Inventory Control and Economic Order Quantity
Inventory control balances ordering cost against holding cost. The economic order quantity (EOQ) is the order size that minimises total annual stock cost under deterministic demand.
EOQ model
Assumptions: constant annual demand D, fixed order cost S per order, holding cost H per unit per year, instantaneous replenishment, no shortages, and constant unit price.
EOQ Q* = √(2DS/H). Number of orders per year = D/Q*. Cycle time = Q*/D (in years). Total annual cost = ordering cost + holding cost = DS/Q* + HQ*/2; at Q* these two components are equal. Reorder point = demand during lead time (plus safety stock if used).
Worked example: D = 10,000 units/year, S = RM50, H = RM4/unit/year. Q* = √(2×10,000×50/4) = √250,000 = 500 units. Orders = 20 per year. Total cost = 10,000(50)/500 + 4(500)/2 = 1000 + 1000 = RM2000. With a 2-week lead time and 50 working weeks per year, weekly demand = 200, so reorder at 400 units.
Traps: using a percentage holding cost as if it were a money amount (convert H = i × unit cost); mixing monthly demand with an annual H; applying the basic EOQ when quantity discounts or shortages are allowed; and omitting safety stock from the reorder point.