Reference no: EM132291650

A paper mill produces a so-called linear board in jumbo reels having a standard width of 68” and each reel has a fixed length. The company’s customers, however, order reels having smaller widths (and the same fixed length as the larger reel). Today’s orders are for:

(i) 110 reels of 22-inch width;

(ii) 120 reels of 20-inch width; and (iii) 80 reels of 12-inch width. These smaller widths are to be cut from the larger standard size reel. Reels of smaller size that result when a jumbo reel is slit are referred to as trim waste. For example, when a jumbo reel slit into two reels of 22” width and one reel of 20” width, the residual reel of 4” width is trim waste. Excess production of the required size reels is also deemed to be waste.

The production scheduler would like to manufacture today’s orders so as to minimize total waste.

a) Formulate the problem as a linear program.

b) Solve the program using EXCEL Solver.

c) Suppose switch-over times are very long. How would the solution change if we can use at most 4 patterns? At most 3 patterns? At most 2 patterns? (Hint: You will need to introduce binary variables.)