Finite Markov chain models skip-free in one direction

Finite Markov processes are considered, with bidimensional state space, such that transitions from state (n, i) to state (m, j) are possible only if m ≤ n + 1. The analysis leads to efficient computational algorithms, to determine the stationary probability distribution, and moments of first passage times.     

Production-location problems

The joint problems of determining the optimal plant location and optimal input mix and plant size are addressed. The interrelationship between input substitutability and plant location is stressed. Conditions under which the location problem can be separated from the determination of the optimal input mix are developed for a number of problem variations. The stability of the optimal location in the face of changes in problem parameters is also discussed. It is demonstrated that consideration of input substitutability often makes the resulting problem no more difficult to solve than problem formulations in which the inherent input substitutability is ignored.     

Scheduling with earliest start and due date constraints on multiple machines

We consider the scheduling of n jobs on m identical machines when the jobs become available for processing at ready times a_i, a_i, ? 0, require d_i time units for processing and must be completed by times b_i for i = 1, 2, … n. The objective chosen is that of minimizing the total elapsed time to complete all jobs subject to the ready time and due date constraints, preemption is not allowed. We present a multi-stage solution algorithm for this problem that is based on an implicit enumeration procedure and also uses the labelling type algorithm which solves the problem when preemption is allowed.     

On sequencing with earliest starts and due dates with application to computing bounds for the (n/m/G/Fmax) problem

Recent efforts to improve lower bounds in implicit enumeration algorithms for the general (n/m/G/F_max) sequencing problem have been directed to the solution of an auxiliary single machine problem that results from the relaxation of some of the interference constraints. We develop an algorithm that obtains optimal and near optimal solutions for this relaxed problem with relatively little computational effort. We report on computational results achieved when this method is used to obtain lower bounds for the general problem. Finally, we show the equivalence of this problem to a single machine sequencing problem with earliest start and due date constraints where the objective is to minimize the maximum lateness.     

Selection of the optimal setup policy

A model is developed taking into consideration all the costs (namely cost of sampling, cost of not detecting a change in the process, cost of a false indication of change, and the cost of readjusting detected changes) incurred when a production process, using an unscheduled setup policy, utilizes fraction-defective control charts to control current production. The model is based on the concept of the expected time between detection of changes calling for setups. It is shown that the combination of unscheduled setups and control charts can be utilized in an optimal way if those combinations of sample size, sampling interval, and extent of control limits from process average are used that provide the minimum expected total cost per unit of time. The costs of a production process that uses unscheduled setups in conjunction with the appropriate optimal control charts are compared to the costs of a production process that uses scheduled setups at optimum intervals in conjunction with its appropriate control charts. This comparison indicates the criteria for selecting production processes with scheduled setups using optimal setup intervals over unscheduled setups. Suggestions are made to evaluate the optimal process setup strategy and the accompanying optimal decision parameters, for any specific cost data, by use of computer enumeration. A numerical example for assumed cost and process data is provided.     

Landmarks in defense literature

The Brain of an Army: a Popular Account of the German General Staff. By Spenser Wilkinson. Archibald Constable, London (1st edition 1890, 2nd edition 1895)     

An inventory problem with obsolescence

A stochastic single product convex cost inventory problem is considered in which there is a probability, π_j, that the product will become obsolete in the future period j. In an interesting paper, Barankin and Denny essentially formulate the model, but do not describe some of its interesting and relevant ramifications. This paper is written not only to bring out some of these ramifications, but also to describe some computational results using this model. The computational results show that if obsolescence is a distinct possibility in the near future, it is quite important that the probabilities of obsolescence be incorporated into the model before computing the optimal policies.