Michael J. Magazine

Quantitative Models for Supply Chain Management

From the Publisher: Quantitative models and computer based tools are essential for making decisions in todays business environment. These tools are of particular importance in the rapidly growing area of supply chain management. This volume is a unified effort to provide a systematic summary of the large variety of new issues being considered, the new set of models being developed, the new techniques for analysis, and the computational methods that have become available recently. The volumes objective is to provide a self-contained, sophisticated research summary - a snapshot at this point of time - in the area of Quantitative Models for Supply Chain Management. This volume can serve as a graduate text, as a reference for researchers and as a guide for further development of this field.

Sequencing of insertions in printed circuit board assembly

Manufacturability of printed circuit boards is a fertile area for operations researchers to aid in productivity improvements for the electronics industry. A class of such problems is described, and a particular problem that arises from an application to a middle sized electronics firm is modeled and solved. The specific problem to determine the best sequence of insertion operations is formulated as a type of directed postman problem. An algorithm is developed for the problem that yields an optimal solution under certain conditions and approximate solutions, with a constant performance bound, when these conditions are relaxed.

A Classified Bibliography of Research on Optimal Design and Control of Queues

This paper presents a classified bibliography organized into six sections-static design models, dynamic control models, models involving queue discipline control, miscellaneous models, tutorial and survey papers, and books that have specific portions devoted to design and control. Some of the above categories are further subdivided when appropriate, and explanations of the types of models in each category and subcategory precede the actual list of references. Papers that fall into more than one category are cross-referenced.

A Taxonomic Review of Supply Chain Management Research

In the previous chapters, we focused largely on quantitative approaches to solving Supply Chain Management (SCM) problems including such issues as: inventory management, supply contracts, information flow, product variety, and international operations. In this chapter, we will broaden our focus to include other approaches to SCM problems, by presenting a broad taxonomy for understanding SCM research.

Fast, effective algorithms for simple assembly line balancing problems

A simple, fast and effective heuristic for the Simple Assembly Line Balancing Type I problem (minimizing the number of workstations) is proposed. A fast and effective branch-and-bound algorithm, which incorporates this heuristic for use in bounding, is developed. The algorithm introduces heuristic fathoming as a technique for reducing the size of the branch-and-bound tree. Methods to solve the Simple Assembly Line Balancing Type II problem (maximizing the production rate) are also described. Upper bounds on all heuristics for both problems are provided.

Batch sizing and job sequencing on a single machine

We study a single-machine scheduling problem in which the items to be processed have to be batched as well as sequenced. Since processed items become available in batches, flow times are defined to be the same for all items in the same batch. A constant set-up delay is incurred between consecutive batches. For any fixed, but arbitrary item sequence, we present an algorithm that finds a sequence of batches such that the total flow time of the items is minimized; we prove that for a set ofn items, the algorithm runs inO(n) time. We show that, among all sequences, the one leading to the minimum flow time has the items in non-decreasing order of running times. Thus, the optimal algorithm for the combined problem, called thebatch-sizing problem, runs inO(n logn) time. We also prove that this algorithm yields an improved solution to a scheduling problem recently studied by Baker [1].

Assembly line balancing as generalized bin packing

Bin packing heuristics are generalized and adapted to solve the assembly line balancing problem. Worst-case analysis is provided. The results are compared to those for a resource constrained scheduling problem considered by Garey, Graham, Johnson and Yao.

A heuristic algorithm for the multidimensional zero-one knapsack problem

Abstract Computational and theoretical aspects of a new heuristic for the multidimensional zero-one knapsack problem are studied. Its computational efficiency is compared with two other well-known heuristics.

Maximizing the value of a space mission

Abstract The problem of selecting and scheduling projects to maximize the scientific, military or commercial value of a space mission has been the subject of ongoing studies for several years. The typical outcome of such studies, even after many man-years of effort, is a heuristic solution with no comparison to optimality. We depart from the traditional, knowledge-based systems, approach and describe a machine scheduling model for the problem. The problem, which is similar to a longest path problem with time windows, is NP-complete in the strong sense. A number of heuristic methods are described, and computational tests reveal that they routinely deliver very close to optimal solutions. We describe two upper bounding procedures, based upon a preemptive relaxation of the problem, and upon the use of Lagragean relaxation. The heuristics and bounding procedures are incorporated into a dynamic programming algorithm, which can solve to optimality randomly generated problem instances with one hundred or more projects. We further demonstrate how, if problems are too large to be solved optimally, a limited-enumeration version of this algorithm can be used to provide very accurate heuristic solutions. We also examine some special cases and variants of the problem.

When the Greedy Solution Solves a Class of Knapsack Problems

This paper analyzes a heuristic for the knapsack problem that recursively determines a solution by making a variable with smallest marginal unit cost as large as possible. Recursive necessary and sufficient conditions for the optimality of such “greedy” solutions and a “good” algorithm for verifying these conditions are given. Maximum absolute error for nonoptimal “greedy” solutions is also examined.