Abstract
How to determine the optimal lot-size for D good items in a job shop is quite important problem. We extend the study on the multiple lotsizing in production to order to the case that machine is in an alternating renewal process (i.e. alternates between operating and failed) with both up and down times are exponential. The numeral solution & procedure is carried out in the case that yield distribution when the machine is operating is the so-called Interrupted Geometric. The number of good items in a lot can be accurately determined only after completing production of that lot. If the number of good items falls short of the outstanding order, the other production will be required until the total good items produced is at least D. Processing each lot entails fixed, per-unit production costs and machine repair cost. The tradeoff is between running large lots which entails potentially costly overproduction, and small lots which may necessitate multiple production runs and their associated setups. The value of repair cost will also affect the optimal lot-size. In this article, first we derive the yield probability by the simulation software “Em-plant”, and then through the probability, we get the optimal lot-sizing ND with demand D by the statistic software “S-plus”. We provide Ⅰ.Under the same demand, the more failure frequency causes the larger ND. Ⅱ. Once the machine has failure, the more setup cost and more failure frequency will make ND have not the property “ND is no more than D”. Ⅲ. The increasing repair cost causes the decreasing ND.