You own a project management company which has been hired to oversee the construction of a...

 

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You own a project management company which has been hired to oversee the construction of a new highway in Sydney. The project is currently in the initial construction stages, and about to break ground. There are three separate road segments (1, 2, and 3) which will be built as part of this new highway, and each road segment, there are four jobs (1,2,3, and 4) that need to be completed as part of the site preparation process. The operations of the jobs need to be performed in their natural order (e.g. 1 before 2, 2 before 3, etc.), however not all road segments require all jobs to be performed. Furthermore, there is only one work crew available to complete each job, so the same job cannot be scheduled at the same time on any two road segments. The four jobs required are 1) Site Clearing 2) Tree Removal, 3) Excavation, and 4) Placing Utilities. The time required to complete each job (i.e. processing time) is denoted Pmi, where m is the road segment and i is the job, varies across the road segments. This information is summarized in the table below. Assume the order the road segments will be scheduled is fixed, and equal to 1, 3, 2. Solve the problem and find the optimal makespan (i.e. minimum time required)? Road Segment Required Job Sequence 1,2,3 1 2 3 Answer: 1,2,4 1,2,3,4 Job-Road Processing Times P11-10, P12 8, P13=4 P21-3, P22-8, P24-5 P31-5, P32-4, P33-3, P34-2 You own a project management company which has been hired to oversee the construction of a new highway in Sydney. The project is currently in the initial construction stages, and about to break ground. There are three separate road segments (1, 2, and 3) which will be built as part of this new highway, and each road segment, there are four jobs (1,2,3, and 4) that need to be completed as part of the site preparation process. The operations of the jobs need to be performed in their natural order (e.g. 1 before 2, 2 before 3, etc.), however not all road segments require all jobs to be performed. Furthermore, there is only one work crew available to complete each job, so the same job cannot be scheduled at the same time on any two road segments. The four jobs required are 1) Site Clearing 2) Tree Removal, 3) Excavation, and 4) Placing Utilities. The time required to complete each job (i.e. processing time) is denoted Pmi, where m is the road segment and i is the job, varies across the road segments. This information is summarized in the table below. Assume the order the road segments will be scheduled is fixed, and equal to 1, 3, 2. Solve the problem and find the optimal makespan (i.e. minimum time required)? Road Segment Required Job Sequence 1,2,3 1 2 3 Answer: 1,2,4 1,2,3,4 Job-Road Processing Times P11-10, P12 8, P13=4 P21-3, P22-8, P24-5 P31-5, P32-4, P33-3, P34-2

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