Now consider the case in which the manufacturer offers a marginal unit quantity discount for the plywood. The first 20,000 square feet of any order are sold at $1 per square foot, the next 20,000 square feet are sold at $0.98 per square foot, and any quantity larger than 40,000 square feet is sold for $0.96 per square foot. What is the optimal lot size for Prefab given this pricing structure? How much cycle inven

We can use the following method to solve the given problem

We are given following

Annual demand,

D = 20000*12

D = 240,000 sqft

Fixed order cost, is given as

S = $ 400

Considering the unit cost, is given as

C = $ 1

Holding cost, H = 1*20% = $ 0.2

EOQ = sqrt (2DS/H)

= √ (2*240000*400/0.2)

= 30,984 sq ft

This is higher than 20,000 and less than 40,000 sq ft. For this reason, the applicable price for this quantity is $ 0.98

For C = $ 0.98, holding cost, H = 0.98*20% = $ 0.196

Revised EOQ = sqrt (2*240000*400/0.196) = 31,298 sq ft

Total annual cost of EOQ policy = D*C + H*Q/2 + S*D/Q

= 240000*0.98 + 0.196*31298/2 + 400*240000/31298

= $ 241,334.5

Now consider the next level of price, C = $ 0.96

Holding cost, H = 0.96*20% = $ 0.192

EOQ = sqrt (2*240000*400/0.192)

= 31633 sqft

This amount is will not be feasible for this price, because it requires a minimum order of 40000 sqft.

Therefore, Q = 40,000

Total annual cost = 240000*0.96 + 0.192*40000/2 + 400*240000/40000

Total annual cost = $ 236,640

Total annual cost is lowest for order quantity of 40,000 sq ft.

1) Optimal lot size = 40,000 sq ft.

2) the annual cost of this policy

= $ 236,640

3) the cycle inventory of plywood at Prefab = Q/2 = 40000/2

At prefeb = 20,000 sq ft

4) let's assume the manufacturer sells all plywood at $ 0.96, then

Holding cost, H = 0.96*20%

H = $ 0.192

EOQ = sqrt (2*240000*400/0.192)

EOQ = 31633 sqft

Total annual cost = 240000*0.96 + 0.192*31633/2 + 400*240000/31633

Total annual cost = $ 236,471.6

Difference in total annual cost = 236640 - 236471.6 = $ 168.4