Consider an inventory system, where the initial stock is $13$units. The demand as well as the lead times are

random variables.

Demand $5)56)47)38)2$

Probability $0\mathrm{.}350\mathrm{.}420\mathrm{.}180\mathrm{.}05$

Lead time $234$

Probability $0\mathrm{.}500\mathrm{.}200\mathrm{.}30$

There are three reorder points, RP$1,$ RP$2$ and RP$3$ at levels of $12$ units, $8$ units and $4$ units respectively

whereas three reorders, quantity of $9$units, $5$units and $3$units respectively, can be outstanding at a time.

Find the service level and the average stock held for the given reorder points and the reorder quantity.

Simulate the system for $10$ days.