The INTPOINT Procedure |

Missing S Supply and Missing D Demand Values |

In some models, you may want a node to be either a supply or demand node but you want the node to supply or demand the optimal number of flow units. To indicate that a node is such a supply node, use a missing S value in the SUPPLY list variable in the ARCDATA= data set or the SUPDEM list variable in the NODEDATA= data set. To indicate that a node is such a demand node, use a missing D value in the DEMAND list variable in the ARCDATA= data set or the SUPDEM list variable in the NODEDATA= data set.

Suppose the oil example in the section Introductory NPSC Example is changed so that crude oil can be obtained from either the Middle East or U.S.A. in any amounts. You should specify that the node middle east is a supply node, but you do not want to stipulate that it supplies 100 units, as before. The node u.s.a. should also remain a supply node, but you do not want to stipulate that it supplies 80 units. You must specify that these nodes have missing S supply capabilities:

title 'Oil Industry Example'; title3 'Crude Oil can come from anywhere'; data miss_s; missing S; input _node_&$15. _sd_; datalines; middle east S u.s.a. S servstn1 gas -95 servstn1 diesel -30 servstn2 gas -40 servstn2 diesel -15 ;

The following PROC INTPOINT run uses the same ARCDATA= and CONDATA= data sets used in the section Introductory NPSC Example:

proc intpoint bytes=100000 nodedata=miss_s /* the supply (missing S) and */ /* demand data */ arcdata=arcd1 /* the arc descriptions */ condata=cond1 /* the side constraints */ conout=solution; /* the solution data set */ run;

proc print; var _from_ _to_ _cost_ _capac_ _lo_ _flow_ _fcost_; sum _fcost_; run;

The following messages appear on the SAS log:

Oil Industry Example |

Crude Oil can come from anywhere |

NOTE: Number of nodes= 14 . |

NOTE: All supply nodes have unspecified (.S) supply capability. Number of these |

nodes= 2 . |

NOTE: Number of demand nodes= 4 . |

NOTE: Total supply= 0 , total demand= 180 . |

NOTE: Number of arcs= 18 . |

NOTE: Number of <= side constraints= 0 . |

NOTE: Number of == side constraints= 2 . |

NOTE: Number of >= side constraints= 2 . |

NOTE: Number of side constraint coefficients= 8 . |

NOTE: The following messages relate to the equivalent Linear Programming |

problem solved by the Interior Point algorithm. |

NOTE: Number of <= constraints= 0 . |

NOTE: Number of == constraints= 17 . |

NOTE: Number of >= constraints= 2 . |

NOTE: Number of constraint coefficients= 48 . |

NOTE: Number of variables= 20 . |

NOTE: After preprocessing, number of <= constraints= 0. |

NOTE: After preprocessing, number of == constraints= 5. |

NOTE: After preprocessing, number of >= constraints= 2. |

NOTE: The preprocessor eliminated 12 constraints from the problem. |

NOTE: The preprocessor eliminated 33 constraint coefficients from the problem. |

NOTE: After preprocessing, number of variables= 6. |

NOTE: The preprocessor eliminated 14 variables from the problem. |

NOTE: 6 columns, 0 rows and 6 coefficients were added to the problem to handle |

unrestricted variables, variables that are split, and constraint slack or |

surplus variables. |

NOTE: There are 19 sub-diagonal nonzeroes in the unfactored A Atranspose matrix. |

NOTE: The 7 factor nodes make up 2 supernodes |

NOTE: There are 4 nonzero sub-rows or sub-columns outside the supernodal |

triangular regions along the factors leading diagonal. |

NOTE: Bound feasibility attained by iteration 1. |

NOTE: Dual feasibility attained by iteration 1. |

NOTE: Constraint feasibility attained by iteration 1. |

NOTE: The Primal-Dual Predictor-Corrector Interior Point algorithm performed 6 |

iterations. |

NOTE: Optimum reached. |

NOTE: Objective= 50075. |

NOTE: The data set WORK.SOLUTION has 18 observations and 10 variables. |

NOTE: There were 18 observations read from the data set WORK.ARCD1. |

NOTE: There were 6 observations read from the data set WORK.MISS_S. |

NOTE: There were 4 observations read from the data set WORK.COND1. |

The CONOUT= data set is shown in Figure 4.11.

Oil Industry Example |

Crude Oil can come from anywhere |

Obs | _from_ | _to_ | _cost_ | _capac_ | _lo_ | _FLOW_ | _FCOST_ |
---|---|---|---|---|---|---|---|

