This question's explanation and your answers so far.
製品Aを1個生産するためには，外部から調達する部品Bを1個必要とする。部品Bは，毎月の第1営業日に発注し，その月の最終営業日に納品され，翌月以降の生産に使用される。製品Aの4月から3か月間の生産計画が表のとおりであるとき，5月の第1営業日に部品Bを最低何個発注する必要があるか。ここで，3月末の部品Bの在庫は6,000個であり，4月第1営業日に6,000個の発注を行っているものとする。また，仕掛残及び安全在庫は考えないものとする。
| 3月 | 4月 | 5月 | 6月 | |
|---|---|---|---|---|
| 製品Aの生産計画 | 5,000個 | 6,000個 | 7,000個 | |
| 部品Bの発注量 | 6,000個 | |||
| 部品Bの月末在庫量 | 6,000個 |
注記 網掛けの部分は，表示していない。
5,000 units misreads the condition that the order placed on the first business day of May is used for production “from the following month onward (＝ June).” It instead treats the order as covering the shortfall of May’s 6,000-unit production and subtracts the carried-over 1,000 units (6,000−1,000). What actually needs to be covered is June’s 7,000-unit production; this answer mistakenly shifts the corresponding month one step earlier.
正解 Because Part B is “delivered at the end of the current month and used in production from the following month onward,” the stock available for a given month’s production is the previous month-end stock. Tracing the stock changes: the 6,000 units in stock at the end of March are consumed by April production (5,000 units), leaving 1,000 units. The 6,000 units ordered on the first business day of April are delivered at the end of April, so the end-of-April stock is 1,000+6,000=7,000 units. Next, consuming them in May production (6,000 units) leaves 1,000 units. Let the quantity ordered on the first business day of May be X units; this batch is delivered at the end of May and is used for June production, so the end-of-May stock is 1,000+X units. June production requires 7,000 units, so the stock available for June production (＝ end-of-May stock) only needs to reach 7,000 units or more. This gives 1,000+X≥7,000, i.e., X≥6,000. The minimum order quantity is 6,000 units, and the correct answer is イ.
7,000 units takes June’s production quantity of 7,000 units directly as the order quantity, but forgets to subtract the 1,000 units of stock carried over at the end of May (the remainder after subtracting May’s 6,000-unit production from the 7,000 units at the end of April). Taking the carry-over into account, the required order is 6,000 units.
8,000 units adds the 1,000 units of carried-over stock—which should have been subtracted—to June’s production quantity of 7,000 units instead (7,000+1,000), or overestimates the stock changes. Since the carried-over 1,000 units can be used, ordering 6,000 units is enough.