Capacity Decisions Research Articles

Capacity Investment with Demand Learning

We study a firm’s optimal strategy to adjust its capacity using demand information. The capacity adjustment is costly and often subject to managerial hurdles which sometimes make it difficult to adjust capacity multiple times. In order to clearly analyze the impact of demand learning on the firm’s decision, we study two scenarios. In the first scenario, the firm’s capacity adjustment cost increases significantly with respect to the number of adjustments because of significant managerial hurdles, and resultantly the firm has a single opportunity to adjust capacity (single adjustment scenario). In the second scenario, the capacity adjustment costs do not change with respect to the number of adjustments because of little managerial hurdles, and therefore the firm has multiple opportunities to adjust capacity (multiple adjustment scenario). For both scenarios, we first formulate the problem as a stochastic dynamic program, and then characterize the firm’s optimal policy: when to adjust and by how much. We show that the optimal decision on when and by how much to change the capacity is not monotone in the likelihood of high demand in the single adjustment scenario, while the optimal decision is monotone under mild conditions and the optimal policy is a control band policy in the multiple adjustment scenario. The sharp contrast reflects the impact of demand learning on the firm’s optimal capacity decision. Since computing and implementing the optimal policy is not tractable for general problems, we develop a data-driven heuristic for each scenario. In the single adjustment scenario, we show that a two-step heuristic which explores demand for an appropriately chosen length of time and adjusts the capacity based on the observed demand is asymptotically optimal, and prove the convergence rate. In the multiple adjustment scenario, we also show that a multi-step heuristic under which the firm adjusts its capacity at a predetermined set of periods with exponentially increasing gap between two consecutive decisions is asymptotically optimal and show its convergence rate. We finally apply our heuristics to a numerical study and demonstrate the performance and robustness of the heuristics.

Managing a closed-loop supply system with random returns and a cyclic delivery schedule

Motivated by an industry example, we develop a mathematical framework to address the inventory replenishment and capacity planning problem for a closed-loop supply system with random returns. The provider needs to deliver new or refurbished products to a group of clients under a fixed cyclic schedule, and also collects back a random portion of the used products in the subsequent delivery cycle for refurbishment. We first address the product replenishment strategy, in which only a random portion of the delivered products will be returned for refurbishment and the supplier must regularly purchase new products to replace the lost units. We then analyze the capacity decision problem where the provider uses his facility to refurbish the returned products for reuse, and the provider could incur extra refurbishing cost to handle the returned product at the end of each cycle due to insufficient capacity. Our models provide a simple decision support tool for making effective replenishment and capacity decisions in managing such a closed-loop supply system.

Technology Choice and Capacity Portfolios under Emissions Regulation

We study the impact of emissions tax and emissions cap‐and‐trade regulation on a firm's technology choice and capacity decisions. We show that emissions price uncertainty under cap‐and‐trade results in greater expected profit than a constant emissions price under an emissions tax, which contradicts popular arguments that the greater uncertainty under cap‐and‐trade will erode value. We further show that two operational drivers underlie this result: (i) the firm's option not to operate, which effectively right‐censors the uncertain emissions price; and (ii) dispatch flexibility, which is the firm's ability to first deploy its most profitable capacity given the realized emissions price. In addition to these managerial insights, we also explore policy implications: the effect of emissions price level, and the effect of investment and production subsidies. Through an illustrative example, we show that production subsidies of higher investment and production cost technologies (such as carbon capture and storage technologies) have no effect on the firm's optimal total capacity when firms own a portfolio of both clean and dirty technologies, but that investment subsidies of these technologies increase the firm's total capacity, conditionally increasing expected emissions. A subsidy of a lower production cost technology, on the other hand, has no effect on the firm's optimal total capacity in multi‐technology portfolios, regardless of whether the subsidy is a production or investment subsidy.

