The Transportation Problem: An Introduction m Sources n Destinations c11 El Paso Juarez S.F. Chih. City c13 Tucson Atlanta cm3 . . cm1 cmn NYC Detroit

Transportation Problem: Assumptions One item: supply si at each of m sources (‘supply points’); demand dj at each of n destinations (‘demand points’). Fixed unit transportation cost cij from source i to destination j (no volume discounts). Decision variables: xij = # of units to ship from source i to destination j.

Transportation Problem: Formulation Total transportation cost:

Transportation Problem: Formulation (cont.) Supply constraints Units shipped out of each source i (to the various destinations) cannot exceed supply at source i.

Transportation Problem: Formulation (cont.) Demand constraints Units shipped to each destination j (from the various sources) should meet demand at destination j.

Transportation Problem: Formulation (cont.) Objective: to find a shipping schedule that minimizes total transportation cost, subject to supply and demand constraints.

Transportation Problem: LP Formulation i = 1,2,...,m s.t. j = 1,2,...,n each i, j

Transportation Problem Solution May be solved using the Simplex Method of Linear Programming (in the LP module of Storm for Windows 4.0). Cumbersome when setting up constraints. As LP problem, transportation problem constraints have only 1’s and 0’s as coefficients of decision variables. Stepping Stone Method more efficient. Application software (e.g., Transportation Problem Module of Storm for Windows 4.0) available.