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PDS #2
| Question | Answer |
|---|---|
| What is the structure of indices matrix for minimum cost flow problem | ________ x12 x13 x23 node 1 (1) --(1)--(0) node 2 (-1) -(0) -(1) node 3 (0) --(-1) (-1) rows = nodes column = arcs if leaves node = 1 if enter node = (-1) otherwise = 0 |
| What is important condition for feasibility of minimum cost flow problem (2) | 1, supply must equal demand 2, if not a artifical/dummy node is necesary |
| How to use dummy variable if in the minimum cost flow problem there is supply≠demand (2) | 1, supply is higher >> add b(dummy) = -supply surplus to the demand side 2,demand is higher > b(dummy) = -demand surplus to the supply side |
| How to solve the maximum flow problem (4) | 1, all nodes are treated as transshipment ones 2, we create artifical variable flow t=end to s=beginning 3, we set x(t,s)>=0 or other high limit 4, we set z*= max x(t,s) as our objective function |
| What is minimum cut problem | seperating s(beginning) and t(end) with cutting minimum capacity |
| What are constrains in minimum cut problem | 1, s∈S (source belongs to S-set) & t∈T (sink belongs to T-set) 2, V = S∪T (all nodes belong to S or T set) 3,S∩T =Ø (S and T are mutally exclusive) |
| What are oficial and unoficial decision variables in Minimum cut problem | Official >> node(i) = node(i)∈S or node(i)∈T Unoficial z(i,j) = 1, if arc(i,j) is cut ........... 0, otherwise |
| What is objective function for minimum cut problem | Official >> u(S,T) = ∑"z(i,j)* " u(i,j) z* = min u(S,T) "z(i,j)*" not in the official presentation |
| When does a u(i,j) count into ∑u(S,T) objective funtion | if S >> T it counts if T >> S IT DOESNT INCREASE ∑u(S,T) |
| How does Production Planning differs from linear programms (2) | 1, we have profit margin (sales prices "pj" - production costs "cj") 2, there is potential maximum sales "dj" |
| How to set conditions Production Planning in maximum sales of products | xj<= dj production of product j is lower/equal to sales contrain of product j |
| What is phylosophy of minimum cut problems | separating source and sink while "cutting" nodes with least capacity possible |
| What is phylosophy of blending problems | of much of multiple raw materials should we mix to produce one product while satisfying quality requirment at low cost THE OPTIMAL PROPORTION |
| What is notation in blending problems (2) | ℓ1, ℓ2, ... ℓn _ minimum quantity of ingredience n u1,u2, .. un .. minimum qunatity of ingredience n |
| How to set condition for blending problem upper and lower limit | ∑a(i,j)x(j) >= ℓ ∑a(i,j) x(j) <= u setting upper and lower level for each ingredient in the end product |
| What is the notation for cutting stock problems (4) | 1, L = lenght of the one original roll 2,ℓ(i) = length of demanded product i 3, b(i) = demand of item type i 4,a(i,j) = number of pieces of type i produced by pattern j |
| What are decision variables in cutting stock problems | x(j) = number of rolls cut according to pattern j |
| What are 2 steps to solve cutting stock problems | 1, indetifying all relevant patterns (relevant = r(j) < min ℓ) 2, use this pattern to find optimal solution |
| What is objective function for cutting stock problem (2) | 1, r(j)= L - ∑ℓ(i)a(i,j) 2, min ∑ r(j)x(j) |
Created by:
semester1.IBWL