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The problem of scheduling jobs on several identical parallel assembly workstations that constitute a production facility and share a common pool of labor within a factory environment is discussed. Labor requirements vary on each workstation depending upon the job being processed, and the workstation is paced so as to maintain a constant cycle time. The labor needed at any point in time is the sum of the labor requirements over all workstations at that instant. The workforce size is defined as the maximum level of labor required at any point during the schedule. A two-stage approach is proposed to find a schedule that minimizes workforce size: the first stage is a mixed integer linear programming model that determines starting times, and the second is a polynomial-time procedure to assign jobs to specific assembly workstations. Moreover, it is shown that the two stages yield decisions that are jointly optimal for an integrated model that determines starting times and assignments simultaneously. A heuristic...

Many students find the translation of a verbal description of a problem into the appropriate mathematical model a difficult task. We describe how semantic networks can be used to assist in the structuring of complicated models and thereby facilitate the modeling process.

There has been much interest in recent years in the relationships among learning, production rate, and program costs. These relationships are of particular interest in military acquisitions research where, because of the nature of the funding process, the government must assess the cost impact of numerous production rate changes. One approach that is often used to analyze the problem is an empirical application of the “Alchian cost function.” Department of Defense analysts routinely use these models for planning purposes. The purpose of this paper is to demonstrate that the models as being applied imply nonsensical contractor behavior.

We present a real-world problem that illustrates how different linear programming formulations allow different interpretations of solution results and sensitivity analyses. The problem involves the allocation of looms to weave various fabrics in a textile mill and the determination of which fabrics should be purchased outside of the mill in order to meet demand. The case has been used as a teaching tool for emphasizing often over-looked model formulation issues.

Some cost models of the made-to-order production situation incorporate learning and production rate as cost factors. The model developed in this paper is more detailed than the previous efforts. Here the build up of work-in-process to a steady state is explicitly modelled. Likewise, the decrease in work-in-process at the end of the programme is modelled. In this paper, we minimize cost to determine the appropriate task sizes and sequence of resources to allocate to crews of assembly workers. Crew cycle times are also determined.