1 | refinery 1 | r1 | 200 | 175 | 50 | 145.000 | 29000.00 |

2 | refinery 2 | r2 | 220 | 100 | 35 | 35.000 | 7700.00 |

3 | r1 | ref1 diesel | 0 | 75 | 0 | 36.250 | 0.00 |

4 | r1 | ref1 gas | 0 | 140 | 0 | 108.750 | 0.00 |

5 | r2 | ref2 diesel | 0 | 75 | 0 | 8.750 | 0.00 |

6 | r2 | ref2 gas | 0 | 100 | 0 | 26.250 | 0.00 |

7 | middle east | refinery 1 | 63 | 95 | 20 | 20.000 | 1260.00 |

8 | u.s.a. | refinery 1 | 55 | 99999999 | 0 | 125.000 | 6875.00 |

9 | middle east | refinery 2 | 81 | 80 | 10 | 10.000 | 810.00 |

10 | u.s.a. | refinery 2 | 49 | 99999999 | 0 | 25.000 | 1225.00 |

11 | ref1 diesel | servstn1 diesel | 18 | 99999999 | 0 | 30.000 | 540.00 |

12 | ref2 diesel | servstn1 diesel | 36 | 99999999 | 0 | 0.000 | 0.00 |

13 | ref1 gas | servstn1 gas | 15 | 70 | 0 | 68.750 | 1031.25 |

14 | ref2 gas | servstn1 gas | 17 | 35 | 5 | 26.250 | 446.25 |

15 | ref1 diesel | servstn2 diesel | 17 | 99999999 | 0 | 6.250 | 106.25 |

16 | ref2 diesel | servstn2 diesel | 23 | 99999999 | 0 | 8.750 | 201.25 |

17 | ref1 gas | servstn2 gas | 22 | 60 | 0 | 40.000 | 880.00 |

18 | ref2 gas | servstn2 gas | 31 | 99999999 | 0 | 0.000 | 0.00 |

50075.00 |

The optimal supplies of nodes middle east and u.s.a. are 30 and 150 units, respectively. For this example, the same optimal solution is obtained if these nodes had supplies less than these values (each supplies 1 unit, for example) and the THRUNET option was specified in the PROC INTPOINT statement. With the THRUNET option active, when total supply exceeds total demand, the specified nonmissing demand values are the lowest number of flow units that must be absorbed by the corresponding node. This is demonstrated in the following PROC INTPOINT run. The missing S is most useful when nodes are to supply optimal numbers of flow units and it turns out that for some nodes, the optimal supply is 0.

data miss_s_x; missing S; input _node_&$15. _sd_; datalines; middle east 1 u.s.a. 1 servstn1 gas -95 servstn1 diesel -30 servstn2 gas -40 servstn2 diesel -15 ; proc intpoint bytes=100000 thrunet nodedata=miss_s_x /* No supply (missing S) */ arcdata=arcd1 /* the arc descriptions */ condata=cond1 /* the side constraints */ conout=solution; /* the solution data set */ run; proc print; var _from_ _to_ _cost_ _capac_ _lo_ _flow_ _fcost_; sum _fcost_; run;

The following messages appear on the SAS log. Note that the Total supply= 2, not 0 as in the last run:

Oil Industry Example |

Crude Oil can come from anywhere |

NOTE: Number of nodes= 14 . |

NOTE: Number of supply nodes= 2 . |

NOTE: Number of demand nodes= 4 . |

NOTE: Total supply= 2 , total demand= 180 . |

NOTE: Number of arcs= 18 . |

NOTE: Number of <= side constraints= 0 . |

NOTE: Number of == side constraints= 2 . |

NOTE: Number of >= side constraints= 2 . |

NOTE: Number of side constraint coefficients= 8 . |

NOTE: The following messages relate to the equivalent Linear Programming problem |

solved by the Interior Point algorithm. |

NOTE: Number of <= constraints= 0 . |

NOTE: Number of == constraints= 17 . |

NOTE: Number of >= constraints= 2 . |

NOTE: Number of constraint coefficients= 48 . |

NOTE: Number of variables= 20 . |

NOTE: After preprocessing, number of <= constraints= 0. |

NOTE: After preprocessing, number of == constraints= 5. |

NOTE: After preprocessing, number of >= constraints= 2. |

NOTE: The preprocessor eliminated 12 constraints from the problem. |

NOTE: The preprocessor eliminated 33 constraint coefficients from the problem. |

NOTE: After preprocessing, number of variables= 6. |

NOTE: The preprocessor eliminated 14 variables from the problem. |

NOTE: 6 columns, 0 rows and 6 coefficients were added to the problem to handle |

unrestricted variables, variables that are split, and constraint slack or |

surplus variables. |

NOTE: There are 19 sub-diagonal nonzeroes in the unfactored A Atranspose matrix. |

NOTE: The 7 factor nodes make up 2 supernodes |

NOTE: There are 4 nonzero sub-rows or sub-columns outside the supernodal triangular |

regions along the factors leading diagonal. |

NOTE: Bound feasibility attained by iteration 1. |

NOTE: Dual feasibility attained by iteration 1. |

NOTE: Constraint feasibility attained by iteration 1. |

NOTE: The Primal-Dual Predictor-Corrector Interior Point algorithm performed 6 |

iterations. |

NOTE: Optimum reached. |

NOTE: Objective= 50075. |

NOTE: The data set WORK.SOLUTION has 18 observations and 10 variables. |

NOTE: There were 18 observations read from the data set WORK.ARCD1. |

NOTE: There were 6 observations read from the data set WORK.MISS_S_X. |

NOTE: There were 4 observations read from the data set WORK.COND1. |

If total supply exceeds total demand, any missing S values are ignored. If total demand exceeds total supply, any missing D values are ignored.

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