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.     

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.     

A Production–Inventory Model for a Push–Pull Manufacturing System with Capacity and Service Level Constraints

We study a hybrid push–pull production system with a two‐stage manufacturing process, which builds and stocks tested components for just‐in‐time configuration of the final product when a specific customer order is received. The first production stage (fabrication) is a push process where parts are replenished, tested, and assembled into components according to product‐level build plans. The component inventory is kept in stock ready for the final assembly of the end products. The second production stage (fulfillment) is a pull‐based assemble‐to‐order process where the final assembly process is initiated when a customer order is received and no finished goods inventory is kept for end products. One important planning issue is to find the right trade‐off between capacity utilization and inventory cost reduction that strives to meet the quarter‐end peak demand. We present a nonlinear optimization model to minimize the total inventory cost subject to the service level constraints and the production capacity constraints. This results in a convex program with linear constraints. An efficient algorithm using decomposition is developed for solving the nonlinear optimization problem. Numerical results are presented to show the performance improvements achieved by the optimized solutions along with managerial insights provided.     

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.     

面向产品生命周期的部分柔性技术选择

本文研究随机需求下产品生命周期不同阶段的部分柔性技术选择与生产能力规划问题。部分柔性技术是相对于完全柔性技术而言的,一种生产技术的柔性程度定义为能生产一产品类中产品个数多少的能力。不同柔性强度的生产技术,其投资成本和运行成本不同。本文首先建立了以计划期上总成本最小为目标的技术选择和生产能力规划模型,然后根据产品在其生命周期不同阶段的特点与市场需求的特点,应用所建立的模型进行仿真并总结产品导入期和成熟期技术选择的特点。     

Measuring the Impact of Increased Product Substitution on Pricing and Capacity Decisions Under Linear Demand Models

We consider two substitutable products and compare two alternative measures of product substitutability for linear demand functions that are commonly used in the literature. While one leads to unrealistically high prices and profits as products become more substitutable, the results obtained using the other measure are in line with intuition. Using the more appropriate measure of product substitutability, we study the optimal investment mix in flexible and dedicated capacities in both monopoly and oligopoly settings. We find that the optimal investment in manufacturing flexibility tends to decrease as the products become closer substitutes; this is because (1) pricing can be used more effectively to balance supply and demand, and (2) the gains obtained by shifting production to the more profitable product are reduced due to increased correlation between the price potentials of the substitutable products. The value of flexibility always increases with demand variability. We also show that, as long as the optimal investments in dedicated capacity for both products are positive, the optimal expected prices and production quantities do not depend on the cost of the flexible capacity. Manufacturing flexibility simply allows the firm to achieve those expected values with lower capacity, while leading to higher expected profits.     

Lowest Cost May Not Lower Total Cost: Using “Spackling” to Smooth Mass‐Customized Production

Consider a manufacturer who mass customizes variants of a product in make‐to‐order fashion, and also produces standard variants as make‐to‐stock. A traditional manufacturing strategy would be to employ two separate manufacturing facilities: a flexible plant for mass‐customized items and an efficient plant for standard items. We contrast this traditional focus strategy with an alternative that better utilizes capacity by combining production of mass‐customized and standard items in one of two alternate spackling strategies: (1) a pure‐spackling strategy, where the manufacturer produces everything in a (single) flexible plant, first manufacturing custom products as demanded each period, and then filling in the production schedule with make‐to‐stock output of standard products; or (2) a layered‐spackling strategy, which uses an efficient plant to make a portion of its standard items and a separate flexible plant where it spackles. We identify the optimal production strategy considering the tradeoff between the cost premium for flexible (versus efficient) production capacity and the opportunity costs of idle capacity. Spackling amortizes fixed costs of capacity more effectively and thus can increase profits from mass customization vis‐à‐vis a focus strategy, even with higher cost production for the standard goods. We illustrate our framework with data from a messenger bag manufacturer.     

COMPONENT COMMONALITY: MODELS WITH PRODUCT‐SPECIFIC SERVICE CONSTRAINTS*

Common components are used extensively for reasons including product postponement and expediting new product development. We consider a two‐stage assemble‐to‐order system with two products having uniformly distributed demand, one common component, and product‐specific components. We develop optimization models in which the cost‐minimizing inventory of the components must be determined and allocated to products in order to meet product‐specific service level constraints. We compare two different commonality models based on whether or not the products are prioritized. A distinctive feature of our study is the use of product‐specific service levels. We compare our results with models using aggregate service levels.     

