The discrete evasion game with three-move lag

The discrete evasion game with three-move lag, formulated over 30 years ago, was one of the earliest games with time-lag complications. This game remains unsolved even though it is well known that the game has a value. In this article we obtain an upper bound for the value by constructing a strategy which consists of 400 conditional probabilities for the minimizing player. This is believed to be the best upper bound known.     

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.     

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.     

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.     

Multi-item service constrained (s,S) policies for spare parts logistics systems

Many organizations providing service support for products or families of products must allocate inventory investment among the parts (or, identically, items) that make up those products or families. The allocation decision is crucial in today's competitive environment in which rapid response and low levels of inventory are both required for providing competitive levels of customer service in marketing a firm's products. This is particularly important in high-tech industries, such as computers, military equipment, and consumer appliances. Such rapid response typically implies regional and local distribution points for final products and for spare parts for repairs. In this article we fix attention on a given product or product family at a single location. This single-location problem is the basic building block of multi-echelon inventory systems based on level-by-level decomposition, and our modeling approach is developed with this application in mind. The product consists of field-replaceable units (i.e., parts), which are to be stocked as spares for field service repair. We assume that each part will be stocked at each location according to an (s, S) stocking policy. Moreover, we distinguish two classes of demand at each location: customer (or emergency) demand and normal replenishment demand from lower levels in the multiechelon system. The basic problem of interest is to determine the appropriate policies (s_i S_i) for each part i in the product under consideration. We formulate an approximate cost function and service level constraint, and we present a greedy heuristic algorithm for solving the resulting approximate constrained optimization problem. We present experimental results showing that the heuristics developed have good cost performance relative to optimal. We also discuss extensions to the multiproduct component commonality problem.     

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