Di LiuFollow

Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Industrial Engineering

Committee Chair/Advisor

Dr. Tuğçe Işık

Committee Member

Dr. Mary Beth Kurz

Committee Member

Dr. David Neyens

Committee Member

Dr. Robert Riggs

Committee Member

Dr. Dan Li


In a production process, it is impossible to produce parts with exact specifications. Thus, specific ranges, i.e., tolerances, are commonly employed to define intervals for the quality characteristics of conforming products (Wu & Tang (1998)). Usually, a product is deemed conforming when the measurement of the quality characteristic falls within the tolerance. If the measurement falls outside the tolerance, the product is nonconforming and it can be reworked or scrapped. One of the important engineering problems commonly faced by practitioners is to determine optimal engineering tolerances to be used in production. As a result, tolerance design techniques are widely used for manufacturing processes. In most of the associated literature, tolerance specifications are presented as a single-tolerance set which includes only one pair of lower and upper specification limits. In contrast, our work is the first to introduce the concept of double-tolerance sets to the tolerance design optimization literature. A double-tolerance set includes inner and outer tolerances for a quality characteristic. In this dissertation, we develop several optimization models that use double-tolerance schemes for single or multiple quality characteristics. These models are used to maximize the long-run average profit in manufacturing and remanufacturing processes by considering the trade-off between production and quality loss costs. Our developments demonstrate that setting outer tolerances can perform better than the traditional single tolerance schemes in a variety of settings.

Researchers have usually considered deterministic models to solve tolerance optimization problems in the literature. However, most production environments are stochastic in nature due to the randomness inherent in the production processes. In the models presented in this dissertation, we assume that the service times for processing, reworking, and refurbishing products are uncertain. Furthermore, the production/refurbishing processes operate as single server queues. Thus, tolerances are optimized in stochastic production environments. To make our models more practical, we also assume that the processing, reworking, and refurbishing operations are imperfect, which indicates that the products could be nonconforming after reworking or refurbishing.

Our goal is to improve the manufacturing and remanufacturing processes by using the new concept of double tolerance schemes. In the three research studies presented in this dissertation, nonlinear optimization models are used to maximize the long-run average profit. Theoretical results are presented as part of our analysis. We provide sufficient conditions or properties for the concavity of the objective functions in different models. We also analyze special cases of some models focusing on simplified systems with no holding costs or symmetric system parameters. Numerical examples in parameter settings of interest are provided to compare the models we developed with chosen benchmark models. For base scenarios included in the numerical examples, sensitivity analyses are done to illustrate the impact of some parameters on the optimal solutions and optimal long-run average profits.

This dissertation uses three different manufacturing settings to study double tolerance schemes. First, we consider a production line with processing and rework stations, as well as instantaneous inspection and scrap operations. Assuming stochastic processing and rework times, we develop optimization models for double-tolerance sets and single tolerance sets, respectively. Our goal is to determine optimal tolerance sets to maximize the long-run average profit on a production line. Theoretical results, numerical examples, and sensitivity analysis are provided. Our analysis shows that in comparison to the single tolerance model, the double tolerance model has the potential to perform more efficiently and improve profits.

Second, we consider a remanufacturing system where nonconforming products returned by customers are refurbished. We focus on two remanufacturing designs with double tolerance sets on independent, dual quality characteristics. These alternative designs differ in the number of quality characteristics they allow to be refurbished for each product. Assuming some refurbished products are sold at discounted prices, we formulate an optimization problem to maximize profits. A system with no refurbishing is considered as a benchmark. To find the best refurbishing design in different scenarios, we provide both theoretical and numerical analysis under different parameter settings.

Finally, we consider a tolerance design problem for product families with multiple variants. We assume that after processing or reworking, all product variants are inspected on the same quality characteristic with different target values. The products that are nonconforming for one product variant could be conforming for another product variant. Within the double tolerance scheme, we introduce a shared outer specification limit (shared-SL) between each pair of adjacent targets to separate the nonconforming products to be reworked for each target. A nonlinear optimization model is used to identify the optimal locations of these shared-SLs to maximize profits. A benchmark model where different variants of products are produced, reworked, and scraped independently is also developed. The numerical study shows that the shared-SL model outperforms the benchmark model.



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