Document Type

Closed Project

Publication Date

Winter 2010


Timothy Anderson

Course Title

Operations Research in Engineering and Technology

Course Number

EMGT 540/640


Operations research -- Case studies, Integer programming, Mathematical optimization, Semiconductor industry -- Management


Purpose – The purpose of this paper is to showcase a case study of how five separate optimization models were used to establish true capacity capabilities for a lab facing a situation in which upper management set a goal, then left the lab to attempt to meet the goal. This paper highlights the first step for this failure analysis laboratory: determining current baseline capacity. It also delves into showing how the lab might demonstrate its ability to successfully increase its capacity from 200 to 400 units of lab evaluations (metrology units or MUs) per week in future.

Design/methodology/approach – An important note in approach is that the researchers developed five separate models in order to more definitely establish baseline capacity. Given the lab problem characteristics, it was determined that integer linear programming (ILP) would form the basis of four of the separate models. One of the models deviated more from this approach by encompassing goal programming for target values of MUs in each metrology. The overall design/approach for each model was to follow as closely as possible the model building approach of 1) Identifying Problem, 2) Formulate and Implement Model, 3) Analyze Model, 4) Test Results/Re-formulate, and 5) Implement Solution. A literature review was used to establish current state of knowledge and fit within capacity optimization research.

Findings – While the topic fits into a general category of capacity optimization, more specifically after examining multiple problems facing the laboratory under study, it was found to be one of a subset of optimizing product-mix production. The models showed that the 400MU goal could not be reached. Instead, the maximum appears to be on the order of 200MUs and is in line with historically assumed throughput. Goal programming to meet targets of MUs in each metrology type was unsatisfactory in that it gave fewer MUs per week. The final model suggested that a second shift, or doubling the equipment and technicians available, could reach the 400MU goal.

Research limitations/implications – Research implications include an example of product-mix problem analysis and associated ILP and GP model for a type of business which is not often under study, laboratory testing. Future work could include aspects of throughput-time (TPT) and/or flow optimization through bottleneck reduction. Cost was not a primary criterion for the lab under study, but future work could include cost as a constraint and/or decision variable – this would align well with a myriad of previous literature on similar problems. If cost becomes more important to the lab, then looking at economic lot quantity (EOQ) could also prove relevant.

Originality/value – This case study provides value with a model which appears somewhat unique in that cost is not of primary importance to the business; so this example could prove invaluable for researchers sifting through a large quantity of product-mix learnings, but finding it difficult to find examples without cost as a primary constraint or decision variable to be minimized. Additionally, this study illustrates the added importance of rigorous understanding of the business problem from the onset. The researchers also provide indication that goal-programming may not be an appropriate approach for similar capacity problems.


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