still allows) users to configure their product by choosing among multiple choices for each option, the current market place seems to have evolved to a make‐to‐stock scenario where Apple offers its IPAD series with multiple models each with a unique storage size, color, and wireless chip technology. The focus of our work is on determining the optimal stocking level of modular end‐products. Our analysis is based on a benchmark model with the aim of maximizing expected profit subject to an aggregate fill rate constraint as well as variant‐specific individual fill rates under a make‐to‐stock setting. To further assess the robustness of our finding, we consider the extensions of correlated market preferences over options, price‐dependent demand, and alternative probability distributions for characterizing uncertainty in market preferences or aggregate demand. Finally we also show how to extend the single period model into a multiple‐period setting. Through extensive computational analysis, we find that more precise estimates of market preferences for various modular options constitute extremely valuable information that goes beyond the usefulness of forecasts of aggregate market demand. From a practical perspective, this might be indicative of another classic marketing‐operations trade‐off. Offering more options for consumers would be preferred by marketing managers since this would reach more consumers and hence, enhance product sales. On the other hand, the ability to obtaining greater forecast accuracy would decline when the number of options increase. Hence, from an operational perspective, it would be preferred to limit option choices (so that better forecasts can be obtained) since this would lead to lower stocking costs and hence, higher profits.     

Shelf Loathing: Cross Docking at an Online Retailer

Online customers expect to wait, sometimes for a delay of many days. At the fulfillment center, there might be an opportunity to fill customer orders earlier than the due date through a cross‐docking transaction: rather than picking the item from inventory, the item moves directly from the receiving to the shipping dock, saving shelving and picking transactions. While cross docking reduces shelving and picking costs, it risks changing customer expectations for how soon a product will be delivered. Given customer order arrivals random in quantity and due dates, random replenishment arrivals, and costs (or benefits) for shipping a product early, we characterize the optimal decision as to whether to cross dock a replenishment item to fulfill demand that is not immediately due or to wait to (hopefully) cross dock in later periods. With multiple demands and due dates, the cross‐docking decision depends on the number of unfulfilled demands in each period across the horizon, the number of units that have just arrived (available for cross docking), picking and shelving costs, and the delay cost (or benefit). We formulate the problem as a Markov decision process, determine the structure of the optimal policy, and propose a well‐performing heuristic.     

Co-production of substitutable products

Co-production occurs when a production run produces, simultaneously, more than one type of product. In this paper, we consider co-production planning problems with stochastic yields, multiple processes, limited capacity and non-transitive product demand substitution. We show that these problems can be transformed to a structure where the demand substitutions are transitive. We address the decisions of how to select processes, to determine production quantities for each process and to allocate inventory to product demands. Finally, we provide simple heuristics and report on computational experiments done on randomly generated test cases.     

Stabilized‐Cycle Strategy for Capacitated Lot Sizing with Multiple Products: Fill‐Rate Constraints in Rolling Schedules

In practice, deterministic, multi‐period lot‐sizing models are implemented in rolling schedules since this allows the revision of decisions beyond the frozen horizon. Thus, rolling schedules are able to take realizations and updated forecasts of uncertain data (e.g., customer demands) into account. Furthermore, it is common to hold safety stocks to ensure given service levels (e.g., fill rate). As we will show, this approach, implemented in rolling schedules, often results in increased setup and holding costs while (over‐)accomplishing given fill rates. A well‐known alternative to deterministic planning models are stochastic, static, multi‐period planning models used in the static uncertainty strategy, which results in stable plans. However, these models have a lack of flexibility to react to the realization of uncertain data. As a result, actual costs may differ widely from planned costs, and downside deviations of actual fill rates from those given are very high. We propose a new strategy, namely the stabilized cycle. This combines and expands upon ideas from the literature for minimizing setup and holding costs in rolling schedules, while controlling actual product‐specific fill rates for a finite reporting period. A computational study with a multi‐item capacitated medium‐term production planning model has been executed in rolling schedules. On the one hand, it demonstrates that the stabilized‐cycle strategy yields a good compromise between costs and downside deviations. Furthermore, the stabilized‐cycle strategy weakly dominates the order‐based strategy for both constant and seasonal demands.     

考虑广告影响下的新产品垄断动态定价研究

针对垄断零售商的新产品定价问题,提出了一个新产品动态定价策略。在顾客对以往的价格和广告具有"学习"能力的条件下,提出了具有"学习"功能的需求函数。在给定各周期广告水平下,给出了零售商最优的动态定价策略,分析了零售商定价规律,发现其定价规律具有"振荡"性,并趋近于一定值。在零售商要同时决策零售价格和广告水平的条件下,给出了各周期最优的零售价格和广告水平。在一定条件下,当周期数趋近无穷大时零售价格趋近于顾客的保留价格或者单位成本。     

Mitigating Hi-tech products risks due to rapid technological innovation

The risks on international trade have increased continuously in recent years. One such risk for Hi-tech products is the result of rapid technological innovation, which results in a significant decline in the component cost, the selling price and the demand (due to newer products introduction). The Hi-tech products include computers and communication consumer products. From a practical viewpoint, there is a need to develop an innovative replenishing policy to consider the impact of the risk. In this paper, an economic order quantity model with finite planning horizon is developed for a buyer, when the component cost, the selling price and the demand rate of the end-consumer decline at a continuous rate. A numerical example and sensitivity analysis for two case studies are carried out to illustrate this model.