Question

# 1.       For product M, a firm has an annual holding cost that is 25% of the...

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

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

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