Advance selling with freebies and limited production capacity

We consider a two-period pricing model in which a seller offers freebies along with the product when making advance sales, and production is constrained by capacity. The seller can offer freebies to increase both market base and customer׳s valuation toward the product in advance. The customers strategically determine whether to purchase the product in advance and gain freebies when their valuation on the product is uncertain, or delay their purchase decision until the regular selling period. We characterize the optimal pricing, quality level of the freebie and production quantity decisions that maximize the expected profits of the seller over the two periods.     

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.     

Equilibrium Joining Strategies and Optimal Control of a Make‐to‐Stock Queue

We consider a make‐to‐stock, finite‐capacity production system with setup cost and delay‐sensitive customers. To balance the setup and inventory related costs, the production manager adopts a two‐critical‐number control policy, where the production starts when the number of waiting customers reaches a certain level and shuts down when a certain quantity of inventory has accumulated. Once the production is set up, the unit production time follows an exponential distribution. Potential customers arrive according to a Poisson process. Customers are strategic, i.e., they make decisions on whether to stay for the product or to leave without purchase based on their utility values, which depend on the production manager's control decisions. We formulate the problem as a Stackelberg game between the production manager and the customers, where the former is the game leader. We first derive the equilibrium customer purchasing strategy and system performance. We then formulate the expected cost rate function for the production system and present a search algorithm for obtaining the optimal values of the two control variables. We further analyze the characteristics of the optimal solution numerically and compare them with the situation where the customers are non‐strategic.     

Coordinating Service‐Sensitive Demand and Capacity by Adaptive Decision Making: An Application of Case‐Based Decision Theory*

The subject of this article is the simultaneous choice of product price and manufacturing capacity if demand is stochastic and service‐level sensitive. In this setting, capacity as well as price have an impact on demand because several aspects of service level depend on capacity. For example, delivery time will be reduced if capacity is increased given a constant demand rate. We illustrate the relationship between service level, capacity, and demand reaction by a stylized application problem from the after‐sales services industry. The reaction of customers to variations in service level and price is represented by a kinked price‐demand‐rate function. We first derive the optimal price‐capacity combination for the resulting decision problem under full information. Subsequently, we focus on a decision maker (DM) who lacks complete knowledge of the demand function. Hence the DM is unable to anticipate the service level and consequently cannot identify the optimal solution. However, the DM will acquire additional information during the sales process and use it in subsequent revisions of the price‐capacity decision. Thus, this decision making is adaptive and based on experience. In contrast to the literature, which assumes certain repetitive procedures somewhat ad hoc, we develop an adaptive decision process based on case‐based decision theory (CBDT) for the price‐capacity problem. Finally, we show that a CBDT DM in our setting eventually finds the optimal solution, if the DM sets the price based on absorption costs and adequately adjusts the capacity with respect to the observed demand.     

不同决策目标下受资金约束零售商的最优采购策略研究

在提前订购和延时采购两种情景下,分别考虑最大化期望收益和最小化违约概率两种决策目标,对受资金约束零售商的最优采购量和相匹配的融资策略进行分析,结果表明,相比于以最大化期望收益为决策目标,以最小化违约概率为决策目标的零售商在提前订购中将奉行"保守"的采购量和融资策略（仅耗尽自有资金量采购而不融资）,而在延时采购中采取"激进"的采购量和融资策略（与最大化期望收益下一致）;在此基础上,对不同决策目标下受资金约束零售商的最优采购时机问题进行研究发现,在最大化期望收益下,零售商的最优采购时机由产品采购成本、市场容量均值、市场容量方差、自有资金量、银行贷款利率等多个参数共同决定,而在最小化违约概率下,零售商将始终选择延时采购。     

Production and Sales Planning in Capacitated New Product Introductions

How should a firm with limited capacity introduce a new product? Should it introduce the product as soon as possible or delay introduction to build up inventory? How do the product and market characteristics affect the firm's decisions? To answer such questions, we analyze new product introductions under capacity restrictions using a two‐period model with diffusion‐type demand. Combining marketing and operations management decisions in a stylized model, we optimize the production and sales plans of the firm for a single product. We identify four different introduction policies and show that when the holding cost is low and the capacity is low to moderate, a (partial) build‐up policy is indeed optimal if consumers are sensitive to delay. Under such a policy, the firm (partially) delays the introduction of its product and incurs short‐term backlog costs to manage its future demand and total costs more effectively. However, as either the holding cost or the capacity increases, or consumer sensitivity to delay decreases, the build‐up policy starts to lose its appeal, and instead, the firm prefers an immediate product introduction. We extend our analysis by studying the optimal capacity decision of the firm and show that capacity shortages may be intentional.     

