多类顾客环境下报童模型中库存分配策略研究

考虑一个报童模型中多类顾客的库存分配问题,将顾客按照他们愿意支付价格的高低划分为不同级别。零售商在销售期初决定产品订货量,并在销售期内决定接受或者拒绝不同顾客的需求,以最大化销售期内的期望总利润。将销售期分成大量足够小的时间单位,通过建立一个反向Bellman动态规划方程,以优化每个时间单位内的库存分配策略,并得到了零售商最优的期初订货量。通过与没有库存分配策略下零售商的期望利润进行比较,算例分析得出库存分配策略可以大幅提高零售商的利润。这主要是因为通过库存分配可以使得零售商从高端顾客中获取更多利润,同时能够减小期初的订货量,以节约采购成本和库存持有成本。     

The Usage of Opportunity Cost to Maximize Performance in Revenue Management*

To meet customer requirements efficiently, a manager needs to supply adequate quantities of products, capacity, or services at the right time with the right prices. Revenue management (RM) techniques can help firms use differential pricing strategies and capacity allocation tactics to maximize revenue. In this article, we propose a marginal revenue‐based capacity management (MRBCM) model to manage stochastic demand in order to create improved revenue opportunities. The new heuristic employs opportunity cost estimation logic that is unique and is the reason for the increased performance. The MRBCM model generates order acceptance policies that allocate available capacity to higher revenue generating market segments in both service and manufacturing environments. To evaluate these models, we design and conduct simulation experiments for 64 scenarios using a wide range of operating conditions. The experimental results show that the MRBCM model generates significantly higher revenues over the first come, first served rule when capacity is tight. In addition, we also show that the MRBCM model generally performs better than a recent RM model published in the literature.     

Reassessing Tradeoffs Inherent to Simultaneous Maintenance and Production Planning

Previous work has considered the simultaneous (as opposed to sequential) optimization of a maintenance policy and a production policy in a multi‐product setting with random yield and product mix constraints. One of the sequential approaches to which the simultaneous approach is compared is a so‐called first‐come‐first‐served (FCFS) approach, i.e., an approach that generates randomized production policies that do not depend on the deterioration state of the machine. However, the model formulation for this approach does not generate policies consistent with this FCFS notion. Therefore, we present a revised FCFS model and analyze its performance using an existing experimental design. The results suggest that previous work overestimates the degree to which a FCFS approach is suboptimal, and underestimates the value of simultaneously optimizing the maintenance and production decisions. Lastly, we conduct additional experiments which suggest that the joint impact of using both simultaneous optimization and a deterioration dependent production policy is quite significant.     

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.     

Rationing Capacity Between Two Product Classes*

In this paper, we study the capacity allocation problem faced by make-to-order manufacturing firms encountering expected total demand in excess of available capacity. Specifically, we focus on firms' manufacturing short-life-cycle or seasonal products such as high fashion apparel. Using a decision-theory-based approach, we develop a capacity allocation policy that allows such firms to discriminate between two classes of products (one yielding a higher profit contribution per unit of capacity allocated to it than the other), resulting in selective rejection of orders for the class with the lower unit contribution. The effectiveness of capacity rationing is investigated under a wide array of conditions characterized by variations in factors such as the ratio of unit profit contributions of the two product classes, the ratio of total available capacity to expected total demand, the ratio of expected demands between the two classes, and the variability in demand for each product class. The results indicate that capacity rationing is very effective in increasing the total profit, and could therefore serve as a valuable decision tool for managers in such firms.     

Inventory Policy with Parametric Demand: Operational Statistics,Linear Correction,and Regression

In this paper, we consider data‐driven approaches to the problem of inventory control. We first consider the approach of operational statistics and review related results which enable us to maximize a priori expected profit uniformly over all parameter values, when the demand distribution is known up to the location and scale parameters. For the case of the unknown shape parameter, we first suggest a heuristic approach based on operational statistics to obtain improved ordering policies and illustrate the same for the case of a Pareto demand distribution. In more general cases where the heuristic is not applicable, we suggest linear correction and support vector regression approaches to better estimate ordering policies, and illustrate these using a Gamma demand distribution. In certain cases, our proposed approaches are found to yield significant improvements.     

基于EMSR方法的订单接受策略研究

选择性的订单接受策略对于按订单生产的制造型企业具有重要意义。本文在单一资源的情况下,采用收益管理中常用的期望边际座位收益EMSR-a和EMSR-b方法,分别得出了利润最大化的订单接受策略。然后,把这两种策略运用到一个算例,与FCFS策略进行比较。数据结果显示在企业利润方面,这两种策略都明显优于FCFS,利润均提高20%以上。     

BlueLinx can benefit from innovative inventory management methods for commodity forward buys

Commodity prices often fluctuate significantly from one purchasing opportunity to the next. These fluctuations allow firms to benefit from forward buying (buying for future demand in addition to current demand) when prices are low. We propose a combined heuristic to determine the optimal number of future periods a firm should purchase at each ordering opportunity in order to maximize total expected profit when there is uncertainty in future demand and future buying price. We compare our heuristic with existing methods via simulation using real demand data from BlueLinx, a two-stage distributor of building products. The results show that our combined heuristic performs better than any existing methods considering forward buying or safety stock separately. We also compare our heuristic to the optimal inventory management policy by full enumeration for a smaller data set. The proposed heuristic is shown to be close to optimal. This study is the first to decide both the optimal number of future periods to buy for uncertain purchase price and the appropriate purchasing quantity with safety stock for uncertain demand simultaneously. The experience suggests that the proposed combined heuristic is simple and can be very beneficial for any company where forward buying is possible.     

