Two‐dimensional failure modeling with minimal repair

In this paper, we discuss two‐dimensional failure modeling for a system where degradation is due to age and usage. We extend the concept of minimal repair for the one‐dimensional case to the two‐dimensional case and characterize the failures over a two‐dimensional region under minimal repair. An application of this important result to a manufacturer's servicing costs for a two‐dimensional warranty policy is given and we compare the minimal repair strategy with the strategy of replacement of failure. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Dichotomous categorical variable formation in mathematical programming discriminant analysis models

Classification models, whether generated by statistical techniques or mathematical programming (MP) discriminant analysis methods, are often simplified by ad hoc formation of dichotomous categorical variables from the original variables with, for example, a dichotomous variable taking value 1 if the original variable is above a threshold level and 0 otherwise. In this paper an MP discriminant analysis method is developed for forming dichotomous categorical variables in problems with discriminant functions that are monotone in the original variables. For each of the original variables from which dichotomous variables may be formed, a set of possible threshold levels for dichotomous variable formation is defined. An MP model is then used to determine both the threshold level for forming each dichotomous variable and the associated discriminant function coefficient. The proposed MP approach is applied to a published problem and a number of simulated problem sets. It is shown that the discriminant functions in dichotomous categorical variables generated by this new MP approach can in some cases outperform the functions generated by standard MP discriminant analysis models using the original variables. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

A robust policy for serial agile production systems

One of the major problems in modeling production systems is how to treat the job arrival process. Restrictive assumptions such as Markovian arrivals do not represent real world systems, especially if the arrival process is generated by job departures from upstream workstations. Under these circumstances, cost‐effective policies that are robust with respect to the nature of the arrival process become of interest. In this paper, we focus on minimizing the expected total holding and setup costs in a two‐stage produce‐to‐order production system operated by a cross‐trained worker. We will show that if setup times are insignificant in comparison with processing times, then near‐optimal policies can be generated with very robust performances with respect to the arrival process. We also present conditions under which these near‐optimal policies can be obtained by using only the arrival and service rates. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

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     

A note on the optimality of index priority rules for search and sequencing problems

We show that the linear objective function of a search problem can be generalized to a power function and/or a logarithmic function and still be minimized by an index priority rule. We prove our result by solving the differential equation resulting from the required invariance condition, therefore, we also prove that any other generalization of this linear objective function will not lead to an index priority rule. We also demonstrate the full equivalence between two related search problems in the sense that a solution to either one can be used to solve the other one and vice versa. Finally, we show that the linear function is the only function leading to an index priority rule for the single‐machine makespan minimization problem with deteriorating jobs and an additive job deterioration function. © 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 Banzhaf value and communication situations

Myerson 3 and 4 proposed and characterized a modification of the Shapley value in the context of communication situations. In this paper we propose several characterizations of the extension of the Banzhaf value proposed by Owen 7 to communication situations. In particular we characterize this value with the properties of fairness, isolation, and pairwise merging. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Vertically restrictive pricing in supply chains with price‐dependent demand

We examine the behavior of a manufacturer and a retailer in a decentralized supply chain under price‐dependent, stochastic demand. We model a retail fixed markup (RFM) policy, which can arise as a form of vertically restrictive pricing in a supply chain, and we examine its effect on supply chain performance. We prove the existence of the optimal pricing and replenishment policies when demand has a linear additive form and the distribution of the uncertainty component has a nondecreasing failure rate. We numerically compare the relative performance of RFM to a price‐only contract and we find that RFM results in greater profit for the supply chain than the price‐only contract in a variety of scenarios. We find that RFM can lead to Pareto‐improving solutions where both the supplier and the retailer earn more profit than under a price‐only contract. Finally, we compare RFM to a buyback contract and explore the implications of allowing the fixed markup parameter to be endogenous to the model. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006.