Results

The original problem description and instance data are taken from [GHP02] (Section 8.2 Production of drinking glasses). The costs and resource usage data for the six glass types are listed in Table Data for six glass types.

The solution of the original problem with the basic demand scenario has a total cost of € 185,899. The resulting detailed production plan is displayed in Table Optimal production plan for basic demand scenario. We find that the available manpower is fully used most of the time (in the first week, 351 hours are worked, in all other weeks the limit of 390 hours is reached) and the machines are used to their full capacity in certain time periods (weeks 1-3 and 5), but the available storage space is in excess of the actual needs.

If we try to introduce robustness to such a tightly constrained problem, the outcome most likely will be 'problem infeasible' as there is no slack to incorporate alternatives. We have therefore somewhat relaxed the original bound on the personnel hours, assuming that its original value represents a rough worst-case estimate and that the actually available working hours are 20% higher. The more fine-grained estimate of absence results in the solution summarized in Table Summary results with robust formulation of absence. The overall cost of € 181,210 is slightly lower than the previous, fixed worst-case absence case.

The scenario-based approach results in a higher total cost of €203,545. In the summary results in Table Summary results with demand scenarios we observe that both, machine capacity and workers' hours, are most of the time used at or close to their capacity limit (850 and 429=1.1·390 respectively). Furthermore, larger quantities of products are held in stock.

For easier comparison, Table Summary results for deterministic model with 1.1CAPW shows the summary results for the original model with the same capacity limits as have been used wit the robust formulation in Table Summary results with demand scenarios, the total cost is in this case €181,432.