Question

A vaccine manufacturer is contracted to deliver the following number of doses over the next 4 quarters: 1000, 2500, 3000, 2000. Each dose has a variable production cost of $10 per dose. The inventory holding cost is $0.05 per quarter per dose. The cost of setting up production in a given quarter is $200. Any doses produced in a given quarter may be used for meeting demand for that quarter or any future quarter. Use the Wagner-Whitin algorithm to find all optimal production policies.

Answer 1

W-W Algorithm:

v4=200+2000*10=20200;

v3=min{200+3000*10+v4, 200+(3000+2000)*10+2000*0.05}=

min{50400, 50300}=50300;

v2=min{200+2500*10+v3, 200+(2500+3000)*10+3000*0.05+v4, 200+(2500+3000+2000)*10+(3000+2*2000)*0.05} =min{75500, 75550, 75550}=75500;

v1=min{200+1000*10+v2, 200+(1000+2500)*10+2500*0.05+v3, 200+(1000+2500+3000)*10+(2500+2*3000)*0.05+v4,

200+(1000+2500+3000+2000)*10+(2500+2*3000+3*2000)*0.05}

=min{85700, 85625, 85825, 85925}=85625;

Thus, the optimal policy is to produce each quarter. The optimal cost $85625;