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Model 2: Transportation Problem

Model 2: Transportation Problem. Roshnika Fernando. Model 2 Summary. 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

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Model 2: Transportation Problem

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  1. Model 2: Transportation Problem Roshnika Fernando

  2. Model 2 Summary

  3. Goal • Minimize cost of shipping cars from car manufacturer to dealership5 12z = ΣΣcijxiji = 1,2,…,5 ; j = 1, 2,…, 12i=1 j=1 x ≥ 0, integer • Subject to supply and demand constraints12 5Σxij = siand Σxij = djj=1 i=1

  4. Linear Equation 5 12min: z = ΣΣcijxiji = 1,2,…,5 ; j = 1, 2,…, 12i=1 j=1 x ≥ 0, integers.t. : 12 5Σxij = siand Σxij = djj=1 i=1Supply equals demand for Model 2 5 12Σsi = 480 = Σdji=1 j=1

  5. MatLab Solution: $10,427

  6. Management Scientist Program Solution: $10,427

  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.

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