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Transportation Problem Analysis and Optimization Techniques

This content covers the fundamental aspects of transportation problems in operations research, including the identification of supply and demand points, their capacities, and unit shipping costs for various routes. It discusses representation methods such as graphical and mathematical approaches, including the use of transportation tableaux and heuristic methods. Practical applications of the simplex method, sensitivity analysis, and parametric analysis using tools like WinQSB are also examined to improve decision-making and optimize transportation plans effectively.

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Transportation Problem Analysis and Optimization Techniques

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  1. Transportation Problem • Required information: • Supply/source points and their capacity • Demand/destination points and their capacity • Unit cost of shipment for all routes • Representation methods: • Graphical • Mathematical • Transportation tableau IE 416, Chap 7, Sept 2009

  2. IE 416, Chap 7, July 99

  3. IE 416, Chap 7, July 99

  4. IE 416, Chap 7, July 99

  5. Balanced Transportation = * If > add dummy demand point with capacity = - , Cij= 0 * If < add dummy supply point with capacity = - , Cij= penalty cost IE 416, Chap 7:1, July 98

  6. Added Transportation Practical Simplex Application Application Dummy Create balanceExtra capacity not used. Demand Cij = 0Do not produce or find new demand points Dummy Create balanceDemand not met. Supply Cij = penaltyCan find new supplier or add to the capacity IE 416, Chap 7, Feb. 99

  7. Transportation Heuristic Methods • Rule of thumb to find initial bfs • North West Corner (NWC) • Minimum Cost (MC) • Vogel Method • and many more IE 416, Chap 7:2, July 98

  8. IE 416, Chap 7, July 99

  9. Foster Generator, Optimal Shipment Plan From To Amount Unit TotalMathematical . Cost Cost Clev Bos 3500 3 10500X11 = 3500 Clev Chi 1500 2 3000X12 = 1500 Bed Chi 2500 5 12500X22 = 2500 Bed Lou 2000 2 4000X23 = 2000 Bed Lex 1500 3 4500X24 = 1500 York Bos 2500 2 5000X31 = 2500 Total cost 39500Z = 39500 IE 416, Chap 7, July 99

  10. Sensitivity Analysis Options for Transportation Using WinQSB: * Range of Optimality: Provides information on possible changes in coefficients of objective function (unit cost of shipment) so that having the same solution (Xij, bfs) but with different minimum cost. * Range of Feasibility: Provides information on possible changes in capacities of supply and demand points so that having the same basis (ship from one node to the other) but with different amount of shipment and minimum cost. * Perform Parametric Analysis: Provides sensitivity analysis (and graph) on a cost of unit shipment, or capacity of a demand point, or capacity of a supply point.

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