GATE 2020 ME (ME2) – Question 57

Production Planning and Control · Inventory control: deterministic models, safety stock, control systems · 2 marks · Numerical answer

Demand is continuous at 10000 units/year, replenishment instantaneous and backorders allowed. An order of Q units first clears backordered S units. Ordering cost is ₹300/order, carrying cost ₹4/unit-year and backordering cost ₹25/unit-year. Minimizing total cost, find maximum on-hand inventory (units), nearest integer.

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Correct answer: 1130 to 1140

Explanation

Optimal batch is $Q^*=\sqrt{2DS(h+p)/(hp)}$. Maximum stock is I=Q*p/(h+p), hence $I=\sqrt{(2DS/h)\,p/(h+p)}=\sqrt{1500000(25/29)}=1137.147$. Rounded **1137 units**. Maximum on-hand inventory differs from total replenishment quantity because part clears backorders.