Design for the Environment: Life‐Cycle Approach Using a Newsvendor Model

Introducing environmental innovations in product and process design can affect the product's cost and demand, as well as the environmental impact in different stages of its life cycle (such as manufacturing and use stages). In this article, we advance understanding on where such design changes can be most effective economically to the firm and examine their corresponding environmental consequences. We consider a profit maximizing firm (newsvendor) deciding on the production quantity as well as its environmentally focused design efforts. We focus our results along the two dimensions of demand characteristics and life‐cycle environmental impact levels, specifically functional vs. innovative products, and higher manufacturing stage environmental impact vs. higher use stage environmental impact. We also discuss the environmental impact of overproduction and how it relates to the different types of products and their salvage options. We find that although the environmental impact per unit always improves when firms use eco‐efficient or demand‐enhancing innovations, the total environmental impact can either increase or decrease due to increased production quantities. We identify the conditions for such cases by looking at the environmentally focused design efforts needed to compensate for the increase in production. We also show that the environmental impact of overproduction plays an important role in the overall environmental impact of the firm. We conclude by applying our model to different product categories.     

Flexible Backup Supply and the Management of Lead‐Time Uncertainty

We consider replenishment decisions for a constant rate demand environment from a supplier with uncertain lead times. We study the potential use of a flexible backup supplier as an emergency response to accurate lead‐time information arriving at (or close after) the beginning of the demand interval and well after an original order with the stochastic lead‐time supplier has been placed. The emergency response decisions involve whether to order and how much from the flexible backup supplier, with the objective of minimizing the cost of meeting demand. We derive the optimal emergency‐response policy and clearly outline its implications on the optimized safety lead time of the original order placement and on the cost of meeting demand. We examine the impact on the use of the flexible backup supplier of factors like the arrival time of accurate lead‐time information and the response lead time of the backup supplier. We further study the potential benefits of the use of the flexible backup supplier in a dual role: as one of the two suppliers in a redundant supply system assigned to originally meet the demand and as an emergency response to later‐arriving lead‐time information. Our numerical studies illustrate the benefits from the use of the flexible backup supplier as an emergency response, but for reasonable purchase premiums and short lead times of flexible backup supply options, their use in a dual (regular and emergency response) role often leads to improved performance over safety lead‐time single and uncertain lead‐time supplier‐replenishment strategies. The benefits of the backup supply options are accentuated the higher the lead‐time uncertainty of the stochastic lead‐time supplier is.     

Responsive Pricing Newsvendor Networks with Discretionary Commonality

Discretionary commonality is a form of operational flexibility used in multi‐product manufacturing environments. Consider a case where a firm produces and sells two products. Without discretionary commonality, each product is made through a unique combination of input and production capacity. With discretionary commonality, one of the inputs could be used for producing both products, and one of the production capacities could be used to process different inputs for producing one of the products. In the latter case, the manager can decide, upon the realization of uncertainty, not only the quantities for different products (outputs) but also the means of transforming inputs into outputs. The objective of this study is to understand how the firm's value, its inventory levels for inputs and capacity levels for resources are affected by the demand characteristics and market conditions. In pursuing this research, we extend Van Mieghem and Rudi ( 2002 )'s newsvendor network model to allow for the modeling of product interdependence, demand functions, random shocks, and firm's ex post pricing decision. Applying the general framework to the network with discretionary commonality, we discover that inventory and capacity management can be quite different compared to a network where commonality is non‐discretionary. Among other results, we find that as the degree of product substitution increases, the relative need for discretionary commonality increases; as the market correlation increases, while the firm's value may increase for complementary products, the discretionary common input decreases but the dedicated input increases. Numerical study shows that discretionary flexibility and responsive pricing are strategic substitutes.     

