Arunachalam Ravindran

A Multiple Objective Nurse Scheduling Model

Abstract The authors present a model for the nurse scheduling problem which works in two phases. In the first phase, the nurses are assigned their day-on/day-off pattern for the two-week scheduling horizon by a goal programming model which allows for consideration of the multiple conflicting objectives inherent in scheduling a nursing staff. The second phase makes specific shift assignments through the use of a heuristic procedure. The two-phase approach results in considerable reductions in problem size, thus reducing the solution effort. Extensions to the basic model are also examined.

Algorithm 431: A computer routine for quadratic and linear programming problems [H]

A computer program based on Lemkes complementary pivot algorithm is presented. This can be used to solve linear and quadratic programming problems. The program has been extensively tested on a wide range of problems and the results have been extremely satisfactory.

A branch and bound algorithm with constraint partitioning for integer goal programming problems

Abstract Using constraint partitioning and variable elimination, the authors have recently developed an efficient algorithm for solving linear goal programming problems. However, many goal programs require some or all of the decision variables to be integer valued. This paper shows how the new partitioning algorithm can be extended with a modified branch and bound strategy to solve both pure and mixed type integer goal programming problems. A potential problem in combining the partitioning algorithm and the branch and bound search scheme is presented and resolved.

Management of Seasonal Style-Goods Inventories

This paper develops an inventory model in which season length is specifically included as a variable for seasonal style goods under the assumption that the demands exhibit a simple contagion pattern, namely, the influence of past demands on future occurrence of demands. The paper first derives an s-S optimal order policy as a function of the selling season, then determines the optimal duration and timing of the selling season, and, finally includes an algorithm for computing the optimal season length.

Computer experiments on quadratic programming algorithms

Abstract This paper compares the computational performance of five quadratic programming algorithms. These include Wolfes simplex method, Lemkes complementary pivot method, convex simplex method and quadratic differential algorithm. Execution time and iteration count are used as the major criteria for comparison. Since Lemkes algorithm out-performed all other methods in the study, a detailed statistical analysis was performed to determine the relative importance of problem parameters on the efficiency of Lemkes algorithm. An analysis of variance showed that the number of variables, the percent of positive linear terms in the objective, the number of constraints, and their interactions were the significant factors for both iteration count and execution time. Finally, regression equations for iteration count and execution time are derived as a function of fifteen problem parameters.

Optimal Location of Coal Blending Plants by Mixed-Integer Programming

Abstract In order to meet increasingly stringent environmental standards, coal burned by utilities and industries must be of an acceptable lower sulfur content. One solution suggested in this paper is the establishment of centralized blending plants that could take coals of varying sulfur content and produce a coal product that would meet the coal consumers needs based upon effluent standards. A mixed integer programming model is developed for studying this problem. A case study is presented with coal data for the State of Indiana. Model results on the number of blending plants to be selected, their site locations, optimal blending ratios, transportation configuration, and cost savings are discussed.

A Linear Programming Model with Shortage Costs for Energy Planning and Allocation

Abstract Since the energy shortage is only a recent phenomenon, most of the quantitative models for energy planning have assumed that the demands can always be met by increasing imports. In this paper, the concept of an energy shortage cost is introduced, and a quantitative energy model with shortages is developed to study the interfuel competition, and optimal allocation policies during an energy shortage. The solution is approached through linear programming methods. In addition to the societal shortage cost for energy, other special features of our model include consideration of all forms of energy resources and new technologies of energy production. The model is illustrated through a number of case studies on an economic region using realistic energy data. Through these applications the model is shown to be a useful tool to assess the impact of future energy shortages, higher fuel prices, introduction of newer technologies, and various allocation policies.

Optimal Storage of Books by Size: An Operations Research Approach.

This paper considers the optimal storage of books by size in libraries. A network model is developed to determine the optimum number of shelf heights to use which will minimize the shelving cost for a given collection of books. The model is analyzed and solved by a well known operations research technique of finding the shortest path in a directed network. Results of an experimental study to apply this model to a sample collection of books from the Purdue University Library are discussed.