Multiobjective flow-shop scheduling

Previous research on the scheduling of multimachine systems has generally focused on the optimization of individual performance measures. This article considers the sequencing of jobs through a multimachine flow shop, where the quality of the resulting schedule is evaluated according to the associated levels of two scheduling criteria, schedule makespan (C_max) and maximum job tardiness (T_max). We present constructive procedures that quantify the trade-off between C_max and T_max. The significance of this trade-off is that the optimal solution for any preference function involving only C_max and T_max must be contained among the set of efficient schedules that comprise the trade-off curve. For the special case of two-machine flow shops, we present an algorithm that identifies the exact set of efficient schedules. Heruistic procedures for approximating the efficient set are also provided for problems involving many jobs or larger flow shops. Computational results are reported for the procedures which indicate that both the number of efficient schedules and the error incurred by heuristically approximating the efficient set are quite small.     

Scheduling peacetime rotation of Pakistan army units

Because Pakistan has varying climates and terrains, the Pakistan Army rotates its units between peacetime locations so that no unit endures inequitable hardship or enjoys unfair advantage. Army policy specifies strict constraints on unit rotations, such as the length of a unit's stay in any location, the number of units moving at any time, and the allowable replacements for any moving unit. Scheduling rotations manually in accordance with these rules, as is currently practiced, is extremely difficult and time consuming. This article presents an integer programming model that finds feasible, minimum-cost schedules for the Pakistan Army's desired planning horizons. The model also ensures that the units are positioned at the end of the planning horizon so that feasible schedules exist for future planners. The model is implemented with commercially available optimization software. Schedules are obtained for realistic test problems in less than an hour on a personal computer. © 1995 John Wiley & Sons, Inc.     

Optimizing ship berthing

Ship berthing plans reserve a location for inbound U.S. Navy surface vessels prior to their port entrance, or reassign ships once in port to allow them to complete, in a timely manner, reprovisioning, repair, maintenance, training, and certification tests prior to redeploying for future operational commitments. Each ship requires different services when in port, such as shore power, crane, ordnance, and fuel. Unfortunately, not all services are offered at all piers, and berth shifting is disruptive and expensive: A port operations scheduler strives to reduce unnecessary berth shifts. We present an optimization model for berth planning and demonstrate it for Norfolk Naval Station, which exhibits all the richness of berthing problems the Navy faces. ® 1994 John Wiley & Sons, Inc.     

A stochastic machine maintenance and sale problem: Results with different production functions

In this article we solve and analyze a stochastic version of the Boiteux problem by employing the stochastic optimal control method. Our setup is close to that of Thompson [22]. Our focus is to analyze, under the same structure, how different production functions and how the variance in machine deterioration/maintenance affect our optimal machine maintenance and sale date decisions. © 1993 John Wiley & Sons, Inc.     

Application of the stein-chen method for bounds and limit theorems in the reliability of coherent structures

The Stein-Chen method for establishing Poisson convergence is used to approximate the reliability of coherent systems with exponential-type distribution functions. These bounds lead to quite general limit theorems for the lifetime distribution of large coherent systems. © 1993 John Wiley & Sons, Inc.     

Nonexistence of the maximum likelihood estimates in the weibull process

With incomplete data the maximum likelihood estimates of the parameters of the Weibull process can only be obtained by solving the likelihood equations iteratively. In this article we show that the solution of the likelihood equations may lie outside of the parameter space if none of the processes can be observed from time zero.     

Optimal strategies for problems of simultaneous attack against an area defense with impact-point prediction

An area to be defended consists of separated point targets. These targets are subject to an attack in which the offensive weapons are assumed to arrive simultaneously. The defense has area defenders, each of which is capable of intercepting any attacker'. Furthermore, the defense has impact-point prediction, i.e., it has knowledge of each attacker's intended target prior to allocation of the area interceptors. For a given attack, the defense wishes to allocate its interceptors against attackers so as to maximize the expected total survival value of the targets. In its first move, the offense seeks an attack allocation which will minimize expected total surviving value against best defense. We develop an algorithm to determine optimal attack and defense strategies and the optimal value of this sequential min-max problem. Branch-and-bound techniques are used to obtain integer solutions, and illustrative computational results are provided.     

Value added analysis for army equipment modernization

This paper describes the Value Added Analysis methodology which is used as part of the U.S. Army's Planning, Programming, Budgeting, and Execution System to assist the Army leadership in evaluating and prioritizing competing weapon system alternatives during the process of building the Army budget. The Value Added Analysis concept uses a family of models to estimate an alternative system's contribution to the Army's effectiveness using a multiattribute value hierarchy. A mathematical optimization model is then used to simultaneously determine an alternative's cost‐benefit and to identify an optimal mix of weapon systems for inclusion in the Army budget. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 233–253, 1999     

A set-processing algorithm for scheduling staff on 4-day or 3-day work weeks

This paper presents an efficient algorithm for scheduling a single-category work force on 4-day or 3-day work weeks. Employees work 4 or 3 days each week, have A out of every B weekends off, and work no more than 5 consecutive days in a work stretch on 4-day work weeks and no more than 4 days in a work stretch on 3-day work weeks. Such conditions often prevail in 7-day-a-week organizations such as hospitals, manufacturing plants, and retail stores. We determine the minimum number of workers required to satisfy the scheduling constraints under any pattern of daily requirements. Then we present the algorithm for assigning days off for each worker, thereby determining the work schedules. We show that the algorithm, by construction, will necessarily satisfy the scheduling constraints. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 839–853, 1998