Gast
#2459725
Hi, kann jemand eine allgemeine Lösungsstrategie vorschlagen? Oder zumindest die Aufgabe einer Disziplin zuordnen (nichtlineare Programmierung?)? In der Realität soll ein Rechner die Lösung automatisch vorschlagen. Wie gesagt - echte Aufgabe aus der Industrie. ---------------------------------------- Task: A small fluid product production plant consists of filling, modification and dosing stages. You are operating this plant. Today, your production order is exactly S=10 tons. In the inlet stage, you are able to fill between a=4 and A=7 tons. In the modification stage, there is no measurement; you have to remember what you fill in and out. In the filling stage, you can dose between b=2.5 and B=3.5 tons. You are not allowed to let the fluid flow anywhere but into these target vessels. You are expected to let in and fill out exactly the ordered amount, with no leftovers at the end. You are allowed to have some leftover in the modification stage between steps, but not allowed to overfill any stage. In what steps will you do it? Possible answer: 10 = 5 + 5 = 3⅓ + 3⅓ + 3⅓ 1. inlet 5 tons (o.k., 5 > a) 2. modify 5 tons 3. fill 3⅓ tons (o.k., b < 3⅓ < B); 1⅔tons remain in modification stage 4. inlet 5 tons (o.k., 5 > a) 5. modify 5+1⅔ tons (o.k., 5+1⅔ < A, no overfill) 6. fill 3⅓ tons (o.k., b < 3⅓ < B) 7. fill 3⅓ tons (o.k., b < 3⅓ < B) (o.k., no leftover) Generalized task: for given minimal inlet quantity a and order size S, find out if production without leftovers and overfills is possible. If yes, find a suitable sequence of steps inlet and fill steps. Priorities: - (most important) as few as possible fill steps - equal fill quantities - as few as possible inlet steps - (least important) equal inlet quantities More difficult case: S=23, a=5. Possible in 7 fill steps, but requires non-equal inlet steps.
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