Analysis of a bicriteria location model

In this article a bicriteria model, formed by the weighted sum of the minisum and minimax functions for a single-location problem, is investigated. It is shown that all efficient solutions generated by either constrained model are also properly efficient. The bicriteria model and the constrained models are theoretically equivalent, but it is more efficient and simpler to generate nondominated solutions using the constrained criterion approach. When solving the bicriteria model, a critical range is found for which all properly efficient solutions are generated.     

Lower bounds for single-machine scheduling problems

This article addresses deterministic, nonpreemptive scheduling of n jobs with unequal release times on a single machine to minimize the sum of job completion times. This problem is known to be NP-hard. The article compares six available lower bounds in the literature and shows that the lower bound based on the optimal solution to the preemptive version of the problem is the dominant lower bound.     

Design and estimation for small sample sensitivity testing

In sensitivity testing for the Department of Defense, the high cost of experimental units necessitates the use of small sample sizes and accentuates the importance of design. This article compares five data collection-estimation procedures. Four of these are modifications of the Robbins-Monro method, and the other is the Langlie. The simulation study is designed as a factorial experiment with response function, sample size, initial design point, gate width, and noise as factors. The estimated V₅₀ and its MSE are the responses compared to assess the small sample behavior of each method. Although there is no single clear-cut winner, the Delayed Robbins-Monro (DRM) with maximum likelihood estimation and the Estimated Quantal Response Curve (Wu [21]) are shown to perform well over a broad variety of conditions.     

Scheduling workers in a constricted area

A generalization of the equi-partitioning problem, termed the 2D-Partition Problem, is formulated. The motivation is an aircraft maintenance scheduling problem with the following characteristics. The complete maintenance overhaul of a single aircraft requires the completion of some 350 tasks. These tasks require a varying number of technicians working at the same time. For large subsets of these 350 tasks, the constraining resource is physical space—tasks must be completed in a physical space of limited size such as the cockpit. Furthermore, there is no precedence relationship among the tasks. For each subset, the problem is to schedule the tasks to minimize makespan. Let m denote the maximum number of technicians that can work at the same time in the physical area under consideration. We present optimization algorithms for m = 2 and 3. © 1996 John Wiley & Sons, Inc.     

A lost sales (S — 1, S) perishable inventory system with renewal demand

This article analyzes a one-to-one ordering perishable inventory model with renewal demands and exponential lifetimes. The leadtimes are independently and exponentially distributed and the demands that occur during stock out periods are lost. Although the items are assumed to decay at a constant rate, the output process is not renewal and the Markov renewal techniques are successfully employed to obtain the operating characteristics. The problem of minimizing the long run expected cost rate is discussed and numerical values of optimal stock level are also provided. © 1996 John Wiley & Sons, Inc.     

An evaluation of scheduling heuristics for dynamic single-processor scheduling with early/tardy costs

In an endeavor to broaden the application of scheduling models to decisions involving the use of a manager's time we use simulation to investigate the performance of a number of simple algorithms (including eight priority rules and a construction heuristic) in a dynamic setting with tasks arriving (randomly) and scheduling decisions being made, over time. We compare these simple methods relative to a bound that uses an adjacent pairwise interchange algorithm. We model uncertainty in task durations, and costs being incurred for early and tardy task completion (representative of JIT settings). In addition to evaluating the efficacy of the scheduling rules and various preemption strategies (using ANOVA), we highlight the managerial implications of the effects of eight environmental parameters. © 1996 John Wiley & Sons, Inc.     

Ordering policies for an inventory system with three supply modes

This article explores ordering policies for inventory systems with three supply modes. This model is particularly interesting because the optimal ordering decision needs to balance the inventory and purchase costs, as well as the costs for earlier and later periods. The latter cost trade-off is present only in inventory systems with three or more supply modes. Therefore, the result not only offers guidelines for the operation of the concerned inventory systems, but also provides valuable insight into the complex cost trade-offs when more supply modes are available. We assume that the difference between the lead times is one period, and the inventory holding and shortage costs are linear. We analyze two cases and obtain the structure of the optimal ordering policy. Moreover, in the first case, explicit formulas are derived to calculate the optimal order-up-to levels. In the second case, although the optimal order-up-to levels are functions of the initial inventory state and are not obtained in closed form, their properties are discussed. We also develop heuristic ordering policies based on the news-vendor model. Our numerical experiments suggest that the heuristic policies perform reasonably well. © 1996 John Wiley & Sons, Inc.     

An exact algorithm for the maximal covering problem

This article develops a robust, exact algorithm for the maximal covering problem (MCP) using dual-based solution methods and greedy heuristics in branch and bound. Based on tests using randomly generated problems with problem parameters similar to those in the existing literature, the hybrid approach developed in this work appears to be effective over a wide range of MCP model parameters. The method is further validated on problems constructed from three real-world data sets. The extensive computational study compares the new method with other existing exact methods using problems that are as big, or larger than, those used in previous work on MCP. The results show that the proposed method is effective in most instances of MCP. In particular, it is shown that bounding schemes using Lagrangian relaxation are effective on MCP as a method of obtaining both exact and heuristic solutions. © 1996 John Wiley & Sons, Inc.