# A Transportation Problem

TomSym implementation of GAMS Example (TRNSPORT,SEQ=1)

This problem finds a least cost shipping schedule that meets requirements at markets and supplies at factories.

Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey, 1963.

This formulation is described in detail in: Rosenthal, R E, Chapter 2: A GAMS Tutorial. In GAMS: A User's Guide. The Scientific Press, Redwood City, California, 1988.

% Capacity of plant i in cases a = [350;600]; % Demand at market j in cases b = [325;300;275]; % Distance in thousands of miles d = [2.5 1.7 1.8 2.5 1.8 1.4]; % Freight in dollars per case per thousand miles f = 90; % Transport cost in thousands of dollars per case c = f*d/1000; % Shipment quantities in cases toms 2x3 x cbnd = (x >= 0); % Define objective function cost = sum(sum(c.*x)); % Observe supply limit at plant i eq1 = {sum(x,2) <= a}; % Satisfy demand at market j eq2 = {sum(x,1)' >= b}; solution = ezsolve(cost,{cbnd, eq1, eq2}); disp(' '); disp('Shipment quantities: '); disp(solution.x);

Problem type appears to be: lp ===== * * * =================================================================== * * * TOMLAB - Tomlab Optimization Inc. Development license 999001. Valid to 2010-02-05 ===================================================================================== Problem: --- 1: f_k 153.674999999999980000 f(x_0) 0.000000000000000000 Solver: CPLEX. EXIT=0. INFORM=1. CPLEX Dual Simplex LP solver Optimal solution found FuncEv 4 Iter 4 Shipment quantities: 50 300 0 275 0 275