2

Q4 (2.3D) The demand for an item over the next our quar ers s , , un s. e  price per unit starts at $20 in the first quarter and is ncrease y eac quar er erea er. e supp er  can provide no more than 400 units in any quarter. oug we can a e a van age o ower pr ces n early quarters, a storage cost $3.50 is incurred per  un quar er. n a on, e max mum num er o units that can be held over from one quarter to the nex canno excee . eve op an an op o p ma schedule for purchasing the item to meet the eman . P K Sahoo, BITS-Hyderabad Campus

1

 X i = Production in quarter i Solution: Consider  X   I i = End inventory for quarter i

Minimize Z= 20X 1 +22X 2 +24X 3 +26X 4 + 3.5(I 1 +I 2 +I 3 ) 1

2

3

4

Demand

300

400

450

250

P K Sahoo, BITS-Hyderabad Campus

2

 X i = Production in quarter i Solution: Consider  X   I i = End inventory for quarter i

Minimize Z= 20X 1 +22X 2 +24X 3 +26X 4 + 3.5(I 1 +I 2 +I 3 ) 1

2

3

4

Demand

300

400

450

250

P K Sahoo, BITS-Hyderabad Campus

2

Constraints:  X 1 =300+I 1

 I 1 +X 2 =400+I 2  I +X =250

= i

 , = , , ,

i

 , = , ,

 I 0 =I 4 =0

P K Sahoo, BITS-Hyderabad Campus

3