Question

a. Berjaya private school annually uses 1200 units of plastic rulers for its mathematics courses. The rulers cost RM1 each, the holding cost per ruler for per month is O.1 percent of the purchase cost, and the fixed cost to place an order is RM15. i. Assume demand increases to 2400 rulers annually. Compute and interpret the total number of rulers need to be bought for each order before and after the increase of the demand. Explain. (6 marks) li. Assume a demand level of 2400 rulers annually. Another supplier offers to supply the rulers at a cost of RMO.85 each if the school will order at least 800 rulers at a time and if the order size is in multiples of 100. Should the school management switch to this new firm or continue with the previous supplier in part i)? (9 marks)

Answer 1

i.

Annual demand of rulers = 1200

Holding cost = 0.1 % of purchase cost per month per rule = 0.1% * 12 * 1 = 0.012 RM (annual holding cost per year per ruler)

Order cost per order =15 RM

Increased demand of rulers = 2400

We will user Economic order quantity (EOQ) method to estimate optimal order quantity of rulers before and increase of demand

EOQ = square root (2 * Annual Demand * Setup cost per order/ Holding cost per unit per year)

EOQ (Before) = square root (2*1200*15/0.012) = 1732 approximately

EOQ (After) = square root (2*2400*15/0.012)= 2450 approximately

Total cost (Before) = (Order quantity/2) * Holding cost per unit per year + (Demand/ Order quantity)* Ordering cost per order

Total cost (Before) = (1732/ 2)*0.012 + (1200/1732)*15 = 10.392 + 10.393 = $20.79

Total cost (After) = (2450/ 2)*0.012 + (2400/2450)*15 = 14.7 + 14.7 = $29.4

ii

Revised Demand = 2400 rulers

Cost per unit (second supplier) =0.85 RM per unit

Holding cost (second supplier) = 0.85 *0.1%*12 = 0.0102

Order size = At least 800 units (in multiples of 100)

Since the holding cost is reduced, school can now order complete 2400 orders at one go.

Total cost in that case would be

Total cost (second supplier ) = (Order quantity/2) * Holding cost per unit per year + (Demand/ Order quantity)* Ordering cost per order

Total cost (second supplier ) = (2400/ 2)*0.0102 + (2400/2400)*15 = 12.24 + 15 = $27.24

Since total cost of second supplier ($27.24) is lower than first supplier ($29.4) hence the school management should switch to new firm.