A streamlined simplex approach to the singly constrained transportation problem

A primal simplex procedure is developed to solve transportation problems with an arbitrary additional linear constraint. The approach is a specialization of the Double Reverse Method of Charnes and Cooper. Efficient procedures for pricing-out the basis, determining representations, and implementing the change of basis are presented. These procedures exploit the pure transportation substructure in such a manner that full advantage may be taken of the computational schemes and list structures used to store and update the basis in codifying the MODI method. Furthermore, the pricing-out and change-of-basis procedures are organized in a manner that permits the calculations for one to be utilized in the other. Computational results are presented which indicate that this method is at least 50 times faster than the state-of-the-art LP code, APEX-III. Methods for obtaining basic primal “feasible” starts and “good” feasible integer solutions are also presented.     

A note on the limitations of goal programming as observed in resource allocation for marine environmental protection

After first formulating the problem of the Marine Environmental Protection program of the Coast Guard as a multiple-objective linear program, we investigate the applicability and limitations of goal programming. We point out how the preemptive goal-programming approach is incompatible with utility preferences. Then we observe the tendency of optimal solutions for standard linear goal programs to occur at extreme points. We also note problems of more general approaches, such as dealing with additively separable approximations to preferences.     

An approximative algorithm for the fixed charge problem

This paper describes an approximate solution method for solving the fixed charge problem. This heuristic approach is applied to a set of test problems to explore the margin of error. The results indicate that the proposed fixed charge simplex algorithm is capable of finding optimal or near optimal solutions to moderate sized fixed charge problems. In the absence of an exact method, this heuristic should prove useful in solving this fundamental nonlinear programming problem.     

MAD: Mathematical analysis of downtime

The MAD model presents a mathematic treatment of the relationship between aircraft reliability and maintainability, system manning and inspection policies, scheduling and sortie length, and aircraft downtime. Log normal distributions are postulated for subsystem repair times and simultaneous repair of malfunctions is assumed. The aircraft downtime for maintenance is computed with the distribution of the largest of k log normal distributions. Waiting time for maintenance men is calculated either by using a multiple-channel queuing model or by generating the distribution of the number of maintenance men required and comparing this to the number of men available to determine the probability of waiting at each inspection.     

Pursuit around a hole

The solution of isaacs¹ problem of optimal pursuit in a plane with a circular disk removed, given constant speeds, zero turning radius, and perfect visibility for both players is presented herein. The hole has three effects: the trivial effect that shortest paths are not straight, the trapping effect to turn the evader from running into the hole, and the screening effect causing an evader retreating behind the hole not to retreat across a line through its center.     

Programming the procurement of airlift and sealift forces: A linear programming model for analysis of the least-cost mix of strategic deployment systems

A linear programming model for analyzing the strategic deployment mix of airlift and sealift forces and prepositioning to accomplish the composite requirements of a set of possible contingencies is described in this paper. It solves for the least-cost mix of deployment means capable of meeting any one of a spectrum of contingencies, or meeting simultaneous contingencies. The model was developed by RAC as part of the U.S. Army's study program and has been used in analyses of deployment systems conducted in support of the U.S. Army, the Joint Chiefs of Staff and the Office of the Secretary of Defense. Results of analyses have influenced the preparation of long-range plans as well as the formulation of the FY67 Department of Defense budget. The paper gives the background and assumptions of the model, describes the model by means of a simple hypothetical example followed by a selected subset of a complete version, and discusses how the model is used.