Industrial engineers are planning the layout of cells i = 1,c, 18 in a rectangular manufacturing facility of x = 1000 by y = 200 feet with a 6-foot-wide, two-way conveyor system along the y = 0 boundary22. It has already been decided that cells will be sequenced along the conveyor in the same order as their i subscripts, but the exact geometry of the cells remains to be fixed.

Analysis of cell loadings has produced lower limits xi and yi on the x and y dimensions of each cell.

Engineers have also specified minimum cell perimeters pi as a surrogate for area (which would lead to nonlinear optimization). Conveyor traffic will enter and exit at input and output stations located at cell x-midpoints along the conveyor, and one-way traffic flows from cell i to cell j are estimated at fi, j. The IEs seek a feasible design that minimizes total travel (flow times distance)

on the conveyor. Formulate an LP model of this layout problem using the decision variables 1i, j = 1,c, 182 xj ! left x@coordinate of cell j yi ! y@depth of cell j di, j

+ ! positive x@distance between I>O stations of cells i and j di, j

- ! negative x@distance between I>O stations of cells i and j