IPA IP 2023 Question 24

The optimal order quantity minimizes the total of ordering and holding costs — in the fixed-quantity ordering system the same quantity is ordered whenever the stock falls to the reorder point.

With steady demand D a year, ordering Q units at a time means D ÷ Q orders a year and an average stock of Q ÷ 2. Larger orders cut the ordering cost but raise the holding cost, and smaller ones do the reverse. The quantity at which the sum of the two is smallest is the economic order quantity, √2DS ÷ H for ordering cost S per order and holding cost H per unit a year, and this fixed quantity is ordered each time.

Answer (a)

Why not others:

• •(b) — for the same annual demand, more orders means smaller orders, so less stock is held and less storage space is needed
• •(c) — ordering on a fixed cycle such as every Friday is the fixed-period (periodic) ordering system; in the fixed-quantity system the timing varies with consumption
• •(d) — calculating each order from a demand forecast is also the fixed-period system, where the quantity varies; the fixed-quantity system orders the same amount every time

Key rule: Fixed-quantity ordering fixes the amount (the economic order quantity) and lets the timing vary; fixed-period ordering fixes the timing and calculates the amount from a forecast.

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