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

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

Benchmark Schedules for Subcontracted Operations: Decentralization Inefficiencies that Arise from Competition and First‐Come‐First‐Served Processing*

Subcontracting has become a prominent business practice across many industries. Subcontracting of industrial production is generally based on short‐term need for additional processing capacity, and is frequently employed by manufacturers to process customer orders more quickly than using only in‐house production. In this article, we study a popular business model where multiple manufacturers, each capable of processing his entire workload in‐house, have the option to subcontract some of their operations to a single third party with a flexible resource. Each manufacturer can deliver customer orders only after his entire batch of jobs, processed in‐house and at the third party, is completed. The third party facility is available to several manufacturers who compete for its use. Current business practice of First‐Come‐First‐Served (FCFS) processing of the subcontracted workloads as well as the competitive Nash equilibrium schedules developed in earlier studies result in two types of inefficiencies; the third party capacity is not maximally utilized, and the manufacturers incur decentralization cost. In this article, we develop models to assess the value created by coordinating the manufacturers' subcontracting decisions by comparing two types of centralized control against FCFS and Nash equilibrium schedules. We present optimal and/or approximate algorithms to quantify the third party underutilization and the manufacturers' decentralization cost. We find that both inefficiencies are more severe with competition than they are when the third party allocates capacity in an FCFS manner. However, in a decentralized setting, a larger percentage of the players prefer Nash equilibrium schedules to FCFS schedules. We extend our analysis to incomplete information scenarios where manufacturers reveal limited demand information, and find that more information dramatically benefits the third party and the manufacturers, however, the marginal benefit of additional information is decreasing. Finally, we discuss an extension wherein each manufacturer's objective takes into account asymmetries in subcontracting, in‐house processing, and delay costs.     

Joint Initial Stocking and Transshipment—Asymptotics and Bounds

A common problem faced by many firms in their supply chains can be abstracted as follows. Periodically, or at the beginning of some selling season, the firm needs to distribute finished goods to a set of stocking locations, which, in turn, supply customer demands. Over the selling season, if and when there is a supply‐demand mismatch somewhere, a re‐distribution or transshipment will be needed. Hence, there are two decisions involved: the one‐time stocking decision at the beginning of the season and the supply/transshipment decision throughout the season. Applying a stochastic dynamic programming formulation to a two‐location model with compound Poisson demand processes, we identify the optimal supply/transshipment policy and show that the optimal initial stocking quantities can be obtained via maximizing a concave function whereas the contribution of transshipment is of order square‐root‐of T. Hence, in the context of high‐volume, fast‐moving products, the initial stocking quantity decision is a much more important contributor to the overall profit. The bounds also lead to a heuristic policy, which exhibits excellent performance in our numerical study; and we further prove both the bounds and the heuristic policy are asymptotically optimal when T approaches infinity. Extension to multiple locations is also discussed.     

基于优先权拍卖的产能分配机制研究

本文考虑一个供应商和两个独立零售商构成的供应链系统。当供应商的产能受到约束时，零售商可能会竞争有限的产能。本文提出将“优先分配权”作为一个有价值的标的物进行拍卖，按照出价高低确定优先分配顺序。本文证明了优先权拍卖机制属于共同价值模型，并提出了两类拍卖机制：事先拍卖和事后拍卖。本文证明两类优先权拍卖机制均会促使零售商提交真实的需求作为订单量，并且满足收益等价定理。而就供应商期望利润而言，事后优先权拍卖机制要高于事先优先权拍卖机制。     

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.     

Inventory Rationing for Multiple Class Demand under Continuous Review

We consider how a firm should ration inventory to multiple classes in a stochastic demand environment with partial, class‐dependent backlogging where the firm incurs a fixed setup cost when ordering from its supplier. We present an infinite‐horizon, average cost criterion Markov decision problem formulation for the case with zero lead times. We provide an algorithm that determines the optimal rationing policy, and show how to find the optimal base‐stock reorder policy. Numerical studies indicate that the optimal policy is similar to that given by the equivalent deterministic problem and relies on tracking both the current inventory and the rate that backorder costs are accumulating. Our study of the case of non‐zero lead time shows that a heuristic combining the optimal, zero lead time policy with an allocation policy based on a single‐period profit management problem is effective.     

