TomSym A Transportation Problem
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This page is part of the TomSym Manual. See TomSym Manual. |
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 Time for symbolic processing: 0.014407 seconds Starting numeric solver ===== * * * =================================================================== * * * TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31 ===================================================================================== Problem: --- 1: f_k 153.675000000000010000 f(x_0) 0.000000000000000000 Solver: CPLEX. EXIT=0. INFORM=1. CPLEX Dual Simplex LP solver Optimal solution found FuncEv 4 Iter 4 Elapsed time: 0.002000 sec. Shipment quantities: 50 300 0 275 0 275