Note--On the Maximal Covering Location Problem and the Generalized Assignment Problem

In many public sector location problems, it is often desirable to locate facilities in such a way to minimize the number (or cost) of facilities while insuring tint all demand centers are within a stated maximal service time front any facility. However, when insufficient resources exist to allow die construction of enough facilities to serve all demand centers within the alloted time, the location problem is frequently restated in order to locate the budgeted facilities to serve the serviced population. Problems of the latter type are generally known as maximal covering location problems, which may have a number of extensions, including mandatory closeness constraints which place an upper bound on the maximal service time requirement for the entire population. This note demonstrates how this class of frequently encountered problems can be formulated as generalized assignment problems within the conceptual framework presented by Ross and Soland (Ross, G. T., R. Soland. 1977. Modeling facility location problems as generalized assignment problems. Management Sci. 24 (3, November) 345-357.) for other discrete public and private location problems.facility location, assignment problem

The p-Median Problem for Cluster Analysis: A Comparative Test Using the Mixture Model Approach

Recently, Mulvey and Crowder (Mulvey, J., H. Crowder. 1979. Cluster analysis: an application of Lagrangian relaxation. Management Sci. 25 329--340.) suggested that the p-median problem might be useful for cluster analysis problems (where the goal is to group objects described by a vector of characteristics in such a way that objects in the same group are somehow more alike than objects in different groups). The intent of this paper is to test Mulvey and Crowder's proposal using the mixture model approach; i.e., by applying a number of algorithms (including one for the p-median problem) to a set of objects randomly sampled from a number of known multivariate populations and comparing the ability of each algorithm to detect the original populations. In order to evaluate the results, a generalized partition comparison measure and its distribution are developed. Using this measure, results from various algorithms are compared.statistics: cluster analysis, programming: integer, applications, facilities/equipment planning: location

Measuring the Impact of a Delay Buffer on Quality Costs with an Unreliable Production Process

In this paper, we consider an unreliable production process which produces nondefective items when operating in control, but produces defective items with a probability \alpha when the process has shifted to an out-of-control state. Following a JIT philosophy, we stop the entire line and repair the machine as soon as detect that the process has shifted to an out-of-control state. To test whether a process shift has occurred, we inspect the last m units for every n units produced and stop the machine if a defective unit is found. More important, we place a "delay buffer" immediately after the unreliable process, which serves to delay the movement of items from the unreliable machine to other processes (or customers) downstream in the production system. When we detect that the machine has shifted to an out-of-control state, we stop the entire line and examine all previously uninspected items in the delay buffer; in this way, the buffer serves to reduce the expected rework and penalty (e.g., warranty) costs downstream when a process shift has occurred. In this paper, we develop a model for this approach and use this model to test the operating characteristics of our system. Computational results illustrate our hypothesis that a delay buffer may significantly reduce expected total costs of a quality control process.quality management, sampling/inspection policies, unreliable production processes, delay buffer

Robust optimization made easy with ROME

10.1287/opre.1110.0944Operations Research594973-985OPRE