A warehouse has an end-of-period capacity of 3 units. During a period in which production takes place, a setup cost of $4 is incurred. A $1 holding cost is assessed against each unit of a period’s...

A warehouse has an end-of-period capacity of 3 units. During a period in which production takes place, a setup cost of $4 is incurred. A $1 holding cost is assessed against each unit of a period’s ending inventory. Also, a variable production cost of $1 per unit is incurred. During each period, demand is equally likely to be 1 or 2 units. All demand must be met on time, and β = .8. The goal is to minimize expected discounted costs over an infinite horizon.

a Use the policy iteration method to determine an optimal stationary policy.

b Use linear programming to determine an optimal stationary policy.

c Perform two iterations of value iteration.