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PDS #1
| Question | Answer |
|---|---|
| What is optimization | choosing an alternative out of a set of at least two alternatives |
| How to write matematically 1, set of feasible solutions 2, vector of decision variables | 1, set of feasible solutions X⊂R^n 2, vector of decision variables x∈X |
| How to matematically note maximization and minimization | maximization z* = max z(x) minimization z* = min z(x) |
| What are important remarks about optimal solution (2) | 1, optimal solution MUST BE feasible 2, there might be several optimal solutions |
| What is interesting about optimization (2) | 1, many problems do not have knwon proven optimality 2, sometimes the proces just tries to improve the current solution |
| What is lower bound in problem with minimization | a point that is definitely not higher than optimum |
| What is difference between variables and parameter | parametres = are fixed values for a given instance variables = are object we assign values to |
| How to calculate maximum relative error | (Z(x´) - Zopt) / Zopt *100% Z upper bound divided with Z lower bound |
| What are Isoquants | line where objective function has the same value |
| What does infrasible instance mean | there is no feasible region >> no possible solution |
| When can we use minimum cost flow problem (3) | 1, we have homogenous flow 2, capacities (constrains) are respected 3, objective function is minimizing |
| What are notation in minimum cost flow problem (5) | V = set of nodes (uzly - body v siti) A = set of arcs (spojnice - tok mezi uzly) c (i,j) = cost u(i,j) = capacity b(i) = quantity of node i |
| What are 3 types of b(i) qunatity nodes | 1, supply nodes with b(i) > 0 2, demand nodes with b(i) < 0 3, transshipment nodes with b(i) = 0 (flow value cannot stay there) |
| What are decision variables in minimum cost flow problem | x(i,j) flow valies that flow over arcs i & j |
| What are constrains in minimum cost flow problem (2) | 1, x(i,j) >= 0 .. each arc flow (i,j) non-negativity constrains 2, x(i,j) <= u(i,j) .. capacity for each between arc flow is respected |
| What is the general constrain formula for minimum cost flow problem | outgoing flow - incoming flow = bi outgoing flow ... positive sign incoming flow ... negative sign bi .. sign depend on type (demand / supply / transshipment) |
| How to form constrain for supply node | outgoing flows = bi bi .. is positive outgoing flows = all the arcs leaving the arc |
| How to form constrain for transshipment node | outgoings flows - incoming flows = 0 0 because bi(transshipment) = 0 |
| How to form constrain for ademand node | - incoming flows = bi bi is NEGATIVE |
| What else do we need to set as restriction (2) | 1, non-negativity restriction for each variable 2, capacity restrictions for every decision variable |
Created by:
semester1.IBWL