Competitive Capacity Investment Under Uncertainty

We consider a long-term capacity investment problem in a competitive market under demand uncertainty. Two firms move sequentially in the competition and a firm’s capacity decision interacts with the other firm’s current and future capacity. Throughout the investment race, a firm can either choose to plan its investments proactively, taking into account possible responses from the other firm, or decide to respond reactively to the competition. In both cases, the optimal decision at each period is determined according to an ISD (Invest, Stayput, Disinvest) policy. We develop two algorithms to efficiently derive proactive ISD policies for the leader and follower firms. Using data from the container shipping market (2000-2015), we show that the optimal capacity determined by our competitive strategy is consistent with the realized investments in practice. By revealing strategical flexibility of proactive strategies, our results demonstrate that firms in the competition can gain more capacity and profit through such a strategy. Using Monte Carlo simulations, we explore the impact of different market conditions and investment irreversibility levels on capacity strategies. In particular, by comparing the results of competitive strategies and strategies that separate firms into different markets, we show that both firms can benefit from the competition and that market downturns likely lead to investment cascades.

Aggregate demand forecast with small data and robust capacity decision in TFT-LCD manufacturing

This study proposes a two-phase research framework to address the problem of capacity-demand mismatch in the high-tech industry. The first phase builds demand forecast models such as linear regression and autoregression models. It also models and employs the latent information (LI) function for generating the virtual data which benefits the data learning process of the neural network for predication enhancement. Based on the resulting forecast demand scenarios, the second phase focuses on the capacity decision and investigates the regrets of capacity surplus and capacity shortage. We compare the expected value (EV) solution, the minimax regret (MMR) approach, and the stochastic programming (SP) technique which support the capacity decision. We conduct an empirical study of a TFT-LCD firm to validate the proposed framework. From the results, we conclude that the proposed framework, in particular the SP technique, provides a robust capacity level addressing the problem of capacity-demand mismatch.

Option contracts: a solution for overloading problems in the delivery service supply chain

Owing to the limited service capacity of express delivery providers, most online retailers have to reject many orders during hot selling seasons. In this paper, we consider an express delivery service supply chain consisting of an express delivery provider and an online retailer whereby the selling season includes both regular periods and online sales periods. Utilizing a modified newsvendor model, we derive the express delivery provider’s optimal capacity decision and find that the overloading problem cannot be avoided because delivery service cannot be inventoried. To solve such a problem, we introduce an option contract to coordinate the supply chain. By allowing the online retailer to book the capacity, the express delivery provider can rent capacity from a third party in advance. Results show this approach can mitigate the problem significantly. We also extend our model to a supply chain consisting of a delivery provider and two retailers.

The aging caregiver with dementia: the issue of capacity decisions for a family member with intellectual disability

The issue of an aging caregiver and her ability to continue to assume responsibility for a family member with intellectual disability (ID) is in question when the caregiver is faced with her own illness. This point of view in the paper highlights the need for awareness of aging caregivers with dementia.

Building Blocks for Volume-oriented Changeability of Assets in Production Plants

Demand volatility and uncertainty in the business environment lead to an increasing relevance of volume-oriented changeability (VoC) for manufacturing companies. Strategic investment decisions are often based on forecasts and predictions, which more frequently fail to materialize due to obsolete assumptions or unpredictable events with extreme impact. If the production output fluctuates, fixed costs of production plants emerging from these investments result in high variance of unit costs, which has an impact on operational performance. Despite these demand and investment risks, managers on the strategic level must make capacity decisions without endangering the plant's performance both in growth and decline phases. Therefore, the paper conceptualizes building blocks for strategizing VoC of assets in production plants. These building blocks systemize capacity strategies for economical and dynamical up- and downscaling of production output. The paper depicts the impact on financial targets and analyzes contextual requirements and interdependencies with the organizational concept. By means of this decision support concept, managers of the production plant can select and combine interdisciplinary measures for developing an asset management strategy in the face of demand volatility and uncertainty.

The optimal resource portfolio under consumer choice and demand risk for vertically differentiated products

We study the optimal resource portfolio of a firm that sells two vertically differentiated products and utilizes resource flexibility and responsive pricing. We model this decision problem as a two-stage stochastic programming problem with recourse: In the first stage, the firm determines its resource mix and capacities so as to maximize the expected profit under demand uncertainty; in the second stage, uncertainty is resolved and the firm determines its production and pricing decision, constrained by its investment decision. We show that the objective function of this decision problem is not well-behaved (ie, it may have multiple local maxima). Using the concept of Pareto dominance, we reduce the feasible investment region, without loss of optimality, to one in which the objective function is well-behaved everywhere. This reduction allows us to derive the necessary and sufficient conditions for the optimal capacity decision and to gain insights.

