Optimal stocking for replacement with minimal repair

Joint stocking and replacement model with minimal repair at failure is considered. A recursive relationship among the optimal replacement intervals is obtained, which shows that replacement intervals are an increasing sequence due to the inventory carrying cost. Using the relationship, a procedure is given for determining how many units to purchase on each order and when to replace each unit after it has begun operating so as to minimize the total cost per unit time over an infinite time span. The problem can be simplified if equal replacement intervals are assumed, and the solution is very close to that of the unconstrained problem.