On the isbell and marlow fire programming problem

A complete solution is derived to the Isbell and Marlow fire programming problem. The original work of Isbell and Marlow has been extended by determining the regions of the initial state space from which optimal paths lead to each of the terminal states of combat. The solution process has involved determining the domain of controllability for each of the terminal states of combat and the determination of dispersal surfaces. This solution process suggests a solution procedure applicable to a wider class of tactical allocation problems, terminal control attrition differential games. The structure of optimal target engagement policies in “fights to the finish” is discussed.     

The discrete max-min problem

The historic max-min problem is examined as a discrete process rather than in its more usual continuous mode. Since the practical application of the max-min model usually involves discrete objects such as ballistic missiles, the discrete formulation of the problem seems quite appropriate. This paper uses an illegal modification to the dynamic programming process to obtain an upper bound to the max-min value. Then a second but legal application of dynamic programming to the minimization part of the problem for a fixed maximizing vector will give a lower bound to the max-min value. Concepts of optimal stopping rules may be applied to indicate when sufficiently near optimal solutions have been obtained.     

A maximum utility solution to a vehicle constrained tanker scheduling problem

A modification to the Dantzig and Fulkerson Tanker Scheduling Problem is described. An insufficient number of vehicles and a utility associated with each vehicle delivery are assumed. The new problem is shown to be equivalent to a Transshipment Problem, the solution of which is the same as the maximal utility solution of the modified Tanker Scheduling Problem. An example is given.     

Simulations to explore alternative sequencing rules

A flexible simulation system has been designed to permit investigation of sequencing rules in a large job shop, with continual input of new work. The objective is to understand what happens rather than to find optimum rules, with many conflicting measures of effectiveness: work in process, finished goods investment, delays, machine and labor utilization, and effort to implement. A few problem areas have been explored.     

Suboptimal algorithms for the quadratic assignment problem

The idea of combining relatively simple continuous methods with discrete procedures is used for the construction of suboptimal algorithms for quadratic assignment problems. Depending on the nature of the special problem these steps may vary in complexity. The simplest procedures require minimum storage space and result in tolerable computation times. Different choices of parameters and random variations may be used in order to obtain statistical distributions of suboptimal solutions. Computational results for sample problems indicate improvements on results of Steinberg, Gilmore, and Hillier and Connors.     

An operator theory of parametric programming for the transportation problem-II

This paper investigates the effect on the optimum solution of a (capacitated) transportation problem when the data of the problem (the rim conditions-i. e., the warehouse supplies and market demands-, the per unit transportation costs and the upper bounds) are continuously varied as a (linear) function of a single parameter. Operators that effect the transformation of optimum solution associated with such data changes, are shown to be a product of basis preserving operators (described in the earlier paper) that operate on a sequence of adjacent basis structures. Algorithms are provided for both rim and cost operators. The paper concludes with a discussion of the economic and managerial interpretations of the operators.     

Simulation of multi-echelon macro-inventory policies

Alternative repair part inventory policies are examined for a multi-echelon logistics system. The policies assessed pertain to the design of multi-echelon systems rather than the evaluation of stock level decisions for individual repair parts. Although the context is one of a military inventory system, the policies examined are of importance in nonmilitary systems where item failure rates are low, and only periodic access to resupply is possible.