The political economy of pricing and capacity decisions for congestible local public goods in a federal state

This paper studies the political economy of pricing and investment for excludable and congestible public goods in a federal state. Although the model applies to many local congestible public facilities (such as libraries, museums and public swimming facilities), our main motivation is the problem of providing and pricing road infrastructure in federal states. The two-region model we develop allows for spill-overs between regions, it takes into account congestion, and it captures demand heterogeneity both between and within regions. Regional decisions are taken by majority voting; federal decisions are taken by a minimum winning coalition in a legislature of regionally elected representatives. We have the following results. First, when users form the majority in at least one region, decentralized decision making performs certainly better than centralized decision making if spill-overs are not too large. Centralized decisions may yield higher welfare than decentralization only if users have a large majority and the infrastructure in a given region is intensively used by both local and outside users. Second, if non-users form a majority in both regions, centralized decision making and decentralized decision making yield the same socially undesirable outcome, with prices that are much too high. Third, the performance of decentralized supply is strongly enhanced by local self-financing rules; this prevents potential exploitation of users within regions.

Capacity Investment under Demand Uncertainty: The Role of Imports in the U.S. Cement Industry

Demand uncertainty is thought to influence irreversible capacity decisions. Suppose that local demand can be sourced from domestic (rigid) production or from (flexible) imports. This paper shows that the optimal domestic capacity is either increasing or decreasing with demand uncertainty, depending on the relative level of the costs of domestic production and imports. We test this relationship with data from the U.S. cement industry, in which the difference in marginal cost between domestic production and imports varies across local U.S. markets because cement is costly to transport over land. Industry data for 1999 to 2010 are consistent with the predictions of the model. The introduction of two technologies to the production set—one rigid and one flexible—is crucial to understanding the relationship between capacity choice and uncertainty in this industry because there is no relationship between these two variables in aggregated U.S. data. Our analysis reveals that the relationship is negative in coastal districts, and significantly more positive in landlocked districts.

Dynamic Capacity Management with General Upgrading

This paper studies a capacity management problem with upgrading. A firm needs to procure multiple classes of capacities and then allocate the capacities to satisfy multiple classes of customers that arrive over time. A general upgrading rule is considered, i.e., unmet demand can be satisfied using multistep upgrade. No replenishment is allowed and the firm has to make the allocation decisions without observing future demand. We first characterize the structure of the optimal allocation policy, which consists of parallel allocation and then sequential rationing. Specifically, the firm first uses capacity to satisfy the same-class demand as much as possible, then considers possible upgrading decisions in a sequential manner. We also propose a heuristic based on certainty equivalence control to solve the problem. Numerical analysis shows that the heuristic is fast and delivers close-to-optimal profit for the firm. Finally, we conduct extensive numerical studies to derive insights into the problem. It is found that under the proposed heuristic, the value of using sophisticated multistep upgrading can be quite significant; however, using simple approximations for the initial capacity leads to negligible profit loss, which suggests that the firm’s profit is not sensitive to the initial capacity decision if the optimal upgrading policy is used.

An empirical investigation of the relationship between workload and performance

Purpose – The purpose of this paper is to examine the effect of workload on quantitative and qualitative job performance. Different levels of workload can affect performance of employees, and it is important for firms to assess the effect of this in order to improve capacity decisions. The literature is not entirely clear on the relationship and calls for further empirical evidence on that matter. Design/methodology/approach – The study uses field data from a mid-sized grocery supplier. In total, 9,210 observations of 27 employees over three years and eight months are analyzed with different statistical models. Employees all work in the same department so that it is a very homogenous data set. Findings – Results show that there is an inverted U-shape relationship between workload and performance. Output of employees increases up to a certain point after which it decreases. Similarly, the quality of performance is highest under moderate levels of workload, which provides evidence against a tradeoff between quantity and quality. Research limitations/implications – The study uses a unique set of data from one firm, which limits generalizability, but adds to an important stream of literature. Practical implications – Results show how workload has a direct effect on performance. Consequently, firms need to balance the workload in order to be able to maximize the performance of their employees. Originality/value – Despite the relevance of the topic, there is hardly any empirical evidence on the relationship between workload and performance. This study thus contributes to the management literature and provides significant evidence on an inverted U-shape between workload and quantitative performance.

