(a) Consider 6 jobs having the processing times Pj, the due-dates d; and the weights w; ofthe jobs j=1, ..., 6, given in the table:Jobs1234632411Pid712186.7W;25313Calculate the total weighted completion time, the maximum lateness, and the totalweighted tardiness of the following schedule: 4, 2, 6, 3, 1, 5.

The total weighted completion time, the maximum lateness and the total weighted tardiness is given…

Answered: (a) Consider 6 jobs having the…

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section20.15: Priority Queuing Models

Problem 4P

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Consider the following Job Scheduling problem. We have one machine and a setof n jobs {1, 2, . . . , n} to run on this machine, one at a time. Each job has a start time sifinish time fi and profit pi where 0 ≤ si < fi < ∞ and pi > 0. Two jobs i and j are compatible if the intervals [si, fi)and [sj , fj ) do not overlap. The goal is to find a set A of mutually compatible jobs with the maximumtotal profit, i.e.,P j∈A pj is maximized.Consider the following two greedy choices. For each one, determine whether it is a “safe” greedy choicefor this Job Scheduling problem. If your answer is yes, prove the “Greedy-choice property”. If your answeris no, please give a counterexample and show that the greedy choice will not lead to an optimal solution. a.Greedy choice 1: Always select a job with the earliest finish time that is compatible with allpreviously selected activities.b.Greedy choice 2: Always select a job with the highest profit per time unit (i.e., pi/(fi − si))that is…
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Simple example in healthcare: Let consider 7 patients with different surgeries times: ST=[4h30, 4h, 3h, 3h, 2h30, 1h30, 1h] We have to decide how to assign patients to the operating rooms. First problem: let consider 3 operating rooms available with their corresponding capacities OR=[7h30, 4h, 4h]. We want to operate the maximum number of patients. Propose a model and solve it using CPLEX

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