This paper addresses the problem of scheduling the timing and quantities of production of n different products over m periods for a single production facility with a prespecified capacity. We assume that the demand is deterministic and can vary from one period to another and from one product to another. The objective is to minimize the sum of production setup and inventory holding costs. For medium-size problems, optimal solution algorithms do not yet exist and therefore heuristic solution algorithms are of interest. Most of the existing heuristics make use of the "forward-pass" concept in one way or the other. Forward pass means we begin by determining the lot sizes for earlier periods before moving to study the later periods. In this paper we study the forward-pass approach as well as a different solution approach which we call the four-step algorithm. We develop the feasibility conditions for pure forward-pass algorithms. Finally, we perform a comparative evaluation study.

In this paper we consider the problem of scheduling "n" independent fades on "m" parallel processors. Each job consists of a single operation with a specific processing time and due date. The processors are identical and the operation of the system is non-preemptive. The objective is to schedule the jobs in such a way that the total tardiness of the n jobs is as small as possible. For the case of a single processor with n jobs, there exists algorithms which provide optimal solutions. On the other hand currently available optimal scheduling algorithms for multiple processors can handle only small problems. Therefore, practitioners are forced to use heuristic methods to schedule their jobs on multiple processors. This raises questions of the following nature: "Are we scheduling our jobs reasonably well? Are there other schedules with which our total tardiness can be lowered substantially? How far off might the heuristic solution be, from the optimal solution?" The study reported in this paper focuses on a heuristic which can handle reasonably large problems, and yet can be simply and economically implemented. Experiments are conducted by establishing lower bounds for the optimal total tardiness of randomly generated scheduling problems. These lower bounds are then compared with the total tardiness obtained from the heuristic. It is found that the heuristic under study provides solutions which are quite close to the optimal ones. The experiments include 560 randomly generated problems that range from "loose" to "tight" in due dates, with varying numbers of jobs and processors. A nonparametric statistical analysis is presented to generalize the results.production/scheduling, statistics: nonparametric, programming: integer algorithms, heuristic

How should a manager make replacement decisions for a chain of machines over time if each is maintained by an optimal control model addressing uncertainty of machine breakdowns? A network representation of the problem involves arcs with interdependent costs. A solution algorithm is presented and replacement considerations under technological change are incorporated into a well-known optimal control model for maintenance under uncertainty (that of Kamien and Schwartz 1971). The method is illustrated by an example.

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