Impact of Price Postponement on Capacity and Flexibility Investment Decisions

Investments in dedicated and flexible capacity have traditionally been based on demand forecasts obtained under the assumption of a predetermined product price. However, the impact on revenue of poor capacity and flexibility decisions can be mitigated by appropriately changing prices. While investment decisions need to be made years before demand is realized, pricing decisions can easily be postponed until product launch, when more accurate demand information is available. We study the effect of this price decision delay on the optimal investments on dedicated and flexible capacity. Computational experiments show that considering price postponement at the planning stage leads to a large reduction in capacity investments, especially in the more expensive flexible capacity, and a significant increase in profits. Its impact depends on demand correlation, elasticity and diversion, ratio of fixed to variable capacity costs, and uncertainty remaining at the times the pricing and production decisions are made.     

Coordination of a multidivisional organization through two levels of management

This paper develops the bilevel multidivisional programming problem (BMPP) as a model for a decentralized organization. In particular, a hierarchical arrangement comprising one superior unit and M subordinate units is proposed where each unit is assumed to control a unique set of decision variables defined over jointly dependent strategy sets. Individual but interdependent objective functions are also assumed so that each unit may influence but not control another. In the formulation, decisions are made in two stages with top management given the first choice followed by the concurrent responses of the divisions. In this way it is possible to account for production externalities at the lower level and coordination activities at the higher level. As such, after outlining the major geometry of the linear case, the usefulness of the general model is discussed from a management perspective. Ramifications relating to opportunity costs, capacity utilization and computational requirements are presented and highlighted through a variety of examples.     

The Use of Flexible Manufacturing Capacity in Pharmaceutical Product Introductions*

This work considers the value of the flexibility offered by production facilities that can easily be configured to produce new products. We focus on technical uncertainty as the driver of this value, while prior works focused only on demand uncertainty. Specifically, we evaluate the use of process flexibility in the context of risky new product development in the pharmaceutical industry. Flexibility has value in this setting due to the time required to build dedicated capacity, the finite duration of patent protection, and the probability that the new product will not reach the market due to technical or regulatory reasons. Having flexible capacity generates real options, which enables firms to delay the decision about constructing product‐specific capacity until the technical uncertainty is resolved. In addition, initiating production in a flexible facility can enable the firm to optimize production processes in dedicated facilities. The stochastic dynamic optimization problem is formulated to analyze the optimal capacity and allocation decisions for a flexible facility, using data from existing literature. A solution to this problem is obtained using linear programming. The result of this analysis shows both the value of flexible capacity and the optimal capacity allocation. Due to the substantial costs involved with flexibility in this context, the optimal level of flexible capacity is relatively small, suggesting products be produced for only short periods before initiating construction of dedicated facilities.     

Supply Diversification with Responsive Pricing

We study sourcing and pricing decisions of a firm with correlated suppliers and a price‐dependent demand. With two suppliers, the insight—cost is the order qualifier while reliability is the order winner—derived in the literature for the case of exogenously determined price and independent suppliers, continues to hold when the suppliers' capacities are correlated. Moreover, a firm orders only from one supplier if the effective purchase cost from him, which includes the imputed cost of his unreliability, is lower than the wholesale price charged by his rival. Otherwise, the firm orders from both. Furthermore, the firm's diversification decision does not depend on the correlation between the two suppliers' random capacities. However, its order quantities do depend on the capacity correlation, and, if the firm's objective function is unimodal, the total order quantity decreases as the capacity correlation increases in the sense of the supermodular order. With more than two suppliers, the insight no longer holds. That is, when ordering from two or more suppliers, one is the lowest‐cost supplier and the others are not selected on the basis of their costs. We conclude the paper by developing a solution algorithm for the firm's optimal diversification problem.     

