Note: Facility location with closest rectangular distances

This paper considers the problem of locating one or more new facilities on a continuous plane, where the destinations or customers, and even the facilities, may be represented by areas and not points. The objective is to locate the facilities in order to minimize a sum of transportation costs. What is new in this study is that the relevant distances are the distances from the closest point in the facility to the closest point in the demand areas. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 77–84, 2000     

Heuristics for the multi‐resource generalized assignment problem

The well‐known generalized assignment problem (GAP) involves the identification of a minimum‐cost assignment of tasks to agents when each agent is constrained by a resource in limited supply. The multi‐resource generalized assignment problem (MRGAP) is the generalization of the GAP in which there are a number of different potentially constraining resources associated with each agent. This paper explores heuristic procedures for the MRGAP. We first define a three‐phase heuristic which seeks to construct a feasible solution to MRGAP and then systematically attempts to improve the solution. We then propose a modification of the heuristic for the MRGAP defined previously by Gavish and Pirkul. The third procedure is a hybrid heuristic that combines the first two heuristics, thus capturing their relative strengths. We discuss extensive computational experience with the heuristics. The hybrid procedure is seen to be extremely effective in solving MRGAPs, generating feasible solutions to more than 99% of the test problems and consistently producing near‐optimal solutions. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 468–483, 2001     

Determining restrictive goals in linear goal programs

Goal programming is a method for solving problems having multiple, conflicting objectives. Information on the characteristics of the goals can help in setting goal weights and levels, determining priority levels, and in conducting postoptimality analysis. One characteristic affecting the outcome of a goal program is the restrictiveness of a goal. A restrictive goal is one whose inclusion in the goal set most degrades the value of the total objective function, or the attainment of the remaining goals. An algorithm is presented that determines restrictive goals.     

A vertex-closing approach to the p-center problem

This article uses a vertex-closing approach to investigate the p-center problem. The optimal set of vertices to close are found in imbedded subgraphs of the original graph. Properties of these subgraphs are presented and then used to characterize the optimal solution, to establish a priori upper and lower bounds, to establish refined lower bounds, and to verify the optimality of solutions. These subgraphs form the foundation of two polynomial algorithms of complexity O(|E| log |E|) and O(|E|²). The algorithms are proven to converge to an optimum for special cases, and computational evidence is provided which suggests that they produce very good solutions more generally. Both algorithms perform very well on problems where p is large relative to the number of vertices n, specifically, when p/n ≥ 0.30. One of the algorithms is especially efficient for solving a sequence of problems on the same graph.     

Two‐machine flow shop scheduling with common due window to minimize weighted number of early and tardy jobs

This article studies two due window scheduling problems to minimize the weighted number of early and tardy jobs in a two‐machine flow shop, where the window size is externally determined. These new scheduling models have many practical applications in real life. However, results on these problems have rarely appeared in the literature because of a lack of structural and optimality properties for solving them. In this article, we derive several dominance properties and theorems, including elimination rules and sequencing rules based on Johnsos order, lower bounds on the penalty, and upper bounds on the window location, which help to significantly trim the search space for the problems. We further show that the problems are NP‐hard in the ordinary sense only. We finally develop efficient pseudopolynomial dynamic programming algorithms for solving the problems. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Scheduling multiple products on parallel machines with setup costs

We consider a class of production scheduling models with m identical machines in parallel and k different product types. It takes a time p_i to produce one unit of product type i on any one of the machines. There is a demand stream for product type i consisting of n_i units with each unit having a given due date. Before a machine starts with the production of a batch of products of type i a setup cost c is incurred. We consider several different objective functions. Each one of the objective functions has three components, namely a total setup cost, a total earliness cost, and a total tardiness cost. In our class of problems we find a relatively large number of problems that can be solved either in polynomial time or in pseudo‐polynomial time. The polynomiality or pseudo‐polynomiality is achieved under certain special conditions that may be of practical interest; for example, a regularity pattern in the string of due dates combined with earliness and tardiness costs that are similar for different types of products. The class of models we consider includes as special cases discrete counterparts of a number of inventory models that have been considered in the literature before, e.g., Wagner and Whitin (Manage Sci 5 (1958), 89–96) and Zangwill (Oper Res 14 (1966), 486–507; Manage Sci 15 (1969), 506–527). © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Scheduling parallel machines with inclusive processing set restrictions

We consider the problem of assigning a set of jobs to different parallel machines of the same processing speed, where each job is compatible to only a subset of those machines. The machines can be linearly ordered such that a higher‐indexed machine can process all those jobs that a lower‐indexed machine can process. The objective is to minimize the makespan of the schedule. This problem is motivated by industrial applications such as cargo handling by cranes with nonidentical weight capacities, computer processor scheduling with memory constraints, and grades of service provision by parallel servers. We develop an efficient algorithm for this problem with a worst‐case performance ratio of + ε, where ε is a positive constant which may be set arbitrarily close to zero. We also present a polynomial time approximation scheme for this problem, which answers an open question in the literature. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Factors that affect the optimal amount of central control in complex systems

Whereas much of the previous research in complex systems has focused on emergent properties resulting from self‐organization of the individual agents that make up the system, this article studies one vital role of central organization. In particular, four factors are conjectured to be key in determining the optimal amount of central control. To validate this hypothesis, these factors are represented as controllable parameters in a mathematical model. For different combinations of parameter values, the optimal amount of central control is found, either analytically or by computer simulation. The model is shown to provide results that match well with the level of control found across a broad spectrum of specific complex systems. This model also provides general guidelines as to how combinations of these factors affect the desirable level of control and specific guidelines for selecting and evaluating leaders. These results indicate that all of these factors, though not exhaustive, should be considered carefully when attempting to determine the amount of control that is best for a system. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Route optimization for multiple searchers

We consider a discrete time‐and‐space route‐optimization problem across a finite time horizon in which multiple searchers seek to detect one or more probabilistically moving targets. This article formulates a novel convex mixed‐integer nonlinear program for this problem that generalizes earlier models to situations with multiple targets, searcher deconfliction, and target‐ and location‐dependent search effectiveness. We present two solution approaches, one based on the cutting‐plane method and the other on linearization. These approaches result in the first practical exact algorithms for solving this important problem, which arises broadly in military, rescue, law enforcement, and border patrol operations. The cutting‐plane approach solves many realistically sized problem instances in a few minutes, while existing branch‐and‐bound algorithms fail. A specialized cut improves solution time by 50[percnt] in difficult problem instances. The approach based on linearization, which is applicable in important special cases, may further reduce solution time with one or two orders of magnitude. The solution time for the cutting‐plane approach tends to remain constant as the number of searchers grows. In part, then, we overcome the difficulty that earlier solution methods have with many searchers. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010