Question

An electronics firm delivering to its customers by making radio production over the next three months will. There are 1200 radio requests for the first month, 300 radio requests for the second month and 300 radio requests for the third month. A radio production for the first two months would cost $10, while the third month would cost $12. A radio if not delivered in the month in which it is produced, the inventory cost is generated. A monthly stock of a product the cost was set at $ 1.5. Fixed $ 250 for any amount of production the cost of production consists of. Production can only be in the amount of 100 and multiples. According to the fact that there is no stock available at the beginning and the demands must be met on time find the optimal production plan for the three months in question using Dynamic Programming. (Each months determine how much production should be done.)

Answer 1

SOLUTION

Month	Demand	Setup Cost	Inventory Cost	Production Cost
1	1200	250	1.5	10
2	300	250	1.5	10
3	300	250	1.5	12

Dynamic Programming (DP) solution -

Month 1-

Q = 1200

Total Cost = 250 +10*1200 = 12250

Month 2 -

TC₁ = 12250+250+10*300 = 15500

TC₂ = 250+1500*10 + 300*1.5 = 15700

therefor TC₁  is the best production plan

Month 3 -

TC₁ = 300+ 1800*10+600*1.5+300*1.5 = 19650

TC₂ = 12250 +250+ 600*10+300*1.5 = 18950

TC₃ = 15500+250+300*12 = 19350

Therefor TC₂ is the optimal way of production plan

Q1 = 1200

Q2 = 300

Q3 = 100

Total Cost = 18950