# Suppose That You Are The Manager Of A Production Department That Uses 400 Boxes Of

Suppose that you are the manager of a production department that uses 400 boxes of bolts per year. The supplier quotes you a price of Rs.850 per box for an order size of 199 boxes or less, a price ofRs.800 per box for orders of200 to 999 boxes, and a price ofRs.750 per box for an order of 1,000 or more boxes. You assign a holding cost of 25 % of the price to this inventory. Ordering cost is Rs.8,000 per order.

a) What order quantity would use if the objective is to minimize total annual cost of holding, purchasing and ordering.

b) What is the reorder level if the company maintain a safety stock of one month demand? Assume that supply lead time is two weeks.

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Explanation:
The answer is shown in the next step. Please refer the below image for the detailed solution.

a) To determine the order quantity that minimizes the total annual cost of holding, purchasing, and ordering, we can use the economic order quantity (EOQ) formula:

EOQ = sqrt(2DS/H)

where:
D = annual demand = 400 boxes
S = ordering cost = Rs.8,000 per order
H = holding cost = 25% of the price = 0.25 x Rs.850 = Rs.212.50

Plugging in the values, we get:

EOQ = sqrt(2 x 400 x 8,000 / 212.50) = sqrt(60,160) = 245.3

Since we can’t order a fractional amount of boxes, we should round up to the nearest whole number. Therefore, the optimal order quantity is 246 boxes.
Explanation:
The answer is shown in the next step. Please refer the below image for the detailed solution.

b) The reorder level can be calculated as:

Reorder Level = (Demand during lead time) Safety Stock

Demand during lead time = (Demand per day) x (Lead time in days)
Demand per day = (Annual demand) / (Number of working days in a year)
Number of working days in a year = 365 – 52 (weekends) – 10 (public holidays) = 303

Demand per day = 400 / 303 = 1.32 boxes per day

Lead time in days = 2 weeks = 14 days

Demand during lead time = 1.32 x 14 = 18.48 boxes

Safety stock = (Demand per day) x (Safety stock period)
Safety stock period = 1 month = 30 days

Safety stock = 1.32 x 30 = 39.6 boxes

Therefore, the reorder level is:

Reorder Level = 18.48 39.6 = 58.08 boxes

Rounding up to the nearest whole number, the company should reorder when the inventory level reaches 59 boxes.