Summary

Question 1

Cut-and-Fix

Answer 1

Fix all Y that are 0 or 1 in LP-Relaxation

Question 2

Relax-and-Fix

Answer 2

Divide Variables into Subsets U and Sets Q. Ex. 4 Subsets of 5 each. First impose first 10 Variables are binary. Solve. Second fix 5 Variables of Q1 to obtained value. Impose Q2u U2 (5-15) binary. Repeat.

Question 3

RINS (Improvement)

Answer 3

Solve LP Relax. get feasible Sol. set all y that are the same in both solutions to that value.

Question 4

Local Branching (Improvement)

Answer 4

Start from feasible solution. Solve MIP where not more than k variables differ from their value in the feasible solution.

Question 5

Exchange (Improvement)

Answer 5

Divide variables into Groups. Fix Variables of one group to value obtained in feas. sol. Relax others to take binary values.

Question 6

PROB

Answer 6

• LS
• WW (LS but without production costs)
• DLSI (LS but can only produce at capacity or nothing)
• DLS (DLSI without inital stock)

Question 7

CAP

Answer 7

• C: Capacities Ct vary over time
• CC: Capacities Ct constant
• U: Uncapacitated

Question 8

VAR

Answer 8

• B (Backlogging)
• SC (Start-Up Costs)
• ST (Start-Up Times)
• LB (Minimum Production Levels)
• SL (Sales and Lost Sales)
• SS (Safety Stocks)

Question 9

B (Backlogging)

Answer 9

You can satisfy demand r later than required at a cost b.

Question 10

SC (Start-Up Costs)

Answer 10

Costs g for set-up for machine y in t if z = 1) (Make sure that set-up happens in t but not in t-1)

Question 11

ST (Start-Up Times)

Answer 11

Capacity is reduced by ST in t. Only occur if there is a start-up z = 1

Question 12

LB (Minimum Production Levels)

Answer 12

Lower Bounds for production

Question 13

SL (Sales and Lost Sales)

Answer 13

Problem -> Profit maximization, Amount v can be sold for c

Question 14

SS (Safety Stocks)

Answer 14

Keep a safety stock

Question 15

EVPI

Answer 15

Expected Value of Perfect Information
EVPI = WS - SP
WS = Wait and See Solution, Solution we would get if we could postpone the decision to take it after a scenario has realized

Question 16

VSS

Answer 16

Value of Stochastic Solution
Value & Advantage of solving stochastic problem instead of deterministic
VSS = SP - EEV
1. Solve EV (Expected Value of of demand)
2. Substitute x into SP (EEV)

Question 17

LUSS

Answer 17

Loss of using the skeleton solution
Does the deterministic solution produce the right non-zero variables?
LUSS = SP - ESSV
1. Solve EV problem -> obtain first stage variables
2. Fix all obtained vars that are zero and solve SP -> obtain first stage solutions
3. Substitute solutions into SP and solve (ESSV)

Question 18

LUDS

Answer 18

Loss of using the deterministic solution
Can the deterministic solution be upgraded to become good or optimal for the SP?
LUDS = SP - EIV
1. Solve EV -> obtain first stage solutions
2. Impose x >= x and solve SP -> obtain first stage solutions
3. Substitute solutions into SP and solve (EIV)

Question 19

Constant trend

Answer 19

• Elementary: p(t+1) = y(t)
• Simple moving average
• Weighted moving average
• exp. smoothing: p(3) = αy(2) + (1-α)p(2)

Question 20

Linear trend

Answer 20

pt(t) = a(T) + b(T)*t

• Elementary: a(T) = y(T), b(T) = y(T) - y(T-1)
• Holt-Method

Question 21

Seasonal Variations with periodicity M

Answer 21

• Elementary: M = 12; p(25) = y(25-12) = y(13)
• Winters: a(t), b(t), s(t+M)
  a(0) = average over all periods
  b(0) = (av. last period - av. first period)/(T-M)