Example 6.3: Capacitated Transportation Network with MINFLOW

The TRANS Procedure

Example 6.3: Capacitated Transportation Network with MINFLOW

Suppose you place a minimum on the flow within each city. Just as capacity restrictions can be interpreted as limits on available transportation, minimum flow restrictions can be interpreted as requirements to ship minimum quantities on certain routes, perhaps as a result of contractual agreements. The following program adds minimum flow requirements on four routes. Because the MINFLOW= data set contains many missing values, named input mode is used to input the data. The solution is displayed following the program in Output 6.3.1.

    title 'Capacitated Transportation Network with MINFLOW';

    data minflw;
       input Chicago= Denver=  San_Fran= Seattle= city= $;
       datalines;
    city=Chicago Chicago=30 San_Fran=40 Seattle=50
    city=Denver  Denver=40
    ;

    proc trans cost=cst capacity=capcty minflow=minflw;
       HEADNODE Atlanta--Washingt;
       TAILNODE city;
       supply supply;
    run;

    proc print;
    run;

The SAS log contains the following message:

   NOTE: Optimal Solution Total = 31458.

Output 6.3.1: Capacitated Transportation Network Solution with MINFLOW

Obs	city	supply	Atlanta	Chicago	Denver	Houston	Los_Ange	Miami	New_York	San_Fran	Seattle	Washingt	_DUAL_
1	_DEMAND_	.	50	75	89	8	27	39	64	100	50	8	.
2	Atlanta	10	10	0	0	0	0	0	0	0	0	0	-138
3	Chicago	150	0	60	0	0	0	0	0	40	50	0	-100
4	Denver	90	11	8	71	0	0	0	0	0	0	0	-37
5	Houston	27	0	0	0	8	0	19	0	0	0	0	-91
6	Los_Ange	80	0	0	18	0	27	0	0	35	0	0	26
7	Miami	26	6	0	0	0	0	20	0	0	0	0	-98
8	New_York	80	8	0	0	0	0	0	64	0	0	8	-84
9	San_Fran	25	0	0	0	0	0	0	0	25	0	0	12
10	Seattle	7	0	7	0	0	0	0	0	0	0	0	44
11	Washingt	15	15	0	0	0	0	0	0	0	0	0	-104
12	_DUAL_	.	158	129	57	111	-6	187	104	8	-24	104	.

Note that the optimal objective value is greater in the minimum flow capacitated network than in the capacitated network. Additional constraints can never decrease the objective value of a minimization problem at optimality.

Chapter Contents
Previous
Next
Top