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A heuristic approach to the batch sizing problem

Many products are produced using a sequential series of operations. Given that losses occur at each operation, production planners must routinely estimate a starting batch size such that a stated customer order quantity is obtained. This paper presents a fast computer heuristic for solving this problem when the yield at each operation is assumed to be a binomial random variable. When the customer order quantity is large, the evaluation of the binomial yield distribution becomes cumbersome. Therefore a normal approximation to the binomial yield and a standardised loss function is used in this heuristic. The approach searches for the starting batch size that maximises an expected profit function composed of the cost to process each unit at each operation, the per unit shortage cost for amounts less than the customer order quantity and the per unit overage costs for amounts greater than the customer order quantity. The search procedure utilises an iterative improvement search algorithm that starts from a simple deterministic solution. Using numerical examples, the effectiveness of the heuristic's normal approximation and search procedure is evaluated. The approach is shown to work well in terms of both run time and solution quality, even when applied to extremely large problems.