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.
This paper discusses an integrated model of batch production and maintenance scheduling on flow shop with two deteriorating machines producing single item to be delivered at a due date. The model describes the trade-off between production and maintenance costs as the production run length increases on two machines. The objective function of the model is to minimize the total cost consisting of in process and completed part inventory costs, setup costs, preventive & corrective maintenance costs and rework costs on two machines. The step-wise optimization algorithm is developed to solve a mixed integer quadratic programming. Comparison with the practice and the model sensitivity analysis are demonstrated to clarify how the algorithm works.
In the manufacturing industry, several identical parts can be processed in batches, and setup time is needed between two consecutive batches. Since the processing times of batches are not always fixed during a scheduling period due to learning and deterioration effects, this research deals with batch scheduling problems with simultaneous learning and deterioration effects. The objective is to minimize total actual flow time, defined as a time interval between the arrival of all parts at the shop and their common due date. The decision variables are the number of batches, integer batch sizes, and the sequence of the resulting batches. This research proposes a heuristic algorithm based on the Lagrange Relaxation. The effectiveness of the proposed algorithm is determined by comparing the resulting solutions of the algorithm to the respective optimal solution obtained from the enumeration method. Numerical experience results show that the average of difference among the solutions is 0.05%.
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