Optimal control of inventory accumulation in selective assembly processes

Assembly is a type of production process in which a number of components are combined to yield a final product. Although the concept of interchangeable parts has long been known as the fundamental principle of assembly processes, randomly picking some bulked components with dimensions varying in predefined tolerances may not be a valid approach to obtain special final products with considerably tighter tolerances. Therefore, each of the components needs to be measured and classified into dimensional groups in advance so that quality products can be obtained by matching components from suitable groups. This assembly scheme is called as “selective assembly.” In this work, we consider an assembly case with a pair of components in which one is manufactured on a given number of parallel processes whose settings can be changed to affect the dimensional distribution of the yield while the other component with a slightly bigger tolerance is manufactured on a single process with constant settings. In order to minimize the number of components which could not have been matched with their counterparts, we develop a nonlinear mathematical model to determine the optimal machine settings corresponding to the nominal mean of the component dimension which follows a normal distribution when it is machined. The solution of the mathematical model not only provides the individual settings for the parallel processes producing the same type of component but also the optimal batch sizes at each trial. We have finally used a simulation model of the whole production system, in order to prove that the solution of the mathematical model is able to provide the machine settings which minimize the number of unmatched parts at each trial.