Asked by Mariano Davila III on May 11, 2024

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Given the following chart of jobs assigned with Johnson's rule suppose that all the jobs (A, B, C, etc) could be evenly divided into two tasks (such as A1 and A2, B1 and B2, etc). Suppose job D is split into two equivalently sized sections, D1 and D2, each with a body work time of 1.5 hours and a paint time of 2 hours (D1 and D2 sum to 3 hours of body work and 4 hours of paint which is equivalent to D). How much is makespan reduced by this splitting of D?
Given the following chart of jobs assigned with Johnson's rule suppose that all the jobs (A, B, C, etc) could be evenly divided into two tasks (such as A1 and A2, B1 and B2, etc). Suppose job D is split into two equivalently sized sections, D1 and D2, each with a body work time of 1.5 hours and a paint time of 2 hours (D1 and D2 sum to 3 hours of body work and 4 hours of paint which is equivalent to D). How much is makespan reduced by this splitting of D?

Johnson's Rule

A scheduling technique that minimizes the total time required to process a group of jobs on two machines by ordering the jobs intelligently.

Body Work Time

The duration of time allocated for or spent on the physical repair or refurbishment of a vehicle's body.

Paint Time

The duration required to apply and dry paint on a product, significant in manufacturing and production scheduling.

  • Evaluate the repercussions of segregating duties on the diminution of the makespan in a production cycle.
  • Apply Johnson's methodology to deduce the most effective job sequence for reducing the makespan in a setup of two machines.
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Paula BissetteMay 15, 2024
Final Answer :
Job D1 could now start paint at t = 1.5 and would finish at t = 3.5 Job D2 could start paint at t = 3, however paint is occupied until t = 3.5. Thus D2 will start paint at t = 3.5 and finish at t = 5.5. However, this does nothing to save makespan time because C will not start on paint until t = 10. The only effect splitting had is to change the idle time for paint from t = 0 through t = 3 and t = 7 to t = 10 into two uneven time slots of t = 0 to t = 1.5 and t = 5.5 to t = 10.