Coordinated Capacitated Lot‐Sizing Problem with Dynamic Demand: A Lagrangian Heuristic

Coordinated replenishment problems are common in manufacturing and distribution when a family of items shares a common production line, supplier, or a mode of transportation. In these situations the coordination of shared, and often limited, resources across items is economically attractive. This paper describes a mixed‐integer programming formulation and Lagrangian relaxation solution procedure for the single‐family coordinated capacitated lot‐sizing problem with dynamic demand. The problem extends both the multi‐item capacitated dynamic demand lot‐sizing problem and the uncapacitated coordinated dynamic demand lot‐sizing problem. We provide the results of computational experiments investigating the mathematical properties of the formulation and the performance of the Lagrangian procedures. The results indicate the superiority of the dual‐based heuristic over linear programming‐based approaches to the problem. The quality of the Lagrangian heuristic solution improved in most instances with increases in problem size. Heuristic solutions averaged 2.52% above optimal. The procedures were applied to an industry test problem yielding a 22.5% reduction in total costs.     

Real‐Time Work Schedule Adjustment Decisions: An Investigation and Evaluation

Service managers often find that available worker capacity does not match with actual demand during a given day. They then must attempt to modify the planned work schedule to improve service and increase profitability. This study, which defines such a setting as the real‐time work schedule adjustment decision, pr oposes mathematical formulations of the real‐time adjustment and develops efficient heuristic approaches for this decision. The study evaluates the relative effectiveness of these heuristics versus experienced service managers, investigates the effect of the degree of schedule adjustment on profitability, and assesses the effect of demand forecast update errors on the performance of the schedule adjustment efforts. First, the results indicate that the computer based heuristics achieve higher profit improvement than experienced managers. Second, there is a trade‐off between schedule stability and profitability so that more extensive schedule revisions (efficiency first heuristics) generally result in higher profitability. However, the incremental return on schedule changes is diminishing. Third, we find that active adjustments of work schedules are beneficial as long as the direction of demand change is accurately identified.     

Demand switching criteria for multiple products: An inventory cost analysis

In this paper, we consider the problem of demand switching and show how a firm can take advantage of the risk-pooling effect to gain more profit. We examine the case of three products under various switching criteria; a model based on the heuristic approach is developed to determine the switching paths and the corresponding switching rates that yield the optimal profit. A constrained model with limited amount of the switched demand is also developed. In general, the profit increases as a result of higher profit margin or smaller demand variation and correlation. Our result indicates that the profit does not necessarily increase as the switching rate increases; in some cases the profit may even decrease as a result of demand switching. Numerical examples are also included to illustrate the derived models. The developed analytical approach may help practitioners to gain more insight in demand switching and facilitate inventory related decision-making process as well.     

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.     

Heuristics for Base‐Stock Levels in Multi‐Echelon Distribution Networks

We study inventory optimization for locally controlled, continuous‐review distribution systems with stochastic customer demands. Each node follows a base‐stock policy and a first‐come, first‐served allocation policy. We develop two heuristics, the recursive optimization (RO) heuristic and the decomposition‐aggregation (DA) heuristic, to approximate the optimal base‐stock levels of all the locations in the system. The RO heuristic applies a bottom‐up approach that sequentially solves single‐variable, convex problems for each location. The DA heuristic decomposes the distribution system into multiple serial systems, solves for the base‐stock levels of these systems using the newsvendor heuristic of Shang and Song (2003), and then aggregates the serial systems back into the distribution system using a procedure we call “backorder matching.” A key advantage of the DA heuristic is that it does not require any evaluation of the cost function (a computationally costly operation that requires numerical convolution). We show that, for both RO and DA, changing some of the parameters, such as leadtime, unit backordering cost, and demand rate, of a location has an impact only on its own local base‐stock level and its upstream locations’ local base‐stock levels. An extensive numerical study shows that both heuristics perform well, with the RO heuristic providing more accurate results and the DA heuristic consuming less computation time. We show that both RO and DA are asymptotically optimal along multiple dimensions for two‐echelon distribution systems. Finally, we show that, with minor changes, both RO and DA are applicable to the balanced allocation policy.     

The Impact of Forecast Errors on Early Order Commitment in a Supply Chain*

Supply chain partnership involves mutual commitments among participating firms. One example is early order commitment, wherein a retailer commits to purchase a fixed‐order quantity and delivery time from a supplier before the real need takes place. This paper explores the value of practicing early order commitment in the supply chain. We investigate the complex interactions between early order commitment and forecast errors by simulating a supply chain with one capacitated supplier and multiple retailers under demand uncertainty. We found that practicing early order commitment can generate significant savings in the supply chain, but the benefits are only valid within a range of order commitment periods. Different components of forecast errors have different cost implications to the supplier and the retailers. The presence of trend in the demand increases the total supply chain cost, but makes early order commitment more appealing. The more retailers sharing the same supplier, the more valuable for the supply chain to practice early order commitment. Except in cases where little capacity cushion is available, our findings are relatively consistent in the environments where cost structure, number of retailers, capacity utilization, and capacity policy are varied.