問28
頻出度★★★
倉庫A，Bにある在庫の全量を店舗C，Dに輸送する。倉庫A，Bの在庫量がそれぞれ35個，15個，店舗C，Dの必要量がそれぞれ20個，30個であり，各倉庫から各店舗への1個当たりの輸送費が表のとおりであるとき，最小となる総輸送費は何万円か。 単位 万円／個
| 店舗C | 店舗D | |
|---|---|---|
| 倉庫A | 4 | 2 |
| 倉庫B | 2 | 1 |
平成28年度 秋期 ITパスポート試験 問28
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 28
Incorrectア
85 comes from assigning each warehouse only to its own cheapest route (A→D 2×35 = 70, B→D 1×15 = 15, total 85). But if both warehouses send everything to D, Store D receives 50 units and Store C receives 0, which fails to meet the requirements of C = 20 and D = 30. It is an infeasible lower bound, so it is wrong.
Incorrectイ
100 is below the achievable minimum cost of 110. It arises from an assignment that ignores the capacity constraint that Warehouse B holds only 15 units (assuming all 20 units for Store C are sent via the cheap B→C route). Because B→C can carry at most 15 units, this assignment does not hold.
- ウ
正解 This is a transportation (optimization) problem. The A→C route is the most expensive (40,000 yen), so keeping the amount sent through it to a minimum is the key. Warehouse A ships out all 35 units of its inventory, but the amount it can route to the cheaper Store D (A→D is 20,000 yen) is capped at Store D's requirement of 30 units. The remaining 5 units must unavoidably go via the pricier A→C (40,000 yen). Store C's remaining 15 units are then covered by Warehouse B→C (20,000 yen), using up Warehouse B's 15 units of inventory exactly (B→D is 0 units). Total cost = A→C 4×5 + A→D 2×30 + B→C 2×15 + B→D 1×0 = 20 + 60 + 30 = 110 (in ten-thousand yen). This is the minimum value that satisfies the supply and demand constraints, so the correct answer is ウ “110”.
Incorrectエ
125 is the highest cost among feasible assignments. If you first cram all 15 units into B's cheapest route B→D, then all 20 units for Store C have to go via the pricier A→C (40,000 yen) (A→C 4×20 + A→D 2×15 + B→D 1×15 = 80 + 30 + 15 = 125). This is a typical mistake of over-prioritizing cheap routes so the total is not minimized; it is not the minimum cost.
ここがポイント
- Transportation problem (linear optimization): minimize the total shipping cost while satisfying the supply and demand constraints. The basic approach is to use the cheaper per-unit routes as much as possible and keep usage of the pricier routes to a minimum.
- If you assign routes first based only on cheap unit price, capacity constraints can later force heavy use of pricier routes and raise the total. Judge from the standpoint of overall optimization.
用語