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.     

Heuristic procedure for a multiproduct dynamic lot-sizing problem with coordinated replenishments

In this article we develop a heuristic procedure for a multiproduct dynamic lot-sizing problem. In this problem a joint setup cost is incurred when at least one product is ordered in a period. In addition to the joint setup cost a separate setup cost for each product ordered is also incurred. The objective is to determine the product lot sizes, over a finite planning horizon, that will minimize the total relevant cost such that the demand in each period for each product is satisfied without backlogging. In this article we present an effective heuristic procedure for this problem. Computational results for the heuristic procedure are also reported. Our computational experience leads us to conclude that the heuristic procedure may be of considerable value as a decision-making aid to production planners in a real-world setting. © 1994 John Wiley & Sons, Inc.     

Optimal replacement policies for multistate deteriorating systems

We consider state-age-dependent replacement policies for a multistate deteriorating system. We assume that operating cost rates and replacement costs are both functions of the underlying states. Replacement times and sojourn times in different states are all state-dependent random variables. The optimization criterion is to minimize the expected long-run cost rate. A policy-improvement algorithm to derive the optimal policy is presented. We show that under reasonable assumptions, the optimal replacement policies have monotonic properties. In particular, when the failure-rate functions are nonincreasing, or when all the replacement costs and the expected replacement times are independent of state, we show that the optimal policies are only state dependent. Examples are given to illustrate the structure of the optimal policies in the special case when the sojourntime distributions are Weibull. © 1994 John Wiley & Sons, Inc.     

Initial point search on weighted trees

An initial point search game on a weighted graph involves a searcher who wants to minimize search and travel costs seeking a hider who wants to maximize these costs. The searcher starts from a specified vertex 0 and searches each vertex in some order. The hider chooses a nonzero vertex and remains there. We solve the game in which the graph is a simple tree, and use this solution to solve a search game on a tree in which each branch is itself a weighted graph with a certain property, and the searcher is obliged to search the entire branch before departing. © 1994 John Wiley & Sons, Inc.     

Unbalanced production line scheduling with partial job specialization

This article presents a mathematical model for manpower scheduling for unbalanced production lines in order to minimize in-process inventory cost. The model extends prior work by adding workers' skill limitations to the system. The model is formulated for a one-period schedule and then extended for multiperiod schedules. An example problem is solved for both single and multiperiods. A heuristic algorithm is also presented for multiperiod and large-scale problems, and computational experiences are reported.     

Minimizing costs of sequential and parallel personnel testing programs

We consider groups of tests for personnel selection purposes in which each test has a known a priori probability of being failed, such failure resulting in outright rejection and termination of testing. Each test has a fixed cost and given duration. We consider the minimization of the total expected cost due to both the fixed costs and the delay costs when the tests may be conducted sequentially or in parallel. In the latter situation, a heuristic algorithm is proposed and illustrated.