0 – 1 integer programming modeling examples - rutgers university.ppt

Chapter 5 - Integer Programming Chapter Topics Integer Programming (IP) Models Integer Programming Graphical Solution Computer Solution of Integer Programming Problems With Excel and QM for Windows University bookstore expansion project. Not enough space available for both a computer department and a clothing department. Data: 0 – 1 Integer Programming Modeling Examples Capital Budgeting Example (1 of 4) x1 = selection of web site project x2 = selection of warehouse project x3 = selection clothing department project x4 = selection of computer department project x5 = selection of ATM project xi = 1 if project “i” is selected, 0 if project “i” is not selected Maximize Z = $120x1 + $85x2 + $105x3 + $140x4 + $70x5 subject to: 55x1 + 45x2 + 60x3 + 50x4 + 30x5 ? 150 40x1 + 35x2 + 25x3 + 35x4 + 30x5 ? 110 25x1 + 20x2 + 30x4 ? 60 x3 + x4 ? 1 xi = 0 or 1 0 – 1 Integer Programming Modeling Examples Capital Budgeting Example (2 of 4) Exhibit 5.16 0 – 1 Integer Programming Modeling Examples Capital Budgeting Example (3 of 4) Exhibit 5.17 0 – 1 Integer Programming Modeling Examples Capital Budgeting Example (4 of 4) 0 – 1 Integer Programming Modeling Examples Fixed Charge and Facility Example (1 of 4) Which of six farms should be purchased that will meet current production capacity at minimum total cost, including annual fixed costs and shipping costs? Data: yi = 0 if farm i is not selected, and 1 if farm i is selected, i = 1,2,3,4,5,6 xij = potatoes (tons, 1000s) shipped from farm i, i = 1,2,3,4,5,6 to plant j, j = A,B,C. Minimize Z = 18x1A + 15x1B + 12x1C + 13x2A + 10x2B + 17x2C + 16x3A + 14x3B + 18x3C + 19x4A + 15x4b + 16x4C + 17x5A + 19x5B + 12x5C + 14x6A + 16x6B + 12x6C + 405y1 + 390y2 + 450y3 + 368y4 + 520y5 + 465y6 subject to: x1A + x1B + x1C - 11.2y1 0 x2A + x2B + x2C -10.5y2 0 x3A + x3B + x3C - 12.8y3 0