Question

An retail firm has to deliver products during the next four weeks. in week 1, 200 products; week 2, 300 products; week 3, 300 products; week 4, 400 products. For each output produced during months 1 and 3, a $10 changing cost is incurred; for each output produced during months 2 and 4, a $12 changing cost is incurred. The inventory cost is $1.5 for each product in stock at the end of a month. The cost of setting up during a month is $200. The products are produced in by 100 batches for each week. Given that the initial inventory level is 0 units, use dynamic programming to determine an optimal production schedule

Answer 1

Changing cost for product produced in week 1 and 3 is 10, whereas week 2 & 4 its 12. Hence there is a advantage of 2 savings in cost if product is produced in week 1&3. However, inventory holding cost of 1.5 for each cost each week shall be charged. So if a product is produced a week in advance then also there will be a net advantage of 0.5 (2 - 1.5).

So we should produce in week 1 for the demand of 1&2 week. Likewise we should produce in week 3 for demand of 3&4 week as we get an advantage of producing week 2 products in week 1 by 0.5 for each unit, similar benefit to produce week 4 products in week 3.

Week 1 Production = 1 week demand + 2nd Week demand = 1200 + 300 = 1500

Week 3 Production = 3rd week demand + 4th Week demand = 300 +400 = 700

Week 2 and Week 4 , no production.