Question

An annual demand for an item is 500 units, ordering cost is 8 $, inventory carrying interest is 20% of the purchase price per year. Purchase prices are as follows as proposed by the vendor/supplier; where the value of unit cost=10 without any discount?

Discount 0% 000≤Q<300   

Discount 2% 300≤Q<450

Discount 3% 450≤Q

a) for inventory model with no discount======================================================================

a1) The economic order quantity = [EOQ] units

a2) The total ordering costs = [TOC] $

a3) The total carrying cost = [TCC] $

a4) The total inventory cost without unit costs = [TC] $

a5) The total inventory cost including unit costs = [TUC] $

b) Adopting 2% discount will yield the following;================================================================

b1) The total price for Q1 units = [F] * Q1 + [FF]

b2) The economic order quantity = [EOQD] units b3) Feasible solution or not = [yn]

b4) The total ordering costs = [TOCD] $

b5) The total carrying cost = [TCCD] $

b6) The total inventory cost without unit costs = [TCD] $

b7) The total inventory cost including unit costs = [TUCD] $

c) Adopting 3% discount will yield the following;================================================================

c1) The total price for Q2 units = [k] * Q2 + [kk]

c2) The economic order quantity = [EOQDD] units c3) Feasible solution or not = [yo]

c4) The total ordering costs = [TOCDD] $

c5) The total carrying cost = [TCCDD] $

c6) The total inventory cost without unit costs = [TCDD] $

c7) The total inventory cost including unit costs = [TUCDD] $

d) The optimal solution for this problem is to choose = [discount]%

Answer 1

Annual demand = D = 500

Ordering cost = C = 8 $

Annual unit inventory carrying cost = I = 20% of $10 = $2

For inventory model with no discount :

A1) Economic order quantity( EOQ ) = Square root ( 2 x D x C/I ) = Square root ( 2 x 500 x 8/2) = 63.24

A2) Total ordering cost = C X D/ EOQ = $8 X 500/63.24 = $63.25

A3) Total carrying cost = I X EOQ/2 = $2 x 63.24/2 = $63.24

A4) Total inventory cost without unit cost = $63,25 +$63.24 = $126.49

A5) Total inventory cost including unit costs = total cost of items + Total ordering cost + Total carrying cost

= $10 x 500 + 63.25 + $63.24

= $5000 + $63.25 + $63.25

= $5126.50

Adopting 2% discount will yield the following :

Unit cost = 98% of $10 = $9.8

Annual unit inventory holding cost = 20% of $9,8 = $1.96

b.1 Total price for Q1 units = $9.8 x 500 = $4900

b2. Economic order quantity = Square root ( 2 x 500 x 8/1.96) = 63.89 b3. feasible solution or not : NOT

B4. Ordering quantity assumed as 300 ( lowest value in the respective quantity slab)

Ordering cost = Ordering cost x Demand/Order quantity = $8 x 500/300 = $13.33

B5.Total carrying cost = Annual unit inventory holding cost x Order quantity/2 = $1.96 x 300/2 = $294

B6. Total inventory cost without unit costs = $13.33 + $294 = $307.33

B7.Total inventory cost including unit cost = $ 4900 + $307.33 = $5207.33

Adopting 3% discount will yiled the following :

Unit cost 97$ of $10 = $9.7

Annual unit inventory holding cost = 20% of $9.7 = $1.94

C1) Total price for Q2 UNITS = 500 X $9.7 = $4850

C2) economic order quantity = Square root ( 2 x 500 x 8/1.94) = 64,21

C3) Feasible solution or not = NOT

C4) ordering quantity assumed to be 450

Ordering cost = ordering cost x Demand/ordering quantity = $8 x 800/450 = $14.22

C5)Total carrying cost = Annual unit inventory holding cost x Order quantity/2 = $1.94 x 450/2= $436.5

C6) Total inventory ost without unit cost = $14,22 + $436,5 =$ 450.72

C7, Total inventory cost including unit cost = $4850 + $450.72 =$5300.72