A Note on Periodic Replacement with Minimal Repair at Failure

Periodic replacement model with minimal repair at failure is extended to the case where quantity purchases are possible. A recursive relationship among 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 the solution of the unconstrained problem.

고장시 응급수리(應急修理)가 가능한 부품(部品)의 정기교환정책(政期交換政策)을 예비품(豫備品)의 다량확보가 가능한 경우로 확장하였다. 최적대치기간(最適代置期間)들은 재고유지비(在庫維持費) 때문에 증가수열(增加數列)을 이루었고, 이로부터 최적(最適) l회 예비품(豫備品) 발주량(發注量) 및 최적(最適) 대치기간(代置期間)들을 구할 수 있었다. 각(各) 부품(部品)의 대치기간(代置期間)을 같게 두면 문제가 간단해 지면서도 최소비용(最小費用)에는 별 차(差)가 없었다.