Optimal part delivery dates in small lot stochastic assembly systems

An important issue in the design and operation of assembly systems is the coordination of part deliveries and processing operations. These decisions can have a significant impact on inventory cost and customer service. The problem is especially complex when actual delivery and processing times are stochastic in nature, as is the case in small lot manufacturing.

In this research a new methodology is developed for determining optimal part delivery dates in stochastic small lot assembly systems. This methodology is based on the descriptive model that comprises of taking the maximum of several random variables. The part arrival and processing times are assumed to follow various known probability distributions. The model includes consideration of limited buffers between stations. The overall objective is to minimize the expected total of part and subassembly inventory cost, makespan cost and tardiness cost.

An approach based on the optimization of individual stations in isolation is used to obtain the part delivery dates at each station. Comparison of the approach with the nonlinear programming based approach to the problem indicates that it generates almost as good solutions in a fraction of the computation time. This approach is then used to study system behavior under various operating conditions. Results indicate that the Iognormal and gamma distributions result in higher total costs than the normal distribution. However, the normal distribution can be used to determine part delivery dates even if the actual distribution is Iognormal or gamma, with relatively small errors compared to the solutions obtained using the correct distribution. Variability is the most important factor in the design of the system, and affects the determination of due dates, buffer capacity requirements, choice of distribution, and estimates of system performance. The role of buffer capacities, however, is not very critical in the design of small lot unbalanced lines.