Q.A manufacturing company has a contract to supply 4000 units of an item per year at uniform rate. The storage cost per unit per year amounts to $\text{\text{₹}}\,50$ and the set-up cost per production run is $\text{\text{₹}}\,160$. If the production run can be started instantaneously and shortages are not permitted, determine the number of units which should be produced per run to minimize the total inventory cost.

The cost-minimising production run size is $Q^{*}=\sqrt{\dfrac{2C_3R}{C_1}}=160$ units.

Given. Annual demand $R=4000$ units, storage cost $C_1=₹50$/unit/year, set-up cost per run $C_3=₹160$, no shortages, instantaneous replenishment.

EOQ formula. Total inventory cost is minimised at

$Q^{*}=\sqrt{\frac{2\,C_3\,R}{C_1}}.$

Substitute:

$Q^{*}=\sqrt{\frac{2\times160\times4000}{50}}=\sqrt{\frac{1{,}280{,}000}{50}}=\sqrt{25600}=160.$

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