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Solving a Sequencing Problem: Allocating Cost Savings
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[QUOTE="Cyn, post: 5968633, member: 614579"] [COLOR=#4d4dff]<Moderator's note: LaTeX code edited.>[/COLOR] [B] 1. Homework Statement [/B] 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).##[h2]Homework Equations[/h2] What is the allocation of the cost savings? [h2]The Attempt at a Solution[/h2] [LEFT][SIZE=4][COLOR=rgb(5, 5, 5)]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##?[/COLOR][/SIZE][/LEFT] [/QUOTE]
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