Product-based service level fulfillment in a limited reporting period in case of stochastic demand and rolling schedules
Final Report Abstract
How annoying when the shelf is empty and the customer either has to wait or reaches for a competitor's product! This is not only annoying for the customer, but also for the supplier, as he might lose revenues. In order to avoid such situations, a supplier usually keeps safety stocks on hand. This allows to meet a certain share of an unexpectedly higher demand. But how high should safety stocks be? If safety stocks are too high, this leads to disproportionately high storage costs; if they are too low, customer anger and lost profits increase. We addressed this well-known decision problem; however, we extended it by taking into account that compliance with an agreed service level is checked in regular intervals – the reporting periods. This procedure is common in industrial practice between a supplier and a buyer. Also, penalties may be charged if the service level agreement is violated. We have developed solution algorithms for three different service level definitions that determine safety stocks needed for compliance and minimize expected costs. The fill rate for grace has proven to be particularly advantageous. It allows a certain number of shortages in a reporting period while shortages in excess of this result in penalties to be paid to the customer, e. g. in the form of price reductions. Here, the supplier has the incentive to avoid penalty payments, while the customer receives a compensation for his trouble if his pain threshold is exceeded at the end of the reporting period. In addition, this service level definition proves to be particularly cost-effective for the supplier compared to a strict compliance with the service level. A flexible adjustment of safety stocks in the reporting period in response to shortages that have occurred so far often also requires a correspondingly flexible adjustment of production plans. Planning these actions has been another focus of the DFG project. A particular challenge here is the representation of the uncertainty of demand in a production planning model with limited capacities (abbreviated: S-CLSP). One option is the use of a small set of representative demand scenarios. For this purpose, we have developed a new, versatile scenario generation heuristic. However, this alone does not enable the solution of an S-CLSP that can make the necessary dynamic adjustments to production quantities during the reporting period while considering a fill rate for grace. In order to solve such a model in a reasonable computation time, we set up an S-CLSP with a static-dynamic uncertainty strategy and decomposed it into solvable subproblems using hierarchical decomposition. Extensive computational tests have shown that, on average, 12.3% of the expected costs can be saved compared to a static uncertainty strategy if the production quantities directives are undercut by a maximum of 10%.