A NUMERICAL ANALYSIS OF CAPACITATED POSTPONEMENT

Customer satisfaction can be achieved by providing rapid delivery of a wide variety of products. High levels of product variety require correspondingly high levels of inventory of each item to quickly respond to customer demand. Delayed product differentiation has been identified as a strategy to reduce final product inventories while providing the required customer service levels. However, it is done so at the cost of devoting large production capacities to the differentiation stage. We study the impact of this postponement capacity on the ability to achieve the benefits of delayed product differentiation. We examine a single‐period capacitated inventory model and consider a manufacturing system that produces a single item that is finished into multiple products. After assembly, some amount of the common generic item is completed as non‐postponed products, whereas some of the common item is kept as in‐process inventory, thereby postponing the commitment to a specific product. The non‐postponed finished‐goods inventory is used first to meet demand. Demand in excess of this inventory is met, if possible, through the completion of the common items. Our results indicate that a relatively small amount of postponement capacity is needed to achieve all of the benefits of completely delaying product differentiation for all customer demand. This important result will permit many firms to adopt this delaying strategy who previously thought it to be either technologically impossible or prohibitively expensive to do so.     

Multi‐Product Quality Competition: Impact of Resource Constraints

We study a multi‐product firm with limited capacity where the products are vertically (quality) differentiated and the customer base is heterogeneous in their valuation of quality. While the demand structure creates opportunities through proliferation, the firm should avoid cannibalization between its own products. Moreover, the oligopolistic market structure puts competitive pressure and limits the firm's market share. On the other hand, the firm has limited resources that cause a supply‐side fight for adequate and profitable production. We explicitly characterize the conditions where each force dominates. Our focus is on understanding how capacity constraints and competition affect a firm's product‐mix decisions. We find that considering capacity constraints could significantly change traditional insights (that ignore capacity) related to product‐line design and the role of competition therein. In particular, we show that when the resources are limited, the firm should offer only the product that has the highest margin per unit capacity. We find that this product could be the diametrically opposite product suggested by the existing literature. In addition, we show that for intermediate capacity levels, whereas the margin per unit capacity effect dominates in a less competitive market, proliferation and cannibalization effects dominate in a more competitive market.     

Looking Upstream: Optimal Policies for a Class of Capacitated Multi‐Stage Inventory Systems

We consider a multi‐stage inventory system with stochastic demand and processing capacity constraints at each stage, for both finite‐horizon and infinite‐horizon, discounted‐cost settings. For a class of such systems characterized by having the smallest capacity at the most downstream stage and system utilization above a certain threshold, we identify the structure of the optimal policy, which represents a novel variation of the order‐up‐to policy. We find the explicit functional form of the optimal order‐up‐to levels, and show that they depend (only) on upstream echelon inventories. We establish that, above the threshold utilization, this optimal policy achieves the decomposition of the multidimensional objective cost function for the system into a sum of single‐dimensional convex functions. This decomposition eliminates the curse of dimensionality and allows us to numerically solve the problem. We provide a fast algorithm to determine a (tight) upper bound on this threshold utilization for capacity‐constrained inventory problems with an arbitrary number of stages. We make use of this algorithm to quantify upper bounds on the threshold utilization for three‐, four‐, and five‐stage capacitated systems over a range of model parameters, and discuss insights that emerge.     

面向多灾点需求的应急资源调度博弈模型及优化

非常规突发事件爆发后经常会造成多个灾点,而各灾点的需求往往是不同的,单独的应急资源中心很难同时满足这种要求,因此如何把多个应急资源中心所储备的应急资源公平合理地调配到各个灾点成为应急决策者亟待解决的现实问题。本文首先描述了各灾点对应急资源需求变化的动态过程即按照应急资源需求信息的变化将整个应急资源调度过程划分成若干阶段,在此基础上构建了基于多灾点多阶段的应急资源调度过程理论模型。随后以博弈论为工具,在进行一系列模型假设和确定各灾点灾情的前提下,建立面向多灾点需求的应急资源博弈调度模型,并采用改进的蚁群算法进行求解,实现对各灾点以最小的“虚拟成本”进行所需应急资源的调度。最后的模型仿真测试和算例分析验证了所建模型的有效性和可行性。该模型与算法也为商业物流中的资源配送提供了新的解决方案和实现途径。     

