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Cyn

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<Moderator's note: LaTeX code edited.>

Hi, I have a question.

I have a sequencing problem ##(N, \sigma_{0}##, ##\{p_{j}\}_{j\in J}, \{c_{i}\}_{i\in N})## with ##N = \{1,2,3\}## the set of players, and ##J = \{A,B,C,D,E,F\}## the set of jobs. The processing times of the jobs are:

$$p_{A} =8\\

p_{B} =10 \\

p_{C} = 15\\

p_{D} = 5 \\

p_{E}=6\\

p_{F}= 12$$

De set jobs van de spelers, ##J(i)##, zijn:

$$J(1) = \{B,E\}, J(2) = \{A,D\}, J(3) =\{C,F\},$$

##c_{1}(\sigma) = 7min\{C_{B}(\sigma),C_{E}(\sigma)\}##,

##c_{2}(\sigma) = 4min\{C_{A}(\sigma),C_{D}(\sigma)\}##,

##c_{3}(\sigma) = 12min\{C_{C}(\sigma),C_{F} (\sigma)\}##,

##\sigma_{0} = (A B C D E F).##

What is the allocation of the cost savings?

1. Homework Statement1. Homework Statement

Hi, I have a question.

I have a sequencing problem ##(N, \sigma_{0}##, ##\{p_{j}\}_{j\in J}, \{c_{i}\}_{i\in N})## with ##N = \{1,2,3\}## the set of players, and ##J = \{A,B,C,D,E,F\}## the set of jobs. The processing times of the jobs are:

$$p_{A} =8\\

p_{B} =10 \\

p_{C} = 15\\

p_{D} = 5 \\

p_{E}=6\\

p_{F}= 12$$

De set jobs van de spelers, ##J(i)##, zijn:

$$J(1) = \{B,E\}, J(2) = \{A,D\}, J(3) =\{C,F\},$$

##c_{1}(\sigma) = 7min\{C_{B}(\sigma),C_{E}(\sigma)\}##,

##c_{2}(\sigma) = 4min\{C_{A}(\sigma),C_{D}(\sigma)\}##,

##c_{3}(\sigma) = 12min\{C_{C}(\sigma),C_{F} (\sigma)\}##,

##\sigma_{0} = (A B C D E F).##

## Homework Equations

What is the allocation of the cost savings?

## The Attempt at a Solution

I have calculated the $\alpha$'s and the optimal order begins with (EFD). Now I want to calculate an allocation of the cost savings.

I have said that my new order becomes ##(EFDCBA)##. So ##MP(\sigma_{0})=\{(A,B), (A,C), (A,D), (A,E), (A,F), (B,C), (B,D), (B,E), (B,F), (C,D), (C,E), (C,F), (D, E), (D,F)\}##

Then, I have calcultated ##g_{ij}. (g_{ij} = \alpha_{j}p_{i}-\alpha_{i}p_{j}).##

##g_{AB} = 16;

g_{AE} = 32;

g_{BC} = 15;

g_{BD} = 5;

g_{BE} = 28;

g_{BF} = 36;

g_{CE} = 33;

g_{DE} = 11##

If we use EGS, is it correct that ##EGS_{1}= 102##?

I have said that my new order becomes ##(EFDCBA)##. So ##MP(\sigma_{0})=\{(A,B), (A,C), (A,D), (A,E), (A,F), (B,C), (B,D), (B,E), (B,F), (C,D), (C,E), (C,F), (D, E), (D,F)\}##

Then, I have calcultated ##g_{ij}. (g_{ij} = \alpha_{j}p_{i}-\alpha_{i}p_{j}).##

##g_{AB} = 16;

g_{AE} = 32;

g_{BC} = 15;

g_{BD} = 5;

g_{BE} = 28;

g_{BF} = 36;

g_{CE} = 33;

g_{DE} = 11##

If we use EGS, is it correct that ##EGS_{1}= 102##?

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