Search and the introduction of improved technologies

Modeling R&D as standard sequential search, we consider a monopolist who can implement a sequence of technological discoveries during the technology search process: he earns revenue on his installed technology while he engages in R&D to find improved technology. What is not standard is that he has a finite number of opportunities to introduce improved technology. We show that his optimal policy is characterized by thresholds ξ_i(x): introduce the newly found technology if and only if it exceeds ξ_i(x) when x is the state of the currently installed technology and i is the number of remaining introductions allowed. We also analyze a nonstationary learning‐by‐doing model in which the monopolist's experience in implementing new technologies imparts increased capability in generating new technologies. Because this nonstationary model is not in the class of monotone stopping problems, a number of surprising results hold and several seemingly obvious properties of the stationary model no longer hold. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Allocating capacity in parallel queues to improve their resilience to deliberate attack

We develop models that lend insight into how to design systems that enjoy economies of scale in their operating costs, when those systems will subsequently face disruptions from accidents, acts of nature, or an intentional attack from a well‐informed attacker. The systems are modeled as parallel M/M/1 queues, and the key question is how to allocate service capacity among the queues to make the system resilient to worst‐case disruptions. We formulate this problem as a three‐level sequential game of perfect information between a defender and a hypothetical attacker. The optimal allocation of service capacity to queues depends on the type of attack one is facing. We distinguish between deterministic incremental attacks, where some, but not all, of the capacity of each attacked queue is knocked out, and zero‐one random‐outcome (ZORO) attacks, where the outcome is random and either all capacity at an attacked queue is knocked out or none is. There are differences in the way one should design systems in the face of incremental or ZORO attacks. For incremental attacks it is best to concentrate capacity. For ZORO attacks the optimal allocation is more complex, typically, but not always, involving spreading the service capacity out somewhat among the servers. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Capacity allocation with traditional and Internet channels

In this paper we study a capacity allocation problem for two firms, each of which has a local store and an online store. Customers may shift among the stores upon encountering a stockout. One question facing each firm is how to allocate its finite capacity (i.e., inventory) between its local and online stores. One firm's allocation affects the decision of the rival, thereby creating a strategic interaction. We consider two scenarios of a single‐product single‐period model and derive corresponding existence and stability conditions for a Nash equilibrium. We then conduct sensitivity analysis of the equilibrium solution with respect to price and cost parameters. We also prove the existence of a Nash equilibrium for a generalized model in which each firm has multiple local stores and a single online store. Finally, we extend the results to a multi‐period model in which each firm decides its total capacity and allocates this capacity between its local and online stores. A myopic solution is derived and shown to be a Nash equilibrium solution of a corresponding “sequential game.” © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

The equivalence of general set-covering and implicit integer programming formulations for shift scheduling

In a recent article we demonstrated that implicit optimal modeling for shift scheduling (P2) has inherent size and execution time advantages over the general set-covering formulation for shift scheduling (P1) [11, 13]. We postulated that the absence of extraordinary overlap (EO) was a requirement for the equivalence of P1 and P2. We have defined EO as the condition in which the earliest and latest starts for a break in one shift are earlier and later than the earliest and latest starts for a break in any other shift(s). In this article, we prove that our earlier postulate was accurate. Additionally, we discuss research extensions and note other scheduling problems for which implicit modeling may be appropriate. © 1996 John Wiley & Sons, Inc.     

Restricted planar location problems and applications

Facility location problems in the plane are among the most widely used tools of Mathematical Programming in modeling real-world problems. In many of these problems restrictions have to be considered which correspond to regions in which a placement of new locations is forbidden. We consider center and median problems where the forbidden set is a union of pairwise disjoint convex sets. As applications we discuss the assembly of printed circuit boards, obnoxious facility location and the location of emergency facilities. © 1995 John Wiley & Sons, Inc.     

A stochastic air combat logistics decision model for Blue versus Red opposition

Technologically advanced aircraft rely on robust and responsive logistics systems to ensure a high state of operational readiness. This paper fills a critical gap in the literature for combat models by closely relating effectiveness of the logistics system to determinants of success in combat. We present a stochastic diffusion model of an aerial battle between Blue and Red forces. The number of aircraft of Blue forces aloft and ready to be aloft on combat missions is limited by the maximum number of assigned aircraft, the reliability of aircraft subsystems, and the logistic system's ability to repair and replenish those subsystems. Our parsimonious model can illustrate important trade‐offs between logistics decision variables and operational success.