A note on duality in homogeneous fractional programming

For a linear fractional programming problem, Sharma and Swarup have constructed a dual problem, also a linear fractional program, in which the objective functions of both primal and dual problems are the same. Craven and Mond have extended this result to a nonlinear fractional programming problem with linear constraints, and a dual problem for which the objective function is the same as that of the primal. This theorem is now further extended from linear to differentiable convex constraints.     

The mixed ordering policy in periodic review stochastic multi-commodity inventory systems

In multi-commodity inventory systems with variable setup costs, the mixed ordering policy assumes that commodities may be ordered either individually, or may be arbitrarily grouped for joint ordering. Thus, for a two-commodity system, commodity one or commodity two or commodities one and two may be ordered incurring respectively fixed order costs of K, K₁, or K₂, where max (K₁, K₂) ≤ K ≤ K₁ + K₂, This paper considers a two-commodity periodic review system. The stationary characteristics of the system are analyzed, and, for a special case, explicit solutions are obtained for the distribution of the stock levels at the beginning of the periods. In a numerical example, optimal policy variables are computed, and the mixed ordering policy is compared with individual and joint ordering policies.     

Constructing bimatrix games with special properties

This work is concerned primarily with presenting techniques for constructing bimatrix games with predetermined equilibrium points. Some partial results on Nash-solvability are also given.     

Statistical auditing of large-scale management information systems

In recent years many large government and commercial organizations have developed large-scale management information systems. During the early phases of any system development, questions are likely to be raised concerning the criteria of completeness and accuracy of the data. How to respond to these questions is difficult, and represents the general subject of this paper. In particular, this paper describes the application of statistical techniques, namely, various kinds of multivariate data analysis, to the problem of assessing the quality of a large-scale data collection system in the U. S. Navy. Results of using these techniques are described and indicate their usefulness as auditing procedures. While the discussion is placed in a particular context, the procedures should be of value for other large-scale information systems.     

Satellite constellation design for forest fire monitoring via a stochastic programing approach

There is significant value in the data collected by satellites during and after a natural disaster. The current operating paradigm in practice is for satellites to passively collect data when they happen to fly over a disaster location. Conversely, this article considers the alternative approach of actively maneuvering satellites to fly directly overhead of the disaster site on a routine basis. Toward this end, we seek to compute a satellite constellation design that minimizes the expected maneuver costs for monitoring an unknown forest fire. In this article, we present a 2‐stage stochastic programing model for this problem as well as a accelerated L‐shaped decomposition approach. A comparison between our approach and the current operating paradigm indicates that our solution provides longer duration data collections and a greater number of data collections. Analysis also shows that our proposed solution is robust over a wide array of scenarios.     

Balancing perfectly periodic service schedules: An application from recycling and waste management

A national recycling and waste management company provides periodic services to its customers from over 160 service centers. The services are performed periodically in units of weeks over a planning horizon. The number of truck‐hours allocated to this effort is determined by the maximum weekly workload during the planning horizon. Therefore, minimizing the maximum weekly workload results in minimum operating expenses. The perfectly periodic service scheduling (PPSS) problem is defined based on the practices of the company. It is shown that the PPSS problem is strongly NP‐hard. Attempts to solve large instances by using an integer programming formulation are unsuccessful. Therefore, greedy BestFit heuristics with three different sorting schemes are designed and tested for six real‐world PPSS instances and 80 randomly generated data files. The heuristics provide effective solutions that are within 2% of optimality on average. When the best found BestFit schedules are compared with the existing schedules, it is shown that operational costs are reduced by 18% on average. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 160–171, 2012