Equipment replacement under technological change

For infinite-horizon replacement economy problems it is common practice to truncate the problem at some finite horizon. We develop bounds on the error due to such a truncation. These bounds differ from previous results in that they include both revenues and costs. Bounds are illustrated through a numerical example from a real case in vehicle replacement. © 1994 John Wiley & Sons, Inc.     

On estimating population characteristics from record-breaking observations II. Nonparametric results

Consider an experiment in which only record-breaking values (e.g., values smaller than all previous ones) are observed. The data available may be represented as X₁,K₁,X₂,K₂, …, where X₁,X₂, … are successive minima and K₁,K₂, … are the numbers of trials needed to obtain new records. Such data arise in life testing and stress testing and in industrial quality-control experiments. When only a single sequence of random records are available, efficient estimation of the underlying distribution F is possible only in a parametric framework (see Samaniego and Whitaker [9]). In the present article we study the problem of estimating certain population quantiles nonparametrically from such data. Furthermore, under the assumption that the process of observing random records can be replicated, we derive and study the nonparametric maximum-likelihood estimator F̂ of F. We establish the strong uniform consistency of this estimator as the number of replications grows large, and identify its asymptotic distribution theory. The performance of F̂ is compared to that of two possible competing estimators.     

The LP/POMDP marriage: Optimization with imperfect information

A new technique for solving large‐scale allocation problems with partially observable states and constrained action and observation resources is introduced. The technique uses a master linear program (LP) to determine allocations among a set of control policies, and uses partially observable Markov decision processes (POMDPs) to determine improving policies using dual prices from the master LP. An application is made to a military problem where aircraft attack targets in a sequence of stages, with information acquired in one stage being used to plan attacks in the next. © 2000 John Wiley & Sons, Inc., Naval Research Logistics 47: 607–619, 2000     

A note on “resource flexibility with responsive pricing”

We revisit the capacity investment decision problem studied in the article “Resource Flexibility with Responsive Pricing” by Chod and Rudi [Operations Research 53, (2005) 532–548]. A monopolist firm producing two dependent (substitutable or complementary) products needs to determine the capacity of one flexible resource under demand risk so as to maximize its expected profit. Product demands are linear functions of the prices of both products, and the market potentials are random and correlated. We perform a comparative statics analysis on how demand variability and correlation impact the optimal capacity and the resulting expected profit. In particular, C&R study this problem under the following assumptions/approximations: (i) demand intercepts follow a bivariate Normal distribution; (ii) demand uncertainty is of an additive form; (iii) and under approximate expressions for the optimal capacity and optimal expected profit. We revisit Propositions 2, 3, 4, 5, and 10 of C&R without these assumptions and approximations, and show that these results continue to hold (i) for the exact expressions for the optimal expected profit and optimal capacity, and (ii) under any arbitrary continuous distribution of demand intercepts. However, we also show that the additive demand uncertainty is a critical assumption for the C&R results to hold. In particular, we provide a case of multiplicative uncertainty under which the C&R results (Propositions 2 and 3) fail. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010     

Revenue management with aircraft reassignment flexibility

A well‐studied problem in airline revenue management is the optimal allocation of seat inventory among different fare‐classes, given a capacity for the flight and a demand distribution for each class. In practice, capacity on a flight does not have to be fixed; airlines can exercise some flexibility on the supply side by swapping aircraft of different capacities between flights as partial booking information is gathered. This provides the airline with the capability to more effectively match their supply and demand. In this paper, we study the seat inventory control problem considering the aircraft swapping option. For theoretical and practical purposes, we restrict our attention to the class of booking limit policies. Our analytical results demonstrate that booking limits considering the swapping option can be considerably different from those under fixed capacity. We also show that principles on the relationship between the optimal booking limits and demand characteristics (size and risk) developed for the fixed‐capacity problem no longer hold when swapping is an option. We develop new principles and insights on how demand characteristics affect the optimal booking limits under the swapping possibility. We also develop an easy to implement heuristic for determining the booking limits under the swapping option and show, through a numerical study, that the heuristic generates revenues close to those under the optimal booking limits. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Capacity expansion under a service‐level constraint for uncertain demand with lead times

For a service provider facing stochastic demand growth, expansion lead times and economies of scale complicate the expansion timing and sizing decisions. We formulate a model to minimize the infinite horizon expected discounted expansion cost under a service‐level constraint. The service level is defined as the proportion of demand over an expansion cycle that is satisfied by available capacity. For demand that follows a geometric Brownian motion process, we impose a stationary policy under which expansions are triggered by a fixed ratio of demand to the capacity position, i.e., the capacity that will be available when any current expansion project is completed, and each expansion increases capacity by the same proportion. The risk of capacity shortage during a cycle is estimated analytically using the value of an up‐and‐out partial barrier call option. A cutting plane procedure identifies the optimal values of the two expansion policy parameters simultaneously. Numerical instances illustrate that if demand grows slowly with low volatility and the expansion lead times are short, then it is optimal to delay the start of expansion beyond when demand exceeds the capacity position. Delays in initiating expansions are coupled with larger expansion sizes. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

A theoretical and computational comparison of “equivalent” mixed-integer formulations

This paper provides a theoretical and computational comparison of alternative mixed integer programming formulations for optimization problems involving certain types of economy-of-scale functions. Such functions arise in a broad range of applications from such diverse areas as vendor selection and communications network design. A “nonstandard” problem formulation is shown to be superior in several respects to the traditional formulation of problems in this class.     

Dynamic multiattribute models for mixed manpower systems

This paper reviews a wide variety of manpower and personnel models of the goal programming variety. This is done from a strategy-oriented point of view addressing the problems of interest for immediate implementation as well as basic problems of manpower model research development. Particular emphasis in this paper is concerned with how analytical models can be brought to bear on the problems of combining military and civilian manpower into one management system. This includes a discussion of the computer support arrangements necessary to implement the models. First, we discuss an extension of multilevel models to provide an integrated approach to program planning which includes the dynamics of the manpower requirements-inventory relationships of mixed military-civilian manpower systems. Then, focus is given to some of the potential Navy applications particularly in terms of ways the outputs from the global multilevel model might be interfaced with assignment models for operational planning. The paper concludes with a discussion of static and dynamic multiattribute assignment models which operate on the individual man-job matching level. It is at this level of detail that dynamic mixed manpower systems might be constructed for use in equal employment opportunity planning and for local organization design studies.