Control of a continuous production inventory system with production quantity restrictions

Motivated by a real-world application in the chemical industry, we consider the problem of controlling a production asset that has to run continuously around the clock. This requirement causes minimum and maximum production quantities per period, resulting from the minimally and maximally feasible production rates. Our goal in this paper is to find a good control rule for this production inventory setting. To this end, we first show that the setting is analytically equivalent to a periodic-review inventory system with an order band, for which a modified base-stock policy is optimal. We then develop an iterative solution algorithm to approximate the optimal base-stock level under a predefined service-level target. This algorithm is easily implementable in a spreadsheet software tool with additional Visual Basic for Applications coding. In a numerical study, we find that the approximation works very well for a broad set of parameters. In contrast, simple rules-of-thumb such as the usage of a “standard” base-stock level that does not consider the order band may result in severe errors. Either the chosen base-stock level is too low, causing the service-level target to be undershot (by up to 40% in our analyzed settings), or it is too high, resulting in an overshoot of the service-level target and thus in excessive inventory. In the real-world application example, the new solution approach identifies an inventory saving potential of about 17%.