In this example, we want to ship product from warehouses to vendors at minimal cost. An in-depth description of this model can be found in Getting Started with LINGO.

MODEL:

! A 6 Warehouse 8 Vendor Transportation Problem;

SETS:

  WAREHOUSES / WH1 WH2 WH3 WH4 WH5 WH6/: CAPACITY;

  VENDORS / V1 V2 V3 V4 V5 V6 V7 V8/   : DEMAND;

  LINKS( WAREHOUSES, VENDORS): COST, VOLUME;

ENDSETS

! The objective;

  MIN = @SUM( LINKS( I, J):

   COST( I, J) * VOLUME( I, J));

! The demand constraints;

  @FOR( VENDORS( J):

   @SUM( WAREHOUSES( I): VOLUME( I, J)) =

    DEMAND( J));

! The capacity constraints;

  @FOR( WAREHOUSES( I):

   @SUM( VENDORS( J): VOLUME( I, J)) <=

    CAPACITY( I));

! Here is the data;

DATA:

  CAPACITY = 60 55 51 43 41 52;

  DEMAND = 35 37 22 32 41 32 43 38;

  COST = 6 2 6 7 4 2 5 9

         4 9 5 3 8 5 8 2

         5 2 1 9 7 4 3 3

         7 6 7 3 9 2 7 1

         2 3 9 5 7 2 6 5

         5 5 2 2 8 1 4 3;

ENDDATA

END

Model: WIDGETS