Longitudinal manpower planning models

A manpower planning model is presented that exploits the longitudinal stability of manpower cohorts. The manpower planning process is described. An infinite horizon linear program for calculating minimum cost manpower input plans is presented and found to have a straightforward solution in a great many cases and to yield an easily implemented approximation technique in other cases.     

Postoptimality analysis in zero-one programming by implicit enumeration

The procedures for postoptimality analysis that are so much a part of linear programming studies have no simple counterparts in an integer programming context. In the case of Balas' Additive Algorithm, however, it would appear that the capacity of the technique to facilitate certain types of postoptimality analysis has not been fully exploited. This paper proposes an extension of the additive algorithm that utilizes insights generated while solving the original problem to do subsequent analysis upon it. In particular, procedures are developed for doing limited parameter ranging and for seeking new optima in light of parameter changes.     

A continuous review inventory model with compound poisson demand process and stochastic lead time

Using Markov renewal theory, we derive analytic expressions for the expected average cost associated with (s, S) policies for a continuous review inventory model with a compound Poisson demand process and stochastic lead time, under the (restrictive) assumption that only one order can be outstanding.     

Integer points on the Gomory fractional cut (hyperplane)

In this paper we show that the Gomory fractional cut (hyperplane) for the integer program is either void of integer points or contains an infinite number of them. The conditions for each case are presented. Also, we derive a stronger cut from the hyperplane which does not intersect integer points.     

An exact branch-and-bound procedure for the quadratic-assignment problem

The quadratic-assignment problem is a difficult combinatorial problem which still remains unsolved. In this study, an exact branch-and-bound procedure, which is able to produce optimal solutions for problems with twelve facilities or less, is developed. The method incorporates the concept of stepped fathoming to reduce the effort expended in searching the decision trees. Computational experience with the procedure is presented.     

The search for an intelligent evader: Strategies for searcher and evader in the two-region problem

This paper considers the search for an evader concealed in one of two regions, each of which is characterized by its detection probability. The single-sided problem, in which the searcher is told the probability of the evader being located in a particular region, has been examined previously. We shall be concerned with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move: his optimal strategy consists of that probability distribution which maximizes the expected time to detection, while the searcher's optimal strategy is the sequence of searches which limits the evader to this expected time. It transpires for this problem that optimal strategies for both searcher and evader may generally be obtained to a surprisingly good degree of approximation by using the optimal strategies for the closely related (but far more easily solved) problem in which the evader is completely free to move between searches.     

A heuristic network procedure for the assembly line balancing problem

Proposed is a Heuristic Network (HN) Procedure for balancing assembly lines. The procedure uses simple heuristic rules to generate a network which is then traversed using a shortest route algorithm to obtain a heuristic solution. The advantages of the HN Procedure are: a) it generally yields better solutions than those obtained by application of the heuristics, and b) sensitivity analysis with different values of cycle time is possible without having to regenerate the network. The rationale for its effectiveness and its application to problems with paralleling are presented. Computational experience with the procedure on up to 50 task test problems is provided.     

A decomposable transshipment algorithm for a multiperiod transportation problem

A dynamic version of the transportation (Hitchcock) problem occurs when there are demands at each of n sinks for T periods which can be fulfilled by shipments from m sources. A requirement in period t₂ can be satisfied by a shipment in the same period (a linear shipping cost is incurred) or by a shipment in period t₁ < t₂ (in addition to the linear shipping cost a linear inventory cost is incurred for every period in which the commodity is stored). A well known method for solving this problem is to transform it into an equivalent single period transportation problem with mT sources and nT sinks. Our approach treats the model as a transshipment problem consisting of T, m source — n sink transportation problems linked together by inventory variables. Storage requirements are proportional to T² for the single period equivalent transportation algorithm, proportional to T, for our algorithm without decomposition, and independent of T for our algorithm with decomposition. This storage saving feature enables much larger problems to be solved than were previously possible. Futhermore, we can easily incorporate upper bounds on inventories. This is not possible in the single period transportation equivalent.