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Poly Products sells packaging tape to industrial customers

Operations Management

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Poly Products sells packaging tape to industrial customers. All tape is sold in 100-foot rolls that are cut in various widths from a master roll, which is 15 inches wide. The product line consists of the following widths: 2?, 3?, 5?, 7?, and 11?. These can be cut in different combinations from a 15-inch master roll. For example, one combination might consist of three cuts of 5? each. Another combination might consist of two 2? cuts and an 11? cut. Both of these combinations use the entire 15-inch roll without any waste, but other combinations are also possible. For example, another combination might consist of two 7? cuts. This combination creates one inch of waste for every roll cut this way.

Each week, Poly Products collects demands from its customers and distributors and must figure out how to configure the cuts in its master rolls. To do so, the production manager lists all possible combinations of cuts and tries to fit them together so that waste is minimized while demand is met. (In particular, demand must be met exactly, because Poly Products does not keep inventories of its tape.) This week’s demands are shown below.

A) How many combinations can be cut from a 15-inch master roll so that there is less than two inches of waste (i.e., the smallest quantity that can be sold) left on the roll?

B) Find a set of combinations that meets demand exactly and generates the minimum amount of waste. (Stated another way, the requirement is to meet or exceed demand for each size, but any excess must be counted as waste.) What is the optimal set of combinations and the minimum amount of waste?

C) Find as many alternate optima as you can. Show all work and formulas in excel including sensitiviy reoprts, and solver setup.