Question

Demand for an item is 18644 units per year. Each order placed costs $94. The annual carrying cost percentage per item in inventory is 20 percent each. The variable purchase cost is $2.5 per unit if less than 3000units will be ordered, $ 2.4 from 3000 units up to (but not including) 4000 units, and $2.3 for at least 4000 units. These are all-units discounts.

(A) What is the optimal order quantity Q* for the unit cost of $2.3? Please round to a whole number.

(B) Is this quantity realizable/feasible? Please answer 'Yes' or 'No'.

(C) What is the optimal realizable/feasible total annual cost at a unit cost of $ 2.3? Please round to a whole number.

(D) What is the optimal order quantity Q* for the unit cost of $2.4? Please round to a whole number.

(E) Is this quantity realizable/feasible? Please answer 'Yes' or 'No'.

(F) What is the optimal realizable/feasible total annual cost at a unit cost of $2.4? Please round to a whole number.

(G) What is the optimal order quantity Q* for the unit cost of $2.5? Please round to a whole number.

(H) Is this quantity realizable/feasible? Please answer 'Yes' or 'No'.

Answer 1

The formula we use

Optimal quantity Q = sqrt(2DS/H)

Total cost TC = HQ/2 + DS/Q + PD

Inventory management cost IC = HQ/2 + DS/Q

Here

D = 18644

S = 94

H = 0.2 of P

P = 2.5/2.4/2.3

A)

If the unit cost is 2.3 then the holding cost H = 0.46

The optimal quantity Q = sqrt(2*18644*94/0.46) = 2760.38 or 2760 units

B)

No.

The minimum order quantity for the price to be 2.3 is 4000 units

C)

At a unit of 2.3 the order quantity Q = 4000. This means total cost is

TC = 0.46*4000/2 + 186448*94/4000 + 2.3*18644 = 48182.73

D)

For unit cost of 2.4, H = 0.48

Q = sqrt(2*18644*94/0.48) = 2702.2 or 2702 units

E)

No

The range for price of 2.4 is 3000 to 4000. 2702 is not in that range

F)

In this case we need to move towards 2702. The closest value in the range is Q = 3000. At this quantity, total cost is

TC = 0.48*3000/2 + 186448*94/3000 + 2.4*18644 = 51307.63