Jan A. Van Mieghem

Commissioned Paper: Capacity Management, Investment, and Hedging: Review and Recent Developments

This paper reviews the literature on strategic capacity management concerned with determining the sizes, types, and timing of capacity investments and adjustments under uncertainty. Specific attention is given to recent developments to incorporate multiple decision makers, multiple capacity types, hedging, and risk aversion. Capacity is a measure of processing abilities and limitations and is represented as a vector of stocks of various processing resources, while investment is the change of capacity and includes expansion and contraction. After discussing general issues in capacity investment problems, the paper reviews models of capacity investment under uncertainty in three settings:The first reviews optimal capacity investment by single and multiple risk-neutral decision makers in a stationary environment where capacity remains constant. Allowing for multiple capacity types, the associated optimal capacity portfolio specifies the amounts and locations of safety capacity in a processing network. Its key feature is that it is unbalanced; i.e., regardless of how uncertainties are realized, one typically will never fully utilize all capacities. The second setting reviews the adjustment of capacity over time and the structure of optimal investment dynamics. The paper ends by reviewing how to incorporate risk aversion in capacity investment and contrasts hedging strategies involving financial versus operational means.

Multi-Resource Investment Strategies: Operational Hedging Under Demand Uncertainty

Consider a firm that markets multiple products, each manufactured using several resources representing various types of capital and labor, and a linear production technology. The firm faces uncertain product demand and has the option to dynamically readjust its resource investment levels, thereby changing the capacities of its linear manufacturing process. The cost to adjust a resource level either up or down is assumed to be linear. The model developed here explicitly incorporates both capacity investment decisions and production decisions, and is general enough to include reversible and irreversible investment. The product demand vectors for successive periods are assumed to be independent and identically distributed. The optimal investment strategy is determined with a multi-dimensional newsvendor model using demand distributions, a technology matrix, prices (product contribution margins), and marginal investment costs. Our analysis highlights an important conceptual distinction between deterministic and stochastic environments: the optimal investment strategy in our stochastic model typically involves some degree of capacity imbalance which can never be optimal when demand is known.

Risk Mitigation in Newsvendor Networks: Resource Diversification, Flexibility, Sharing, and Hedging

This paper studies how judicious resource allocation in networks mitigates risk. Theory is presented for general utility functions and mean-variance formulations and is illustrated with networks featuring resource diversification, flexibility (e.g., inventory substitution), and sharing (commonality). In contrast to single-resource settings, risk-averse newsvendors may invest more in networks than risk-neutral newsvendors: some resources and even total spending may exceed risk-neutral levels. With normally distributed demand, risk-averse newsvendors change resource levels roughly proportionally to demand variance, while risk-neutral agents adjust only proportionally to standard deviation. Two effects explain this operational hedge and suggest rules of thumb for strategic placement of safety capacity and inventory in networks: (1) Risk pooling suggests rebalancing capacity toward inexpensive resources that serve lower-profit variance markets. This highlights the role of profit variance (instead of demand variance) in risk-averse network investment. (2) Ex post revenue maximization suggests rebalancing capacity toward substitutable flexible but away from shared capacity when markets differ in profitability. Capacity imbalance and allocation flexibility thus mitigate profit risk and truly are operational hedges.

Operational Flexibility and Financial Hedging: Complements or Substitutes?

We consider a firm that invests in capacity under demand uncertainty and thus faces two related but distinct types of risk: mismatch between capacity and demand and profit variability. Whereas mismatch risk can be mitigated with greater operational flexibility, profit variability can be reduced through financial hedging. We show that the relationship between these two risk mitigating strategies depends on the type of flexibility: Product flexibility and financial hedging tend to be complements (substitutes)---i.e., product flexibility tends to increase (decrease) the value of financial hedging, and, vice versa, financial hedging tends to increase (decrease) the value of product flexibility---when product demands are positively (negatively) correlated. In contrast to product flexibility, postponement flexibility is a substitute to financial hedging as intuitively expected. Although our analytical results assume perfect flexibility and perfect hedging and rely on a linear approximation of the value of hedging, we validate their robustness in an extensive numerical study.

Global Dual Sourcing: Tailored Base-Surge Allocation to Near-and Offshore Production

When designing a sourcing strategy in practice, a key task is to determine the average order rates placed to each source because that affects cost and supplier management. We consider a firm that has access to a responsive nearshore source (e.g., Mexico) and a low-cost offshore source (e.g., China). The firm must determine an inventory sourcing policy to satisfy random demand over time. Unfortunately, the optimal policy is too complex to allow a direct answer to our key question. Therefore, we analyze a tailored base-surge (TBS) sourcing policy that is simple, used in practice, and captures the classic trade-off between cost and responsiveness. The TBS policy combines push and pull controls by replenishing at a constant rate from the offshore source and producing at the nearshore plant only when inventory is below a target. The constant base allocation allows the offshore facility to focus on cost efficiency, whereas the nearshore facilitys quick response capability is utilized only dynamically to guarantee high service. The research goals are to (i) determine the allocation of random demand into base and surge capacity, (ii) estimate corresponding working capital requirements, and (iii) identify and value the key drivers of dual sourcing. We present performance bounds on the optimal cost and prove that economic optimization brings the system into heavy traffic. We analyze the sourcing policy that is asymptotically optimal for high-volume systems and present a simple “square-root” formula that is insightful to answer our questions and sufficiently accurate for practice, as is demonstrated with a validation study.

