Question

1.       For product M, a firm has an annual holding cost that is 25% of the item cost, an ordering cost of $10 per order, and annual demand of 1560 units. If ordering at least 85 units, the price per unit is $16; if ordering at least 95 units, the price per unit is $14.5. Lead time is 5 days. The firm operates 260 days.

a)     Determine the most cost-effective ordering quantity

b)     What is the total cost for the order quantity determined in a).

c)     Calculate reorder point

Summarize the inventory policy based on your calculation results

Answer 1

Following data are provided :

Annual demand for product M = D = 1560 units

Ordering cost = Co = $10

Annual unit holding cost = Ch = 25% of price / unit

Since , price per unit varies depending on quantity slabs, Ch will also vary depending on quantity slabs

The formula for optimum order quantity ( EOQ ) = Square root ( 2 x Co x D / Ch )

Since Ch will vary with price/ unit , EOQ also will change with changing price .

Following table presents different values of EOQ at different price levels corresponding to quantity slabs .

Order quantity	Price / unit ( $)	Ch ( 25% of price / unit)	EOQ ( ROUNDED TO NEAREST WHOLE NUMBER)
85 – 94	16	4	88
95 units and more	14.5	3.625	93

Since calculated value of EOQ = 88 matches with corresponding Order quantity slab of 85 – 94 , it should be the optimum order quantity which minimizes annual ordering cost plus annual inventory cost.

However , we need to minimize sum of annual purchasing cost , annual ordering cost and annual holding cost.

Such analysis will be done for order quantity of 88 ( EOQ ) and 95 units ( beginning of next quantity slab)

Order quantity = 88 :

Annual purchasing cost = Annual demand x Price/ unit = $ 1560 x 16      = $ 24960

Annual ordering cost = Ordering cost x Number of orders = Co x annual demand / order qty = $10 x 1560 / 88    = $177.27

Annual inventory holding cost = Ch x Average inventory = Ch x Order quantity / 2 = 4 x 88 / 2 = $ 176

Total cost = $24960 + $177.27 + $176 = $25313.27

Order quantity = 95 :

Annual purchasing cost = Annual demand x Price/ unit = $ 1560 x   14.5     = $ 22620

Annual ordering cost = Ordering cost x Number of orders = Co x annual demand / order qty = $10 x 1560 / 95     = $164.21

Annual inventory holding cost = Ch x Average inventory = Ch x Order quantity / 2 = 3.625 x 95/2 = $172.18

Total cost = $22620 + $164.21 + $172.18 = $22956.39

Since total annual cost for order quantity of 95 < Total annual cost of order quantity of 88 , the most cost effective order quantity will be 95

MOST COST EFFECTIVE ORDER QUANTITY = 95 UNITS OF PRODUCT M

TOTAL COST OF ORDR QUANTITY = $22956.39

Daily demand = 1560 units/ 260 days = 6 units

Reorder point = Daily demand x Lead time = 6 units/ day x 5 days = 30 days

REORDER POINT = 30 DAYS

We therefore have now a continuous inventory review policy of ( 95, 30 ) i.e. order 95 units every time and order this quantity of 95 everytime order quantity in hand becomes 30 units