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This paper discusses an integrated model of batch production and maintenance scheduling on a deteriorating machine producing multiple items to be delivered at a common due date. The model describes the trade-off between total inventory cost and maintenance cost as the increase of production run length. The production run length is a time bucket between two consecutive preventive maintenance activities. The objective function of the model is to minimize total cost consisting of in process and completed part inventory costs, setup cost, preventive and corrective maintenance costs and rework cost. The problem is to determine the optimal production run length and to schedule the batches obtained from determining the production run length in order to minimize total cost.

This research discusses an integer batch scheduling problems for a single-machine with positiondependent batch processing time due to the simultaneous effect of learning and forgetting. The decision variables are the number of batches, batch sizes, and the sequence of the resulting batches. The objective is to minimize total actual flow time, defined as total interval time between the arrival times of parts in all respective batches and their common due date. There are two proposed algorithms to solve the problems. The first is developed by using the Integer Composition method, and it produces an optimal solution. Since the problems can be solved by the first algorithm in a worst-case time complexity O(n2 n-1 ), this research proposes the second algorithm. It is a heuristic algorithm based on the Lagrange Relaxation method. Numerical experiments show that the heuristic algorithm gives outstanding results.

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