Optimal Flexibility Configurations in Newsvendor Networks: Going Beyond Chaining and Pairing

We study the classical problem of capacity and flexible technology selection with a newsvendor network model of resource portfolio investment. The resources differ by their level of flexibility, where “level-k flexibility” refers to the ability to process k different product types. We present an exact set-theoretic methodology to analyze newsvendor networks with multiple products and parallel resources. This simple approach is sufficiently powerful to prove that (i) flexibility exhibits decreasing returns and (ii) the optimal portfolio will invest in at most two, adjacent levels of flexibility in symmetric systems, and to characterize (iii) the optimal flexibility configuration for asymmetric systems as well. The optimal flexibility configuration can serve as a theoretical performance benchmark for other configurations suggested in the literature. For example, although chaining is not optimal in our setting, the gap is small and the inclusion of scale economies quickly favors chaining over pairing. We also demonstrate how this methodology can be applied to other settings such as product substitution and queuing systems with parameter uncertainty.

Strategically Seeking Service: How Competition Can Generate Poisson Arrivals

We consider a simple game in which strategic agents select arrival times to a service facility. Agents find congestion costly and, hence, try to arrive when the system is underutilized. Working in discrete time, we characterize pure-strategy Nash equilibria for the case of ample service capacity. In this case, agents try to spread themselves out as much as possible and their self-interested actions will lead to a socially optimal outcome if all agents have the same well-behaved delay cost function. For even modest sized problems, the set of possible pure-strategy Nash equilibria is quite large, making implementation potentially cumbersome. We consequently examine mixed-strategy Nash equilibria and show that there is a unique symmetric Nash equilibrium. Not only is this equilibrium independent of the number of agents and their individual delay cost functions, the arrival pattern it generates approaches a discrete-time Poisson process as the number of agents and arrival points gets large. Our results extend to the case of time varying preferences. With an appropriate initialization, the results also extend to a system with limited capacity. Our model lends support to the traditional literature on managing service systems. This work has generally ignored customers strategically choosing arrival times. Rather it is commonly assumed that customers seek service according to some well-behaved process (e.g., that interarrival times follow a renewal process). We show that assuming Poisson arrivals is an acceptable assumption even with strategic customers if the population is large and the horizon is long.

Multimarket Facility Network Design with Offshoring Applications

Moving production to low-wage countries may reduce manufacturing costs, but it increases logistics costs and is subject to foreign trade barriers, among others. This paper studies a manufacturers multimarket facility network design problem and investigates the offshoring decision from a network capacity investment perspective. We analyze a firm that manufactures two products to serve two geographically separated markets using a common component and two localized final assemblies. The common part can be transported between the two markets that have different economic and demand characteristics. Two strategic network design questions arise naturally: (1) Should the common part be produced centrally or in two local facilities? (2) If a centralization strategy is adopted, in which market should the facility be located? We present a transportation cost threshold that captures costs, revenues, and demand risks, and below which centralization is optimal. The optimal location of commonality crucially depends on the relative magnitude of price and manufacturing cost differentials but also on demand size and uncertainty. Incorporating scale economies further enlarges the centralizations optimality region.

A Little Flexibility Is All You Need: On the Asymptotic Value of Flexible Capacity in Parallel Queuing Systems

We analytically study optimal capacity and flexible technology selection in parallel queuing systems. We consider N stochastic arrival streams that may wait in N queues before being processed by one of many resources technologies that differ in their flexibility. A resources ability to process k different arrival types or classes is referred to as level-k flexibility. We determine the capacity portfolio consisting of all resources at all levels of flexibility that minimizes linear capacity and linear holding costs in high-volume systems where the arrival rate λ → ∞. We prove that “a little flexibility is all you need”: the optimal portfolio invests Oλ in specialized resources and only O√λ in flexible resources and these optimal capacity choices bring the system into heavy traffic. Further, considering symmetric systems with type-independent parameters, a novel “folding” methodology allows the specification of the asymptotic queue count process for any capacity portfolio under longest-queue scheduling in closed form that is amenable to optimization. This allows us to sharpen “a little flexibility is all you need”: the asymptotically optimal flexibility configuration for symmetric systems with mild economies of scope invests a lot in specialized resources but only a little in flexible resources and only in level-2 flexibility, but effectively nothing o√λ in level-k > 2 flexibility. We characterize “tailored pairing” as the theoretical benchmark configuration that maximizes the value of flexibility when demand and service uncertainty are the main concerns.

Global Dual Sourcing and Order Smoothing: The Impact of Capacity and Lead Times

After decades of offshoring production across the world, companies are rethinking their global networks. Local sourcing is receiving more attention, but it remains challenging to balance the offshore sourcing cost advantage against the increased inventories, because of its longer lead time, and against the cost and volume flexibility of each sources capacity. To guide strategic allocation in this global network decision, this paper establishes reasonably simple prescriptions that capture the key drivers. We adopt a conventional discrete-time inventory model with a linear control rule that smoothes orders and allows an exact and analytically tractable analysis of single-and dual-sourcing policies under normal demand. Distinguishing features of our model are that it captures each sources lead time, capacity cost, and flexibility to work overtime. We use Lagranges inversion theorem to provide exact and simple square-root bound formulae for the strategic sourcing allocations and the value of dual sourcing. The formulae provide structural insight on the impact of financial, operational, and demand parameters, and a starting point for quantitative decision making. We investigate the robustness of our results by comparing the smoothing policy with existing single-and dual-sourcing models in a simulation study that relaxes model assumptions. This paper was accepted by Yossi Aviv, operations management.