Operational tolerance allocation and machine assignment under process capability and product value constraints
Process planning is an activity within the production process that translates design requirements into a detailed description of instructions for transforming a raw stock of material into a completed product. The instructions contain a sequence of operations that should be followed to arrive at the final product that satisfies design requirements. Over the years, many researchers have examined the modeling and analysis of process plans for the production of discrete parts. As a result, a number of mathematical models have been proposed. Input to these models is usually a sequence of operations required to complete the part with each operation having associated processing equipment with certain capability. These models can be used to check the feasibility of the process plan or to calculate operational tolerances such that the final product is produced within design specifications. The existing models allocate operational tolerances under specific assumptions. For example, when these models consider the process capability, they formulate it as a single fixed value that represents the worst case performance of a process capability. None of the existing models consider the stochastic nature of process capability. In addition, the current tolerance allocation research does not place emphasis on the value of the product under consideration. It is logical that high-value products should be assigned to highly capable processes in order to increase the confidence level in their production to design specifications. Furthermore, the existing tolerance allocation methods typically associate single processing equipment (machine) with certain capability to each operation in the process plan. Because there is no option for choosing a different machine automatically in case the assigned machine results in an infeasible plan. Actually, assigning a single machine to each operation can result in sub optimality in terms of the allocated tolerances and may lead to scheduling inflexibility. This research proposes a model which simultaneously allocates operational tolerances and assigns the most economical machines. Two versions of the model are developed, stochastic and fuzzy. The stochastic version of the model captures the stochastic nature of process capability in which, a stochastic distribution is used to represent the capability of a process. Alternatively, the fuzzy version evaluates the process capability utilizing expert's knowledge. Both the proposed versions introduce flexibility and optimality to the modeling of the production process by considering multiple available machines for each type of operation. This helps in selecting the machine with the lowest capability possible to make the process plan feasible while allocating maximum tolerances to each operation. Furthermore, a formula that determines the value of product considering the change of product value through the different stages of the production process is presented and integrated with the proposed models. Both versions of the proposed model can be easily solved by common of-the-shelf software. The models are implemented and analyzed using literature-application example. Experimental results confirm the effectiveness of the proposed model.
Thesis (Ph.D.)--Wichita State University, College of Engineering, Dept. of of Industrial and Manufacturing Engineering.