Problem #$9$

Total Points $(10)$

A power plant near a coal mine demands $81,000$ tons of coal per year. The coal mine produces $202,500$ tons of coal per year. The mine is operational for $250$ days in a year and the lead time is $3$ days. The cost per ton of coal produced is $$0\mathrm{.}40,$ cost per setup is $$5\mathrm{.}40,$ holding cost per ton of coal in the stockyard annually is $$0\mathrm{.}072.$

Use the appropriate inventory management model to cater to the demands of the coal power plant in the most economically efficient way. Hence calculate

i$.$ the optimal size of a production run

ii$.$ total cost of production

iii. time of depletion run

iv$.$ total cycle time

v$.$ maximum level of coal that can be stored in a given point of time

vi$.$ reorder point.

vii. Also calculate the practical Cycle time in days using the following rule

To find a practical $T$ :

Calculate $T^{**}$

Pick a base time period $($day$,$ week, etc.$)$

Find the lowest value of $k$ that satisfies: