*******************************************************
*   Mosel Example Problems
*   ======================
*
* Origin file contract.mos
*   `````````````````
*   TYPE:         Contract allocation problem
*   DIFFICULTY:   2
*   FEATURES:     simple MIP problem, semi-continuous variables,
*                 graphical representation of results
*   DESCRIPTION:  A public utility, which is divided into six regional
*                 districts, wishes to allocate ten power generation
*                 contracts to its regions as cheaply as possible. The cost
*                 per unit of power generated by each region for each
*                 contract is known.  If part of a contract is allocated to
*                 a region than it must be at least as big as a certain
*                 minimum size (5 units). For reliability reasons, no
*                 contract may be placed exclusively with only one district.
*                 Each district has a limited power generation capacity.
*   FURTHER INFO: `Applications of optimization with Xpress-MP teaching
*                 material', Section 2.2 `Semi-continuous variables:
*                 contract allocation';
*                 `Applications of optimization with Xpress-MP',
*                 Section 3.4.3 `Semi-continuous variables'
*
*   (c) 2001 Dash Associates
*       author: S. Heipcke
********************************************************

* model "Contract allocation"

* Districts
Set DISTRICT /d1*d6  / ;
* Contracts
Set CONTRACT /c1*c10 / ;
* Maximum output per district
Parameter OUTPUT[DISTRICT] / d1 50 , d2 40 , d3 10 , d4 20 , d5 70 , d6 50 / ;
* Cost per district
Parameter COST[DISTRICT]   / d1 50 , d2 20 , d3 25 , d4 30 , d5 45 , d6 40 / ;
* Cost per district
Parameter VOLUME[CONTRACT] / c1 20 , c2 10 , c3 30 , c4 15 , c5  20 ,
                             c6 30 , c7 10 , c8 50 , c9 10 , c10 20 / ;

Binary Variable alloc[DISTRICT,CONTRACT]  ;
* 1 if a bid is chosen, 0 otherwise

Variable        quant[DISTRICT,CONTRACT]  ,
* Quantities allocated to contractors
                Total_Cost                ;

Equation Eq_1(CONTRACT)              ,
         Eq_2(CONTRACT)              ,
         Eq_Output(DISTRICT)            ,
         MinAlloc(DISTRICT,CONTRACT) ,
         Def_Obj                     ;


* Cover the req. contract volume
Eq_1(CONTRACT)..
  Sum{DISTRICT, quant[DISTRICT,CONTRACT] } =g= VOLUME[CONTRACT] ;
* At least 2 districts per contract
Eq_2(CONTRACT)..
  Sum{DISTRICT, alloc[DISTRICT,CONTRACT] } =g= 2                ;

* Do not exceed maximum output of any district
Eq_Output(DISTRICT)..
    Sum{CONTRACT, quant[DISTRICT,CONTRACT] } =l= OUTPUT[DISTRICT] ;

* If a contract is allocated to a district, then at least 1 unit is
* allocated to it
MinAlloc(DISTRICT,CONTRACT)..
    alloc[DISTRICT,CONTRACT] =l= quant[DISTRICT,CONTRACT] ;

* Objective function: total cost
Def_obj..
    Total_Cost =e= Sum{(DISTRICT,CONTRACT), COST[DISTRICT]*quant[DISTRICT,CONTRACT] } ;

quant.up[DISTRICT,CONTRACT] = OUTPUT[DISTRICT]

* Solve the problem
Model Contract_allocation / all / ;

Solve Contract_allocation using MIP minimazing Total_Cost ;

Display Total_Cost.l ;