Railway crew capacity planning problem with connectivity of schedules

We study a tactical level crew capacity planning problem in railways which determines the minimum required crew size in a region while both feasibility and connectivity of schedules are maintained. We present alternative mathematical formulations which depend on network representations of the problem. A path-based formulation in the form of a set-covering problem along with a column-and-row generation algorithm is proposed. An arc-based formulation of the problem is solved with a commercial linear programming solver. The computational study illustrates the effect of schedule connectivity on crew capacity decisions and shows that arc-based formulation is a viable approach.

An integrated shipment planning and storage capacity decision under uncertainty

Purpose – In transportation and distribution systems, the shipment decisions, fleet capacity, and storage capacity are interrelated in a complex way, especially when the authors take into account uncertainty of the demand rate and shipment lead time. While shipment planning is tactical or operational in nature, increasing storage capacity often requires top management’s authority. The purpose of this paper is to present a new method to integrate both operational and strategic decision parameters, namely shipment planning and storage capacity decision under uncertainty. The ultimate goal is to provide a near optimal solution that leads to a striking balance between the total logistics costs and product availability, critical in maritime logistics of bulk shipment of commodity items. Design/methodology/approach – The authors use simulation as research method. The authors develop a simulation model to investigate the effects of various factors on costs and service levels of a distribution system. The model mimics the transportation and distribution problems of bulk cement in a major cement company in Indonesia consisting of a silo at the port of origin, two silos at two ports of destination, and a number of ships that transport the bulk cement. The authors develop a number of “what-if” scenarios by varying the storage capacity at the port of origin as well as at the ports of destinations, number of ships operated, operating hours of ports, and dispatching rules for the ships. Each scenario is evaluated in terms of costs and service level. A full factorial experiment has been conducted and analysis of variance has been used to analyze the results. Findings – The results suggest that the number of ships deployed, silo capacity, working hours of ports, and the dispatching rules of ships significantly affect both total costs and service level. Interestingly, operating fewer ships enables the company to achieve almost the same service level and gaining substantial cost savings if constraints in other part of the system are alleviated, i.e., storage capacities and working hours of ports are extended. Practical implications – Cost is a competitive factor for bulk items like cement, and thus the proposed scenarios could be implemented by the company to substantially reduce the transportation and distribution costs. Alleviating storage capacity constraint is obviously an idea that needs to be considered when optimizing shipment planning alone could not give significant improvements. Originality/value – Existing research has so far focussed on the optimization of shipment planning/scheduling, and considers shipment planning/scheduling as the objective function while treating the storage capacity as constraints. The simulation model enables “what-if” analyses to be performed and has overcome the difficulties and impracticalities of analytical methods especially when the system incorporates stochastic variables exhibited in the case example. The use of efficient frontier analysis for analyzing the simulation results is a novel idea which has been proven to be effective in screening non-dominated solutions. This has provided the authors with near optimal solutions to trade-off logistics costs and service levels (availability), with minimal experimentation times.

Analysis of production systems with potential for severe disruptions

Organizations often have to make production capacity decisions in a setting where production disruptions occur. This presents managers with a combination of strategic capacity decisions and operational inventory management options to manage disruptions. This paper uses Bayesian methods to analyze operational data where data on parameters required in logistics models are unavailable, then models production and inventory management in systems that have the potential for major disruptions. The produce-to-stock with production disruptions model is applicable to systems where the decision on production rate is coupled with the setting of the base stock level when production disruptions are possible. The model is applied to a proposed food processing facility at a correctional institution that is subject to disruptions due to safety and security issues.

