Seri Murni Trading: EOQ, Quantity Discounts and a Warehouse Limit
Seri Murni Trading sells 12,000 units of a filter cartridge a year at a steady rate. Each order costs RM45 to process. Holding cost is 20% per year of the unit purchase price. The supplier quotes RM15 per unit for orders below 500, RM14.25 for orders of 500 to 999, and RM13.80 for orders of 1,000 or more. The present policy is to order 500 units at a time. The warehouse can store at most 800 cartridges, and unused space cannot be used for anything else. Renting an adjacent unit would add RM3,500 a year and would remove the 800-unit limit. Management suspects the current order size is too small but is unwilling to rent space without evidence. Assume demand is certain and no shortages are allowed.
1. Calculate the EOQ using the RM15 price and explain why it cannot be implemented directly.
Read the worked answer
D = 12,000 units/year, S = RM45 per order, H = 0.20 x RM15 = RM3 per unit per year.
EOQ = sqrt(2DS/H) = sqrt(2 x 12,000 x 45 / 3) = sqrt(360,000) = 600 units.
This cannot be implemented at RM15 because an order of 600 units falls in the 500-999 bracket, where the price is RM14.25. The calculation is internally inconsistent: it uses a price that is not available at the calculated quantity. The EOQ must be recalculated within each relevant price bracket, and the total annual cost compared at the bracket boundaries.
2. Evaluate the feasible order quantities under the 800-unit warehouse limit and recommend an order size. Compare with the present policy of 500 units.
Read the worked answer
Within the 500-999 bracket, P = RM14.25, so H = 0.20 x 14.25 = RM2.85.
EOQ = sqrt(2 x 12,000 x 45 / 2.85) = sqrt(378,947) = 615.6 units.
This lies inside the bracket and below the 800 limit, so it is feasible. Total annual cost: Purchase = 12,000 x 14.25 = RM171,000 Ordering = (12,000/615.6) x 45 = RM877 Holding = (615.6/2) x 2.85 = RM877 Total = RM172,754.
At Q = 500: purchase RM171,000; ordering 24 x 45 = RM1,080; holding 250 x 2.85 = RM712.50; total RM172,792.50.
At Q = 800: purchase RM171,000; ordering 15 x 45 = RM675; holding 400 x 2.85 = RM1,140; total RM172,815.
So Q = 616 is best within the limit. The present Q = 500 is only about RM38 worse, so the current policy is not badly wrong. Ordering 800 is not optimal: the holding-cost increase outweighs the ordering-cost saving.
3. Should Seri Murni rent the adjacent space? Support your answer with an annual cost comparison, and state the main caveat.
Read the worked answer
Renting removes the 800-unit limit, so Q = 1,000 becomes possible and qualifies for P = RM13.80. Then H = 0.20 x 13.80 = RM2.76.
At Q = 1,000: Purchase = 12,000 x 13.80 = RM165,600 Ordering = 12 x 45 = RM540 Holding = 500 x 2.76 = RM1,380 Total = RM167,520. Add rent RM3,500: total = RM171,020.
Best without rent = RM172,754. Renting saves about RM1,734 per year, so on these figures it is worthwhile. The EOQ at RM13.80 would be sqrt(2 x 12,000 x 45 / 2.76) = 625.5, outside the 1,000+ bracket, so the discount forces an order above the unconstrained EOQ.
Caveat: the saving is small, about 1% of annual cost. It depends on steady demand, the discount continuing, and the rent staying at RM3,500. If any of these is uncertain, the decision is marginal and should be reviewed before signing a long lease.