Pool‐Point Distribution of Zero‐Inventory Products

We study zero‐inventory production‐distribution systems under pool‐point delivery. The zero‐inventory production and distribution paradigm is supported in a variety of industries in which a product cannot be inventoried because of its short shelf life. The advantages of pool‐point (or hub‐and‐spoke) distribution, explored extensively in the literature, include the efficient use of transportation resources and effective day‐to‐day management of operations. The setting of our analysis is as follows: A production facility (plant) with a finite production rate distributes its single product, which cannot be inventoried, to several pool points. Each pool point may require multiple truckloads to satisfy its customers' demand. A third‐party logistics provider then transports the product to individual customers surrounding each pool point. The production rate can be increased up to a certain limit by incurring additional cost. The delivery of the product is done by identical trucks, each having limited capacity and non‐negligible traveling time between the plant and the pool points. Our objective is to coordinate the production and transportation operations so that the total cost of production and distribution is minimized, while respecting the product lifetime and the delivery capacity constraints. This study attempts to develop intuition into zero‐inventory production‐distribution systems under pool‐point delivery by considering several variants of the above setting. These include multiple trucks, a modifiable production rate, and alternative objectives. Using a combination of theoretical analysis and computational experiments, we gain insights into optimizing the total cost of a production‐delivery plan by understanding the trade‐off between production and transportation.     

Hold Safety Inventory Before,At, or After the Fan‐Out Point?

We consider a product sold in multiple variants, each with uncertain demand, produced in a multi‐stage process from a standard (i.e., generic) sub‐assembly. The fan‐out point is defined as the last process stage at which outputs are generic (outputs at every subsequent stage are variant‐specific). Insights gained from an analytical study of the system are used to develop heuristics that determine the stage(s) at which safety inventory should be held. We offer a relatively‐simple heuristic that approaches globally‐optimal results even though it uses only two relatively‐local parameters. We call this the VAPT, or value‐added/processing time heuristic, because it determines whether a (local) stage should hold inventory based only on the value added at that local stage relative to its downstream stage, along with the processing time at that local stage relative to its downstream stage. Another key insight is that, contrary to possible intuition, safety inventory should not always be held at the fan‐out point, although a fan‐out point does hold inventory under a wider range of conditions. We also explore when postponement is most valuable and illustrate that postponement may often be less beneficial than suggested by Lee and Tang (1997).     

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.     

竞争环境下新创企业产量柔性技术战略决策研究

考虑新创企业与成熟企业相互竞争,重点研究竞争环境下,两企业的产量柔性技术选择及产能投资决策。首先分析了四种不同策略组合下两企业的最优产能决策、新创企业的最大生存概率以及成熟企业的最大利润;然后用传统博弈论的方法得出了二者的竞争均衡,并分析影响两企业产量柔性战略决策的因素;最后用数值实验进行验证。研究结果表明：在竞争中,新创企业更加关注成本因素,倾向于选择成本较小的无柔性技术;成熟企业对市场需求的波动更为敏感,当市场需求波动较大时,选择产量柔性技术能提高其收益;当产量柔性技术单位产量调整成本较大时,选择无柔性技术对两企业更为有利。     

Sequential and Simultaneous Decision Making for Optimizing Health Care Resource Flexibilities

Health care administrators commonly employ two types of resource flexibilities (demand upgrades and staffing flexibility) to efficiently coordinate two critical internal resources, nursing staff and beds, and an external resource (contract nurses) to satisfy stochastic patient demand. Under demand upgrades, when beds are unavailable for patients in a less acute unit, patients are upgraded to a more acute unit if space is available in that unit. Under staffing flexibility, nurses cross‐trained to work in more than one unit are used in addition to dedicated and contract nurses. Resource decisions (beds and staffing) can be made at a single point in time (simultaneous decision making) or at different points in time (sequential decision making). In this article, we address the following questions: for each flexibility configuration, under sequential and simultaneous decision making, what is the optimal resource level required to meet stochastic demand at minimum cost? Is one type of flexibility (e.g., demand upgrades) better than the other type of flexibility (e.g., staffing flexibility)? We use two‐stage stochastic programming to find optimal resource levels for two nonhomogeneous hospital units that face stochastic demand following a continuous, general distribution. We conduct a full‐factorial numerical experiment and find that the benefit of using staffing flexibility on average is greater than the benefit of using demand upgrades. However, the two types of flexibilities have a positive interaction effect and they complement each other. The type of flexibility and decision timing has an independent effect on system performance (capacity and staffing costs). The benefits of cross‐training can be largely realized even if beds and staffing levels have been determined prior to the establishment of a cross‐training initiative.