A Bayesian Inventory Model Using Real‐Time Condition Monitoring Information

Lack of coordination between machinery fault diagnosis and inventory management for spare parts can lead to increased inventory costs and disruptions in production activity. We develop a framework for incorporating real‐time condition monitoring information into inventory decisions for spare parts. We consider a manufacturer who periodically replenishes inventory for a machine part that is subject to deterioration. The deterioration is captured via condition monitoring and modeled using a Wiener process. The resulting degradation model is used to derive the life distribution of a functioning part and to estimate the demand distribution for spare parts. This estimation is periodically updated, in a Bayesian manner, as additional information on part deterioration is obtained. We develop an inventory model that incorporates this updated demand distribution and demonstrate that a dynamic base‐stock policy, in which the optimal base‐stock level is a function of some subset of the observed condition monitoring information, is optimal. We propose a myopic critical fractile policy that captures the essence of the optimal policy, but is easier to compute. Computational experiments indicate that this heuristic performs quite well relative to the optimal policy. Adaptive inventory policies such as these can help manufacturers to increase machine availability and reduce inventory costs.     

Flexible Capacity Investments and Product Mix: Optimal Decisions and Value of Postponement Options

In this article, we study a firm's interdependent decisions in investing in flexible capacity, capacity allocation to individual products, and eventual production quantities and pricing in meeting uncertain demand. We propose a three‐stage sequential decision model to analyze the firm's decisions, with the firm being a value maximizer owned by risk‐averse investors. At the beginning of the time horizon, the firm sets the flexible capacity level using an aggregate demand forecast on the envelope of products its flexible resources can accommodate. The aggregate demand forecast evolves as a Geometric Brownian Motion process. The potential market share of each product is determined by the Multinomial Logit model. At a later time and before the end of the time horizon, the firm makes a capacity commitment decision on the allocation of the flexible capacity to each product. Finally, at the end of the time horizon, the firm observes the demand and makes the production quantity and pricing decisions for end products. We obtain the optimal solutions at each decision stage and investigate their optimal properties. Our numerical study investigates the value of the postponed capacity commitment option in supplying uncertain operation environments.     

Analysis of postponement strategy by EPQ-based models with planned backorders

This paper develops economic production quantity (EPQ)-based models with planned backorders to evaluate the impact of the postponement strategy on a manufacturer in a supply chain. We derive the optimal total average costs per unit time for producing and keeping n end-products in a postponement system and a non-postponement system, respectively. By comparing the optimal total average costs of the two systems, we evaluate the impact of postponement on the manufacturer under four circumstances. Our results show that postponement strategy can give a lower total average cost under certain circumstances. We also find that the key factors in postponement decisions are the variance of the machine utilization rates and the variance of the backorder costs.     

电网企业购买电能与电力备用的MSV风险控制方法

如何通过优化电能和电力备用市场的购电量来降低风险购电成本,从而降低用户的用电成本对电网企业提高管理效率有着重要的意义。本文将两市场购电价格视为风险因素,结合电网企业风险管理的实践,运用均半方差(Mean Semi-variance--MSV)理论代替均方差(Mean variance-MV)理论来描述风险购电问题,并给出最优购电策略基本计算公式。其中,备用率是影响最优购电策略取值的一个不确定性自变量,运用模糊隶属度函数描述专家对合理备用率的不确定性认识,进而通过扩张原理推求出最优购电策略的模糊隶属度函数,并运用重心法得到解模糊后的最优购电策略。模型很好地融合了专家的定性认识与定量分析技术,提供了一条新的解决购电问题的思路,这些在算例中可以得到很好地体现。     

Capacity Sharing and Cost Allocation among Independent Firms with Congestion

We analyze the benefit of production/service capacity sharing for a set of independent firms. Firms have the choice of either operating their own production/service facilities or investing in a facility that is shared. Facilities are modeled as queueing systems with finite service rates. Firms decide on capacity levels (the service rate) to minimize delay costs and capacity investment costs possibly subject to service‐level constraints on delay. If firms decide to operate a shared facility they must also decide on a scheme for sharing the capacity cost. We formulate the problem as a cooperative game and identify settings under which capacity sharing is beneficial and there is a cost allocation that is in the core under either the first‐come, first‐served policy or an optimal priority policy. We show that capacity sharing may not be beneficial in settings where firms have heterogeneous work contents and service variabilities. In such cases, we specify conditions under which capacity sharing may still be beneficial for a subset of the firms.     

