An interactive optimization system for bulk-cargo ship scheduling

This article considers the efficient scheduling of a fleet of ships engaged in pickup and delivery of bulk cargoes. Our optimization system begins by generating a menu of candidate schedules for each ship. This menu can contain all feasible solutions, which guarantees we will find an optimal solution or can be heuristically limited to contain only those schedules likely to be in an optimal solution. The problem of choosing from this menu an optimal schedule for the fleet is formulated as a set-packing problem and solved with a dual algorithm. Computational experience is presented based on real data obtained from the Military Sealift Command of the U. S. Navy. Run times for this data were reasonable and solutions were generated with the potential of saving up to about $30 million per year over the manual system currently in place. We also describe a color-graphics interface developed to facilitate interaction with the optimization system.     

On the robustness of the modified beta distribution for acceptance sampling in statistical quality control

The purpose of this article is to examine the robustness of the modified Beta distribution as a probability distribution of lot fraction defectives in Bayesian acceptance sampling for statistical quality control. In complex manufacturing systems, a production process may consist of multiple production stages in a serial or nonserial fashion. Hence, inputs to a production station can be a result of subassembly of several inputs, or outputs of some inspection stations for some prior work stages. We investigate the effectiveness of the modified Beta distribution as an approximation to the lot fraction defectives probability of inputs at intermediate work stations. The robustness of the modified Beta distribution simplifies both the determination of the optimal sampling plan for acceptance sampling, and the calibration of distributions resulted from subassembly or inspection operations in complex manufacturing systems.     

Approximate semieconomic design of control charts with multiple control limtis

Statistical quality control of complicated production processes subject to a multiplicity of assignable causes may require the utilization of control charts with multiple control limits. This article presents an approximate semieconomic design of such charts, which is easily implementable in practical situations. Evaluations of the semieconomic control chart design show that the proposed approximate method results in solutions that are very close to the true optima and can be obtained with minimal computational effort.     

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.     

Service levels in distribution systems with random customer order size

An approximate method for measuring the service levels of the warehouse-retailer system operating under (s, S) policy is presented. All the retailers are identical and the demand process at each retailer follows a stationary stuttering Poisson process. This type of demand process allows customer orders to be for a random number of units, which gives rise to the undershoot quantity at both the warehouse and retailer levels. Exact analyses of the distribution of the undershoot quantity and the number of orders place by a retailer during the warehouse reordering lead time are derived. By using this distribution together with probability approximation and other heuristic approaches, we model the behavior of the warehouse level. Based on the results of the warehouse level and on an existing framework from previous work, the service level at the retailer level is estimated. Results of the approximate method are then compared with those of simulation. © 1995 John Wiley & Sons, Inc.     

A bayesian approach to environmental stress screening

The article presents a Bayesian analysis for the environmental stress screening problem. The decision problem of deriving optimal stress screen durations is solved. Given a screen duration, the optimal stress level can also be determined. Indicators of the quality of a screen of any duration are derived. A statistical model is presented which allows a posterior density for the rate of early failures of the production process to be calculated. This enables the user to update his opinion about the quality of the process. © 1994 John Wiley & Sons, Inc.     

Queueing processes and trade-offs during ship-to-shore transfer of cargo

This article examines the ship-to-shore transfer of cargo from ships that are located offshore. In these situations, cargo is transferred from the ships to smaller craft, which in turn transport the cargo the remaining distance to shore. These craft cycle back and forth from the ship to the shore until the transfer is complete. Queueing of these craft often occurs, as they must wait at either the ship or the shore for a loading or unloading position to become free. Two different methods of modeling this ship-to-shore transfer of cargo are developed and applied. One is an analytic queueing model and the other is a more traditional simulation model. The analytic model is found to produce results quite similar to the simulation model. Examples are shown that use these models to analyze trade-offs between variables affecting the ship-to-shore transfer of cargo and the total time to transfer a given amount of cargo ashore. © 1994 John Wiley & Sons, Inc.     

The parallel machine min-max weighted absolute lateness scheduling problem

Given a set of jobs, a processing time and a weight for each job, several parallel and identical machines, and a common due date that is not too early to constrain the scheduling decision, we want to find an optimal job schedule so as to minimize the maximum weighted absolute lateness. We show that this problem is NP-complete even for the single-machine case, and is strongly NP-complete for the general case. We present a polynomial time heuristic for this problem and analyze its worst-case performance. Empirical testing of the heuristic is reported, and the results suggest that the performance is asymptotically optimal as the number of jobs tends to infinity. © 1994 John Wiley & Sons, Inc.     

Equipment replacement under technological change

For infinite-horizon replacement economy problems it is common practice to truncate the problem at some finite horizon. We develop bounds on the error due to such a truncation. These bounds differ from previous results in that they include both revenues and costs. Bounds are illustrated through a numerical example from a real case in vehicle replacement. © 1994 John Wiley & Sons, Inc.     

A dual-based optimization procedure for the two-echelon uncapacitated facility location problem

The two-echelon uncapacitated facility location problem (TUFLP) is a generalization of the uncapacitated facility location problem (UFLP) and multiactivity facility location problem (MAFLP). In TUFLP there are two echelons of facilities through which products may flow in route to final customers. The objective is to determine the least-cost number and locations of facilities at each echelon in the system, the flow of product between facilities, and the assignment of customers to supplying facilities. We propose a new dual-based solution procedure for TUFLP that can be used as a heuristic or incorporated into branch-and-bound procedures to obtain optimal solutions to TUFLP. The algorithm is an extension of the dual ascent and adjustment procedures developed by Erlenkotter for UFLP. We report computational experience gained by solving over 420 test problems. The largest problems solved have 25 possible facility locations at each echelon and 35 customer zones, implying 650 integer variables and 21,875 continuous variables.