Operations Research and Operations Management · Production Control · 2 marks · Numerical answer
Annual demand is 5000 units, ordering cost ₹400/order and annual holding rate 30% of unit price. All-units prices are ₹10 for Q < 1200, ₹8 for 1200 ≤ Q < 2000, and ₹7 for Q ≥ 2000. Find optimal order size (integer).
At each price use $Q^*=\sqrt{2DS/(0.3p)}$, adjusting upward to a feasible price-break quantity when needed. Candidates are about 1154.7 at ₹10, 1291.0 at ₹8, and 2000 at ₹7. Annual cost $Dp+DS/Q+0.3pQ/2$ is approximately ₹53464, ₹43098 and ₹38100 respectively. The lowest is the ₹7 tier at **Q = 2000 units**.
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