問26
頻出度★★★
ある商店で販売している商品Aの1週間の売上個数の分布は表のとおりである。商品Aの発注から納入までのリードタイムが1週間のとき，品切れになる確率を10％未満にするため，発注時に最低限必要な在庫は幾つか。
| 売上個数 | 86 | 87 | 88 | 89 | 90 | 91 | 92 | 93 | 94 | 分布計 |
|---|---|---|---|---|---|---|---|---|---|---|
| 分布（％） | 1 | 5 | 11 | 20 | 26 | 20 | 11 | 5 | 1 | 100 |
平成23年度 秋期 ITパスポート試験 問26
ストラテジ系企業活動 › 業務分析・データ利活用
This question's explanation and your answers so far.
解説
問 26
Incorrectア
With a stock of 87 units, a stockout occurs whenever 88 or more units are sold. That probability is 11+20+26+20+11+5+1=94%, so far from being below 10%, a stockout is almost certain. This wrong answer is easy to pick if you accumulate from the lower side of the table (the side with fewer units sold), see that 1+5=6% is below 10%, and misread that as meaning 87 units is enough; but the accumulation from the lower side is the probability that stock is left over, not the probability of a stockout.
Incorrectイ
With a stock of 88 units, a stockout occurs whenever 89 or more units are sold. That probability is 20+26+20+11+5+1=83%, which does not satisfy the condition of being below 10% at all. It also corresponds to the mistake of accumulating from the lower side to get 1+5+11=17% and comparing that with 10% as if it were the boundary; but what should be accumulated is the sales that exceed the stock, that is, the probabilities on the upper side.
- ウ
正解 Since the lead time is one week, an order placed now is not delivered until a week later. In other words, the stock held at the time of ordering must cover the coming week of sales all by itself. A stockout occurs when “units sold in one week > stock at the time of ordering”, so if the stock is x units, the stockout probability is the sum of the probabilities in the table for all sales figures greater than x. Accumulating from the upper side (the side with more units sold) gives: 94 units = 1%, 93 units or more = 6%, 92 units or more = 17%. With a stock of 92 units, the stockout probability is the 5%+1%=6% for selling 93 or 94 units, which satisfies the requirement of being below 10%. With a stock of 91 units, on the other hand, it becomes 11%+5%+1%=17% for 92, 93 and 94 units, which is 10% or more and does not satisfy the condition. Therefore the smallest stock that satisfies the condition is 92 units, and the correct answer is ウ.
Incorrectエ
With a stock of 93 units, the stockout probability is only the 1% for selling 94 units, so it does indeed satisfy the condition of being below 10%. However, what the question asks for is the minimum stock required to satisfy the condition. Since 92 units already gives a stockout probability of 6% and satisfies the condition, 93 units is one unit more than needed and is not the minimum. It is the wrong answer you get by going one step too far past the first boundary at which the upper-side cumulative probability falls below 10%.
ここがポイント
- Demand during the lead time (the period from ordering to delivery) must be covered by the stock on hand, so the stockout probability is the probability that “demand during the lead time > stock on hand”, obtained by accumulating from the upper side the probabilities of the sales figures that exceed the stock level.
- When asked for “the minimum stock that keeps the stockout probability below ◯%”, accumulate the probabilities starting from the side with the largest sales figures and choose the stock level at which that cumulative value first falls below the specified value. Even if several values satisfy the condition, the answer is the smallest one.
用語