George O. Wesolowsky

NETWORK DESIGN: SELECTION AND DESIGN OF LINKS AND FACILITY LOCATION

In this paper we introduce new network design problems. A network of potential links is given. Each link can be either constructed or not at a given cost. Also, each constructed link can be constructed either as a one-way or two-way link. The objective is to minimize the total construction and transportation costs. Two different transportation costs are considered: (i) traffic is generated between any pair of nodes and the transportation cost is the total cost for the users and (ii) demand for service is generated at each node and a facility is to be located on a node to satisfy the demand. The transportation cost in this case is the total cost for a round trip from the facility to each node and back. We will consider two options in regard to the links between nodes. They can either be two-way only, or mixed, with both two-way and one-way (in either direction) allowed. When these options are combined with the two objective functions, four basic problems are created. These problems are solved by a descent algorithm, simulated annealing, tabu search, and a genetic algorithm. Extensive computational results are presented.

Optimal Control of a Linear Trend Process with Quadratic Loss

Abstract This paper deals wth the problem of optimizing the start and finish points for runs in a process which has a linearly drifting average. Deviations fr om a target value are penalized by a quadratic loss function which may have a different constant for negative or positive deviations.

A Maximin Location Problem with Maximum Distance Constraints

Abstract This paper deal with the problem where a facility must be placed among n points so that the shortest weighted distance to a point is as large as possible. At the same time the facility must be within a pre-specified distance from each point; the facility is to be located on a plane and Euclidean distances are used. Applications include the location of facilities that are obnoxious in the sense that they should be placed as far away from certain points as possible but still be within a pre-specified “reach” of these points.

On the circle closest to a set of points

The objective of this paper is to find a circle whose circumference is as close as possible to a given set of points. Three objectives are considered: minimizing the sum of squares of distances, minimizing the maximum distance, and minimizing the sum of distances. We prove that these problems are equivalent to minimizing the variance, minimizing the range, and minimizing the mean absolute deviation, respectively. These problems are formulated and heuristically solved as mathematical programs. Special efficient heuristic algorithms are designed for two cases: the sum of squares, and the minimax. Computational experience is reported.

The Weber Problem On The Plane With Some Negative Weights

AbstractThis paper analyzes the properties of the Weber problem on the plane when some of the weights are negative. We provide exact solutions when distances are rectilinear or squared Euclidean. For the Euclidean case, we provide a theorem that limits the region of the plane where optimal points can be located. Heuristic algorithms based on this theorem are suggested and computational experience is described.

Multi-stage production with variable lot sizes and transportation of partial lots

Abstract This paper describes a model for a multi-stage production/inventory system where lots may be of different sizes. In addition, either completed lots or partial lots, called batches, may be transported to succeeding stages. The model incorporates constraints on lot and batch-sizes and thus provides a rather comprehensive set of possibilities for organizing a production/inventory system. A heuristic solution procedure is developed and is shown to be ‘close to optimal’ by bounding.

Technical Note—The Optimal Location of New Facilities Using Rectangular Distances

This note describes a method for locating any number of facilities optimally in relation to any number of existing facilities. The objective is to minimize the total of load-times-distance costs in the system. Any amount of loading may be present between the new facilities and the existing facilities and between the new facilities themselves. Distances are assumed to be rectangular.

Locating service facilities whose reliability is distance dependent

Abstract We consider the problem where there is a probability, depending on the distance from the facility, that the facility may not be able to provide satisfactory service to a customer. This probability is equal to 0 at distance zero, and is a monotonically increasing function of the distance. We need to locate m facilities on a network such that the expected service level for all demand points combined, will be maximized. Alternatively, one can state the problem as minimizing the expected demand that will not get satisfactory service. The problem is formulated and properties of the solution are proved. Five metaheuristic algorithms are developed for its solution and are compared with computational results on a set of test problems. Scope and purpose In order to be competitive, companies must provide satisfactory service to their customers. The level of service provided is very often related to the distance of customers from the service facilities. In this paper, we consider such a model where the probability that satisfactory service will be provided is a function of the distance from customers to the facilities. The closer the customers are to the facilities, the greater is the likelihood that satisfactory service will be provided (e.g. emergency response systems). The objective is to find the location of the facilities that maximize the expected demand that receives satisfactory service.

Multi-buyer discount pricing

Abstract This article gives an exact optimal solution to the problem of finding the optimal discount price and price break quantity for a seller dealing with one buyer. It also gives a method for solving the problem when one seller offers a single quantity discount schedule to many buyers. The discount is of the ‘all quantity’ type and the model of the cost structure was originally proposed by Crowther.

The variable radius covering problem

In this paper we propose a covering problem where the covering radius of a facility is controlled by the decision-maker; the cost of achieving a certain covering distance is assumed to be a monotonically increasing function of the distance (i.e., it costs more to establish a facility with a greater covering radius). The problem is to cover all demand points at a minimum cost by finding optimal number, locations and coverage radii for the facilities. Both, the planar and discrete versions of the model are considered. Heuristic approaches are suggested for solving large problems in the plane. These methods were tested on a set of planar problems. Mathematical programming formulations are proposed for the discrete problem, and a solution approach is suggested and tested.