Consider the stock management system shown below. Sales rate depletes inventory, while production rate increases inventory. The equations for the auxiliaries and the flow “Production Rate” are given below:

Production Rate = Inventory Shortfall/Time to Correct Inventory

Inventory Shortfall = (Desired Inventory – Inventory)

1. Determine the equilibrium value of the stock (“Inventory”) in terms of other variables and parameters shown.

2. When the system is in equilibrium, does Inventory equal its desired value? Yes? No?

3. Suggest an alternative policy for production rate that assures Inventory equal its desired value in equilibrium (Hint: you need to modify the equation that you derived in A).
    

Inventory Sales Rate Production Rate Time to Correct Inventory Desired Inventory Shortfall Inventory