The canning problem revisited: The case of capacitated production and fixed demand

We report on optimizing a ‘variable yield’ machine-fill type of production process with limited capacity n, a fixed demand d and a process yield rate that depends on a controllable mean setting. Using a profit function that includes both the cost of production and a penalty for under-production, we show that obtaining an optimal mean setting is straightforward. As the ingredient cost becomes small compared to recycling and production costs, the relative profit is found to be a strongly asymmetric function of the process mean. The resulting managerial insights suggest that, with respect to optimal mean setting, for a wide variety of cost parameters, overfilling is in general better than underfilling.