INEN 420 Final Project Rhoda Daniel Javier Grummins Engine Company Facts Produces 2 types of diesel trucks 300 year Selling prices and manufacturing costs Government regulation Pollution emission Cost 2 000 00 to hold a truck Maximum Demand for Trucks Year Type 1 Type 2 1 100 200 2 200 100 3 300 150 Grummins Engine Company Assumptions Zero trucks in stock at the end of the 3rd year Should not keep more trucks in inventory than demand predicts so production is regulated by the amount of trucks in inventory and the amount of trucks that can be sold Trucks are only produced and sold not acquired by any other method such as auctions trading etc Grummins Engine Company Formulation Decision variables Pij Number of trucks each type i produced for each year j Sij Number of trucks each type i sold for each year j Rij Number of trucks each type i that remain in stock at the end of each year j For i 1 2 j 1 2 3 Grummins Engine Company Formulation Objective Function Max Z 20 S11 S12 S13 17 S21 S22 S23 15 P11 P12 P13 14 P21 P22 P23 2 R11 R12 R21 R22 in thousands Grummins Engine Company Formulation Constraints P11 P21 P12 P22 P13 P23 S11 S12 S13 S21 S22 S23 320 320 320 100 200 300 200 100 150 Production Sale Grummins Engine Company Formulation Constraints R11 P11 S11 0 Remain in stock R21 P21 S21 0 R12 P12 S12 R11 0 R22 P22 S22 R21 0 P13 R12 S13 0 P23 R22 S23 0 5P11 5P12 5P13 5P21 5P22 5P23 0 Emissions requirement Pij Sij Rij 0 Grummins Engine Company Optimal Solution using LINDO Excel Solver Z S11 S12 S13 S21 S22 S23 3 600 00 in thousands 100 200 150 200 100 150 Grummins Engine Company Optimal Solution P11 P12 P13 P21 P22 P23 R11 R12 R21 R22 100 200 150 200 100 150 0 0 0 0 Grummins Engine Company Optimal Solution 10 iterations Company should sell every truck they make each year Grummins Engine Company Sensitivity Analysis Decision Variables Current Sale Production thousands Range of Increase Decrease Objective Function Coefficient Range of Decision Variables S11 20 0 20 C11 S12 20 0 20 C12 S13 20 5 0 15 C13 20 S21 17 8 9 C21 S22 17 8 9 C22 S23 17 8 9 C23 P11 15 2 0 13 C14 15 P12 15 2 0 13 C15 15 Grummins Engine Company Sensitivity Analysis Decision Variables Current Sale Production thousands Range of Increase Decrease Objective Function Coefficient Range of Decision Variables P13 15 0 2 15 C16 17 P21 14 2 8 12 C24 22 P22 14 2 2 12 C25 16 P23 14 2 C26 16 R11 2 2 0 C1 R12 2 2 0 C2 R21 2 2 0 C3 R22 2 2 0 C4 Grummins Engine Company Sensitivity Analysis Decision Variable Current RightHand Side Range of Increase Decrease Ranges of RightHand Sides b1 320 20 300 b1 b2 320 20 300 b2 b3 320 20 300 b3 b4 100 20 20 80 b4 120 b5 200 20 20 180 b5 220 b6 300 150 150 b6 b7 200 150 20 50 b7 220 Grummins Engine Company Sensitivity Analysis Decision Variable Current RightHand Side Range of Increase Decrease Ranges of RightHand Sides b8 100 100 20 0 b8 120 b9 150 150 10 0 b9 160 b10 0 20 20 20 b10 20 b11 0 20 150 20 b11 150 b12 0 20 20 20 b12 20 b13 0 20 100 20 b13 100 b14 0 150 150 150 b14 150 b15 0 150 10 150 b15 10 b16 0 750 100 750 b16 100 Wheat Warehouse Facts Capacity 20 000 bushels Month 1 6 000 bushels Sell up to the initial stock at the current month s selling price Buy as much wheat as wanted Up to 20K Month Selling Price Purchase Price 1 3 8 2 6 8 3 7 2 4 1 3 5 4 4 6 5 3 7 5 3 8 1 2 9 3 5 10 2 5 Wheat Warehouse Assumptions Wheat can only be sold or purchased at the given rates Ending inventory Ending inventory beginning inventory amount sold amount purchased Wheat Warehouse Formulation Decision variables si amount of wheat in thousands sold during month i i 1 10 pi amount of wheat in thousands purchased during month i i 1 10 ej of bushels in thousands left at the end of month j j 1 9 Wheat Warehouse Formulation Objective Function Max Z 3s1 8p1 6s2 8p2 7s3 2p3 s4 3p4 4s5 4p5 5s6 3p6 5s7 3p7 s8 2p8 3s9 5p9 2s10 5p10 in thousands Wheat Warehouse Formulation Constraints s1 s2 e1 s3 e2 s4 e3 s5 e4 s6 e5 s7 e6 s8 e7 s9 e8 s10 e9 6 0 0 0 0 0 0 0 0 0 selling restrictions Wheat Warehouse Formulation Constraints p1 s1 p2 s2 e1 p3 s3 e2 p4 s4 e3 p5 s5 e4 p6 s6 e5 p7 s7 e6 p8 s8 e7 p9 s9 e8 p10 s10 e9 14 purchasing restrictions 20 20 20 20 20 20 20 20 20 Wheat Warehouse Formulation Constraints e1 s1 p1 6 ending inventory e2 s2 p2 e1 0 e3 s3 p3 e2 0 e4 s4 p4 e3 0 e5 s5 p5 e4 0 e6 s6 p6 e5 0 e7 s7 p7 e6 0 e8 s8 p8 e7 0 e9 s9 p9 e8 0 si pi 0 i 1 10 ei 0 i 1 9 Wheat Warehouse Optimal Solution using LINDO Excel Solver after 20 iterations Z 162 in thousands s3 6 000 p3 20 000 s5 0 p5 0 s6 20 000 p6 20 000 s7 20 000 p7 0 p8 20 000 s9 20 000 s10 0 Wheat Warehouse Sensitivity Analysis Decision Variable Current Selling Purchase Price Range of Increase Decrease Objective Function Coefficient Ranges of Decision Variables s1 3 4 c1 7 p1 8 1 7 c11 s2 6 1 c2 7 p2 8 1 7 c21 s3 7 1 1 6 c3 8 p3 2 1 1 1 c31 3 s4 1 1 c4 2 p4 3 1 2 c41 s5 4 2 0 2 c5 4 p5 4 0 4 c51 Wheat Warehouse Sensitivity Analysis Decision Variable Current Selling Purchase Price Range of Increase Decrease Objective Function Coefficient Ranges of Decision Variables s6 5 1 4 c6 p6 3 2 c61 5 s7 5 2 3 c7 p7 3 1 2 2 c71 5 s8 1 1 c8 2 p8 2 1 1 1 c81 3 s9 3 1 2 2 c9 5 p9 5 2 3 c91 s10 2 2 1 0 c10 3 p10 5 5 0 c11 Wheat Warehouse Sensitivity Analysis Decision Variable Current RightHand Side Range of Increase Decrease Ranges of Right Hand Sides b1 6 6 0 b1 b2 0 6 6 b2 b3 0 6 6 b3 b4 0 20 20 b4 b5 0 20 20 b5 b6 0 20 20 b6 b7 0 0 0 b7 b8 0 0 0 b8 b9 0 0 0 b9 Wheat Warehouse Sensitivity Analysis Decision Variable …