| This research develops a cost minimization model for certain design and operational decisions in batch manufacturing. The decision variables in the model are machine setup times (that can be decreased through investment) and product lot sizes. The model treats demand for products as stochastic, and estimates the joint effect of setup times and lot sizes on the expected manufacturing flow times for products. It then calculates the carrying cost for work-in-process (WIP) and safety stock as a function of expected flow time. The total cost function includes (i) carrying cost for cycle stock, WIP, and safety stock, (ii) direct setup cost, and (iii) investment cost of setup time reduction. Next, this model is transformed into a constrained geometric program, and computational results are reported for several numerical examples.; This research also compares the predictions of the above theoretical model with those of a computer simulation model under similar conditions. In particular, for given demand rates, product routings, and other relevant manufacturing data, the expected product flow times predicted by the theoretical and simulation models are compared. Such comparisons are made for four different combinations of statistical distributions of product demand and jobshop dispatching rules.; The results of these comparisons suggest how the recommendations of the theoretical model ought to be modified before being implemented. In particular, the theoretical model over-estimates expected flow time for given lot sizes, typically by 100% or more. Also, a reduction in lot sizes below the "optimal" lot sizes determined by the theoretical model, generally reduces expected flow time. Finally, compared to product lot size, the distribution of product demand and the jobshop dispatching rule appear to have weaker and less consistent effects on expected flow time and flow time variability. |
