Variability management

7 important questions on Variability management

Considering a job shop what is:
  • n
  • m
  • (i,j)
  • pij

Answers
  • n = jobs
  • m = machines
  • (i,j) operation, processing ob job j on machine i
  • pij processing time operation (i,j)

What is the objective and goal of the job shop?

Schedule the jobs on the machines without overlap minimizing the makespan.

What is the equation used to describe a disjunctive graph?

G = ( N, A, B)
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What do the following stand for on G = (N, A, B)
  • N
  • A
  • B
  • U
  • V

  • N nodes, for every operation (i,j) there is one node
  • A Conjunctive arcs, order of operations of jobs
  • B Disjunctive arcs, operations are done on the same machine are connected through arcs.
  • U connected first jobs
  • V connected last jobs

Consider a subset D on B
  • When is it called a selection?
  • When is the selection called a feasible selection?

  • Called a selection if it contains from each pair of disjunctive arcs exactly one;
  • When the resulting directed graph G(D) = (N, A on D) is acyclic;

What are [3] consequences of a feasible selection?

  1. A feasible selection leads to a sequence in which operations have to be processed;
  2. Each feasible selection leads to a feasible schedule;
  3. A feasible schedule induces a feasible selection;

How do you calculate the schedule for a selection in Job Shop?

Calculating the longest paths from U to all other nodes in G(D)
  • weight of the nodes is ( i, j ) bij pij and nodes U and V are 0
  • length is the sum of the weight of the previous nodes
  • An operation (i, j) starts at time lij

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