In this model, we have three products with known demand, production rates, setup costs, and holding costs. The question is how much of each product should we produce to minimize total setup and holding costs without exceeding the capacity of our production facility.

MODEL:

! Production capacity constrained EOQ;

! Demand rates for three products;

  d1 = 400; d2 = 300; d3 = 300;

! Production rates;

  p1 = 1300; p2 = 1100; p3 = 900;

! Setup costs for producing individual products;

  sc1 = 10000; sc2 = 12000; sc3 = 13000;

! Per unit holding costs;

  hc1 = 1; hc2 = 1.1; hc3 = 1.4;

!

 The model;

!  Single machine capacity constraint; [CAP]

   d1 / p1 + d2 / p2 + d3 / p3

     + 1.5 * ( d1 / q1 + d2 / q2 + d3 / q3) <= 1;

!  Minimize setup + holding costs;

   min = setup + holding;

!  Total setup costs;

   setup = (sc1 * d1 / q1) + (sc2 * d2 / q2)

                           + (sc3 * d3 / q3);

!  Total holding costs;

   holding = ( hc1 * q1 * ( 1 - d1 / p1)

             + hc2 * q2 * ( 1 - d2 / p2)

             + hc3 * q3 * ( 1 - d3 / p3)) / 2;

!;

@BND( .01, Q1, 99999);

@BND( .01, Q2, 99999);

@BND( .01, Q3, 99999);

@FREE( SETUP);

@FREE( HOLDING);

 

END

Model: EOQCAP