This paper discusses the integration model of batch production and preventive maintenance scheduling on a single machine producing, an item to be delivered at a common due date. The machine is a deteriorating machine that requires preventive maintenance to ensure the availability of the machine at a desired service level. Decision variables of the model are the number of preventive maintenances, the schedule, length of production runs, as well as the number of batches, batch sizes and the production schedule of the resulting batches for each production run. The objective function of the model is to minimize the total cost consisting of inventory costs during parts processing, setup cost and cost of preventive maintenance. The results show three important points: First, the sequence of optimal batches always follows the SPT (short processing time). Second, variation of preventive maintenance unit cost does not influence the sequence of batches. Third, the first production run length from production starting time is smaller than the next production run length and this pattern continues until the due date. When in process inventory unit cost is increased, the pattern will continue until a specified cost limit, and beyond the limit the pattern will change to be the opposite pattern.
In business environment, advertisement is very important. Companies spent a lot of money to advertise their products. When there are several players which have the same product to market, the competition will be quite tough since the market size is finite. The amount of the money spent for advertisement will affect the sale of the product. The profit for each company will depend on the amount of money spent for advertisement. However, this will also depend on the money spent by other companies, making the determination of the optimum profit become difficult. For two and three companies, exact value of the optimum profit for each company can be found. However, the analysis for more than three companies is quite complicated so we must resort to numerical method. Examples for the cases of two, three and four companies are given. A company with the smallest effectiveness factor and gross profit will have the smallest optimum profit. Maple has been widely used to derive formulas and to solve the case studies in this paper.
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