A Note on the Relationship Among Capacity,Pricing, and Inventory in a Make‐to‐Stock System

We address the simultaneous determination of pricing, production, and capacity investment decisions by a monopolistic firm in a multi‐period setting under demand uncertainty. We analyze the optimal decision with particular emphasis on the relationship between price and capacity. We consider models that allow for either bi‐directional price changes or models with markdowns only, and in the latter case we prove that capacity and price are strategic substitutes.     

Coordinating pricing and production decisions for multiple products

We consider a dynamic problem of joint pricing and production decisions for a profit-maximizing firm that produces multiple products. We model the problem as a mixed integer nonlinear program, incorporating capacity constraints, setup costs, and dynamic demand. We assume demand functions to be convex, continuous, differentiable, and strictly decreasing in price. We present a solution approach which is more general than previous approaches that require the assumption of a specific demand function. Using real-world data from a manufacturer, we study problem instances for different demand scenarios and capacities and solve for optimal prices and production plans. We present analytical results that provide managerial insights on how the optimal prices change for different production plans and capacities. We extend some of the earlier works that consider single product problems to the case of multiple products and time variant production capacities. We also benchmark performance of proposed algorithm with a commercial solver and show that it outperforms the solver both in terms of solution quality and computational times.     

Panel Size and Overbooking Decisions for Appointment‐Based Services under Patient No‐Shows

Many service systems that work with appointments, particularly those in healthcare, suffer from high no‐show rates. While there are many reasons why patients become no‐shows, empirical studies found that the probability of a patient being a no‐show typically increases with the patient's appointment delay, i.e., the time between the call for the appointment and the appointment date. This paper investigates how demand and capacity control decisions should be made while taking this relationship into account. We use stylized single server queueing models to model the appointments scheduled for a provider, and consider two different problems. In the first problem, the service capacity is fixed and the decision variable is the panel size; in the second problem, both the panel size and the service capacity (i.e., overbooking level) are decision variables. The objective in both cases is to maximize some net reward function, which reduces to system throughput for the first problem. We give partial or complete characterizations for the optimal decisions, and use these characterizations to provide insights into how optimal decisions depend on patient's no‐show behavior in regards to their appointment delay. These insights especially provide guidance to service providers who are already engaged in or considering interventions such as sending reminders in order to decrease no‐show probabilities. We find that in addition to the magnitudes of patient show‐up probabilities, patients' sensitivity to incremental delays is an important determinant of how demand and capacity decisions should be adjusted in response to anticipated changes in patients' no‐show behavior.     

Simultaneous Determination of Joint Product Cost Allocations and Cost-Plus Prices*

Use of the net realizable value approach for joint manufacturing cost allocations requires knowledge of selling prices of joint products. However, joint product selling prices themselves are functions of the allocated costs under a cost-plus pricing policy. In this case, it is necessary to determine joint cost allocations and joint product prices simultaneously. This paper applies a nonlinear programming (NLP) approach to simultaneously determine the optimal joint production decision, joint product cost-plus prices, and joint cost allocations using the net realizable value method. The NLP solution provides not only the optimal joint production and pricing decisions, but also the necessary conditions for such optimal decisions.     

无人零售业态下自动售卖机联合补货策略研究

研究无人零售业态下自动售卖机的多产品联合补货问题,建立由补货成本、库存持有成本、缺货成本构成的平均补货成本模型,分析容量约束与固定补货阈值下的最优补货策略。结果表明,企业会倾向于在剩余较少产品时进行补货,剩余的产品往往是投影面积最小使得相同面积可容纳最多数量的产品;比较最优补货时间与平均补货成本发现,延长补货时间可以降低平均补货成本,在补货阈值越大、固定补货成本越低或售卖机容量越小时,最优补货时间会降低,反之,平均补货成本会增加。此外,分析不同成本变动对平均成本的影响发现,单位成本变动均会引起平均补货成本的增加,且在单位库存持有成本变动时,最优补货策略会发生转移,向单位库存持有成本降低至一定程度的产品或向投影面积最低即相同面积可容纳数量最小的产品转移。