1. Model 2: Transportation Problem Roshnika Fernando

2. Model 2 Summary Dealerships 123456789101112 supply Manufacturers 1253631202733272124352124100 237232835193123252827193190 3261917282736312421271730120 442251533232829332629202780 519314537313427313230222590 demand354228521733626143372842

3. Goal Minimize cost of shipping cars from car manufacturer to dealership 5 12 z = Σ Σ c ij x ij i = 1,2,…,5 ; j = 1, 2,…, 12 i=1 j=1 x ≥ 0, integer Subject to supply and demand constraints 12 5 Σ x ij = s i and Σ x ij = d j j=1 i=1

4. Linear Equation 5 12 min: z = Σ Σ c ij x ij i = 1,2,…,5 ; j = 1, 2,…, 12 i=1 j=1 x ≥ 0, integer s.t. : 12 5 Σ x ij = s i and Σ x ij = d j j=1 i=1 Supply equals demand for Model 2 5 12 Σ s i = 480 = Σ d j i=1 j=1

5. MatLab Solution: $10,427 Dealers Manufacturers 123456789101112Supply 1 25 36 31 20 27 33 27 21 24 35 21 24 100 52 48 2 37 2328 3519 31232528 271931 90 17 624 7 3 26 19 17 28 27 36 31 24 21 27 1730 120 42 943 26 4 42 2515 3323 2829 3326 292027 80 28 33 172 5 19 31 45 37 31 34 27 31 32 30 22 25 90 35 13 42 Demand354228521733626143372842480

6. Management Scientist Program Solution: $10,427 Dealers Manufacturers 123456789101112Supply 1 25 36 31 20 27 33 27 21 24 35 21 24 100 52 48 2 37 2328 3519 31232528 271931 90 17 626 5 3 26 19 17 28 27 36 31 24 21 27 1730 120 42 743 28 4 42 2515 3323 2829 3326 292027 80 28 33 19 5 31 45 37 31 34 27 31 32 30 22 25 90 35 13 42 Demand354228521733626143372842480

7. Analysis of Solutions Minimum cost of shipping is $10,427 Multiple solutions exist

8. Sensitivity Analysis Demand > Supply? No optimal solution – need more information (i.e. level of priority for each dealer) or more constraints. Demand < Supply? Optimal solution exists

9. Questions?

10. Citation Kolman, Bernard, and Robert E. Beck. Elementary Linear Programming with Applications. 2nd ed. New York: Academic Press, 1995. Print.