$($a$)$ Use programming to develop the $(,)$ inventory model described in next page.

In Problem $($a$),$ students will create a comprehensive inventory system simulator

capable of modeling various aspects such as demand patterns, lead times, inventory

costs, and order quantities. The simulator should accurately reflect real$-$world

scenarios and enable experimentation with different settings.

$($b$)$ Use Simple Random Search, Localized Random Search, and Enhanced Localized

Random Search to find all local optima. The total computational budget at $10,000$

observations. Please draw three performance trajectories $([$Total cost per period$]$

vs$.$ number of observations consumed up to $10,000)$ corresponding to three

algorithms in one plot.

$($c$)$ Design your own heuristic algorithm to solve the same problem. Please explain the

concept of your algorithm and draw the performance trajectory as Problem $($b$).$