                              SIPS  
                           version 1.0 

                            Qiang  Li             
                      University of Tsukuba     
                            Yike Guo               
                Dept. of Computing, Imperial College  
                                           
                      Co-operated under AITEC      
                       research projet 1997      
                                         

This is a solver for stochastic integer programming. The solver aims
to solve a class of stochastic integer programming problems of
scheduling n job types on m machines. It also can be used to solve other
stochastic integer problems with minor modification. This solver
runs on Sun UltraSparc with SunOS 5.5.1.

1. Compile the package:

 %gcc -lm sips.c -o sips

2. Start the solver:

% sips
********************************************
*                                          *
*                  SIPS                    *
*               version 1.0                *
*                                          *
*                 Qiang  Li                *
*            University of Tsukuba         *
*                Yike Guo                  *
*   Dept. of Computing, Imperial College   *
*                                          *
*           Co-operated under AITEC        *
*            research projet 1997          *
*                                          *
********************************************


3. Some inputs :
This program has three input parts: RIP(reduced integer programming),
complicated constraints, and probabilistic constraints. We explain the
following steps with a example (job n=1,machine m=2).

(1) RIP input :

    Input equations :
           x 3 + x 4 = 3 ,
           x 3 - 3 x 1 + x 5 = 0 ,
           x 4 - 3 x 2 + x 6 = 0 ,
           x 1 + x 7 = 1 ,
           x 2 + x 8 = 1 .
    Input function cx :
           5 x 1 + 3 x 2 + 12 x 3 + 16 x 4 .

(2) Complicated constraints:
       4 x 3 + x 1 =< 10 ,
       4 x 4 + x 2 =< 10 .

(3) Probabilistic constraints:
       d 1 x 3 + x 1 =< 10 ,
       d 1 x 4 + x 2 =< 10 .

    Probability prob=0.83
    lot splitting M=3
    Number of samples sn=100

    100 samples:

12 2 8  9  1  4  1  6  21  1  0  20 2  12 30 3  9  10  4  8
10 3 5  10 4  84 9  5  24  12 5  2  4  58 9  9  91  93 9  3
2  1 50 10 11 8  3  2  1  11  10 3  12 10 9  12 0  10  0  0
6  7 6  0  3  12 3  0  10 11  9  7  0  3  8  7  1  1   8  12
3  9 0  77 1  6  42 18 2  77  9  20 50 3  15 2  17 3   6  4 .

4. Some output:

 (1) If the problem is feasible, the output is as follows.

  Result:
  Probability = 0.83 Cost=48
  Optimal solution:
  x1=1, x2=1, x3=2, x4=1, x5=1, x6=2, x7=0, x8=0, 

 (2) If the problem is infeasible, the output is as follows.

  Result:
  The problem has no optimal solution.

5. See file "Example-SIPS" , which includes some instances.
   