Dynamic Capacity Management with General Upgrading

This paper studies a capacity management problem with upgrading. A firm needs to procure multiple classes of capacities and then allocate the capacities to satisfy multiple classes of customers that arrive over time. A general upgrading rule is considered, i.e., unmet demand can be satisfied using multi-step upgrade. No replenishment is allowed and the firm has to make the allocation decisions without observing future demand. We first characterize the structure of the optimal allocation policy, which consists of parallel allocation and then sequential rationing. Specifically, the firm first uses capacity to satisfy the same-class demand as much as possible, then considers possible upgrading decisions in a sequential manner. We also propose a heuristic based on certainty equivalence control to solve the problem. Numerical analysis shows that the heuristic is fast and delivers close-to-optimal profit for the firm. Finally, we conduct extensive numerical studies to derive insights into the problem. It is found that under the proposed heuristic, the value of using sophisticated multi-step upgrading can be quite significant; however, using simple approximations for the initial capacity leads to negligible profit loss, which suggests that the firm's profit is not sensitive to the initial capacity decision if the optimal upgrading policy is used.

StratBAM: A Discrete-Event Simulation Model to Support Strategic Hospital Bed Capacity Decisions.

The ability to accurately measure and assess current and potential health care system capacities is an issue of local and national significance. Recent joint statements by the Institute of Medicine and the Agency for Healthcare Research and Quality have emphasized the need to apply industrial and systems engineering principles to improving health care quality and patient safety outcomes. To address this need, a decision support tool was developed for planning and budgeting of current and future bed capacity, and evaluating potential process improvement efforts. The Strategic Bed Analysis Model (StratBAM) is a discrete-event simulation model created after a thorough analysis of patient flow and data from Geisinger Health System's (GHS) electronic health records. Key inputs include: timing, quantity and category of patient arrivals and discharges; unit-level length of care; patient paths; and projected patient volume and length of stay. Key outputs include: admission wait time by arrival source and receiving unit, and occupancy rates. Electronic health records were used to estimate parameters for probability distributions and to build empirical distributions for unit-level length of care and for patient paths. Validation of the simulation model against GHS operational data confirmed its ability to model real-world data consistently and accurately. StratBAM was successfully used to evaluate the system impact of forecasted patient volumes and length of stay in terms of patient wait times, occupancy rates, and cost. The model is generalizable and can be appropriately scaled for larger and smaller health care settings.

Point‐of‐Dispensing Location and Capacity Optimization via a Decision Support System

Dispensing of mass prophylaxis can be critical to public health during emergency situations and involves complex decisions that must be made in a short period of time. This study presents a model and solution approach for optimizing point‐of‐dispensing (POD) location and capacity decisions. This approach is part of a decision support system designed to help officials prepare for and respond to public health emergencies. The model selects PODs from a candidate set and suggests how to staff each POD so that average travel and waiting times are minimized. A genetic algorithm (GA) quickly solves the problem based on travel and queuing approximations (QAs) and it has the ability to relax soft constraints when the dispensing goals cannot be met. We show that the proposed approach returns solutions comparable with other systems and it is able to evaluate alternative courses of action when the resources are not sufficient to meet the performance targets.

Manufacturing Capacity Decisions with Demand Uncertainty and Tax Cross-Crediting

The U.S. tax law taxes the global income of multinational firms (MNFs) at their home country tax rate. To avoid double taxation, it permits tax cross-crediting. Through this strategy, global firms can use excess foreign tax credits (FTCs), the portion of foreign tax payments that exceed their home country tax liabilities, generated from a subsidiary located in a high-tax country to offset the tax liabilities of their low-tax divisions. This paper studies manufacturing capacity decisions in the subsidiary of an MNF with tax cross-crediting. Casting the problem on a newsvendor model, and assuming the objective of maximizing the global firm’s worldwide after-tax profits, we show that the optimal capacity decision under the effects of tax cross-crediting can behave very differently from that of the traditional newsvendor model. In particular, we show that an improvement in the firm’s after-tax profitability (through tax cross-crediting, an increased profit margin, or a reduced tax rate) might reduce the optimal capacity and that the optimal capacity decision under certain circumstances can be made without the knowledge of the demand distribution. We also discuss the issue of motivating the division manager to use an after-tax performance measure with a managerial tax rate.