# Cassimy_Evan_Homework04.doc - Evan Cassimy MGMT 651...

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Evan Cassimy MGMT 651 2/2/2020 Professor Avijit Sarkar Homework 4 1. (15 points) Chapter 6 Problem 2 Part A Transportation problem: Arises frequently in planning for the distribution of goods and services from several supply locations to several demand locations. m = origins n = destinations X ij = number of units shipped from origin i to destination i = 1,2, m j = 1, 2, 3, n X 11 = the amount transferred from Jefferson City to Des Moines X 12 = the amount transferred from Jefferson City to Kansas City X 13 = the amount transferred from Jefferson City to St. Louis X 21 = the amount transferred from Omaha to Des Moines X 22 = the amount transferred from Omaha to Kansas City X 23 = the amount transferred from Omaha to St. Louis Cost expression : Transportation for units shipped from Jefferson City = 14x 11 + 9x 12 + 7x 13 Transportation for units shipped from Omaha = 8x 21 + 10x 22 + 5x 23 Supply Constraints : Jefferson City = 30 = X 11+ X 12 + X X 11+ X 12 + X 13 < 30 Jefferson City Omaha = 20 = X 21 + X 22 + X X 21 + X 22 + X 23 < 20 Omaha Demand Constraints: X 11 + X 21 = 25 Des Moines X 12 + X 22 = 15 Kansas City X 13 + X 23 = 10 St. Louis Minimum : Submit your homework as one single attachment. IncludePOM-QM input and output screenshots wherever applicable. If you submit your homework as an MS-Excel document, make sure that it is properly formatted to 8.5x11 page size!! j 13 23 1 of 17
14X 11 + 9X 12 + 7X 13 + 8X 21 + 10X 22 + 5X 23 S.t. X 11 + X 12 + X 13 < 30 X 21 + X 22 + X 23 < 20 X 11 + X 21 = 25 X 12 + X 22 = 15 X 13 + X 23 = 10 X 11 , X 12 , X 13 , X 21 , X 22 , X 23 > 0 Part B Optimal Solution: Route Des Moines Kansas City St. Louis Supply Jefferson City 14 9 7 30 5 15 10 Omaha 8 10 5 20 20 Demand 25 15 10 50 Total Costs: Route Units Shipped Cost per unit Total cost From: To: Jefferson City Des Moines \$5 \$14 \$70 Jefferson City Kansas City \$15 \$9 \$135 Jefferson City St. Louis \$10 \$7 \$70 Omaha Des Moines \$20 \$8 \$160 Total Cost \$435 Distribution system total optimal cost = \$435 Submit your homework as one single attachment. IncludePOM-QM input and output screenshots wherever applicable. If you submit your homework as an MS-Excel document, make sure that it is properly formatted to 8.5x11 page size!! 2 of 17
2. (15 points) Chapter 6 Problem 3 Part A 10 20 15 12 15 18 Part B Max Z = 10X 11 + 20X 12 + 15X 13 + 12X 21 + 15X 22 + 18X 23 X 11 = the number of units shipped from Southern Gas to Hamilton X 12 = the number of units shipped from Southern Gas to Butler X 13 = the number of units shipped from Southern Gas to Clermont X 21 = the number of units shipped from Northwest Gas to Hamilton X 22 = the number of units shipped from Northwest Gas to Butler X 23 = the number of units shipped from Northwest Gas to Clermont Constraint: Submit your homework as one single attachment. IncludePOM-QM input and output screenshots wherever applicable. If you submit your homework as an MS-Excel document, make sure that it is properly formatted to 8.5x11 page size!! 3 of 17 Southern Gas Northwes t Gas Hamilto n Butler Clermon t Supplies 400 500 Distribution Rates Demands 300 200 400
500