The mathematical programming formulation of this Bottleneck Multiple Subset Sum Problem is given by
A real-world problem for (MSSP) from a company producing objects of marble. Every week a shipment of m marble slabs from a quarry is received by the company. These slabs have a uniform size and are much longer than wide. The company produces different products, which first have to be cut from the marble slabs and are then further processed. In particular, each product requires a piece with a specified length from a marble slab. Depending on current stock, the company prepares a list of products that it would be interested to produce. Out of this list, some products should be selected and cut from the slabs so that the total amount of wasted marble is minimized. This problem was modeled as a (MSSP) with the slabs corresponding to the knapsacks and the lengths corresponding to the weights.
- U. Pferschy, D. Pisinger, Knapsack Problems, 2004, DOI