Operations Research Applications and Algorithms 4th edition System Design: Proje

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Operations Research Applications and Algorithms 4th edition

System Design: Project Management† CASE 9 I also need the formulations. Thanks.

System Design (SD) is a small corporation that contracts to manage systems and industrial engineering projects. In this case it must manage the design and construction of a power plant's data-processing and data-collection system. SD's role in the project is to hire subcontractors, ensure each task is completed within specification, determine how much labor to assign to each task, and generally ensure the project's success.

SD is really a subcontractor within the larger project of building the power plant. Table 24 details SD's plant-construction and data-system-design tasks. SD is directly in charge of tasks 2, 6, 7, 10, 14, 15 and 19. The remaining tasks in Table 24 interact with those in SD's charge. Assume that the remaining tasks (1) will start whenever their predecessor tasks are complete and (2) will finish exactly after their duration.

To shorten the seven SD tasks, you must pay additional labor and overhead costs. Table 25 lists the functions you can use to compute the cost of changing each task duration to a new value. (Note: tj is the original duration of task j; dj is the minimum duration of task j.) The table also lists the lowest possible task-duration value. You may not increase the duration of any task.

The revenue that SD obtains from the project depends not only on its tasks but also on when the total project is completed. The project is due at day 900, and SD receives the contract price of $600,000 if the project is done then. If the project is finished x days early, then SD receives a total of $600,000 + $15,000x0.7 in revenue. If SD finishes x days late, then it receives $600,000 - $20,000x1.4 in revenue.

Expediting tasks can be profitable and necessary to meet deadlines, although employees do not really like it. Task completion quality is a function of the task completion time, and we would like to have a high quality. This may conflict with our objective of maximizing profit. Because quality affects future revenues, it is difficult to estimate the dollar impact of poor quality. If tj is the original duration of task j and xj is the expedited duration time for task j, then quality, measured on a scale of 0-100 (with 100 being the best), can be represented by the function 100 - min[100, (tj - xj)2.2]

This is only the quality for a task. It is unclear how one might quantify the quality of the project. Your job is to determine how we should proceed with our tasks. Your analysis should answer some of the following questions:

-- What tasks are critical to project completion? What tasks will you expedite?

--How are you measuring system system quality, and how does your recommendation measure up relative to that objective?

--How much money do you make on the project?

--What will you give the decision maker to help with the decision?

--If we can move minimum duration days to lower values, then which values would you like to reduce?

--If you could control additional tasks by paying more money, which ones would you like to take, and how much would you be willing to pay for control?

TABLE 24 Task Information Immediate Predecessor Tasks Task Duration (Days) 40 100 Task No. Task Name Preliminary system description Develop specifications Client approval Develop input-output summary Develop alarm list Develop log formats Software definition Hardware requirements Finalize input-output summary Analysis performance calculations Automatic turbine startup analysis Boiler guides analysis Fabricate and ship Software preparation Install and check Termination and wiring lists Schematic wiring lists Pulling terminals and cables Operational test First firing 3, 5 3 35 35 5 10 65 30 200 12 10, 11, 12 7, 10, 11 13, 14 7 130 30 0 16 17 18 19 20 16 15, 17 18 19 125 TABLE 25 Expediting Costs ($1,000) and Limits Duration (Days) Task No. Current 100 40 70 20 20 Cost to Decrease ty by x Days 1.5x18 212.0 70 80 130 125 1.8r19 1.9x1.6 0.9512.7 0.9x29 10 15 19 2 0 0 80

Explanation / Answer

The critical path and the critical activities with their earliest starting times are as follows:

The original project duration is calculated as 926 days with all tasks taking normal durations. Ctitical tasks are 1,2,4,5,6,9,10,13,15,17,18,19,20

The data given in table is not very much clear , in particularly about cost to decrease having expressions of exponential (power) x.

In order to complete the project in 900 days, it is required to reduce the duration of critical tasks. Which ever task has the minimum cost per unit of time should be given the preference over others.

SD should focus on tasks 2, 6, 10, 15, and 19.

Earliest Latest Task No. Predec. Time Start Finish Start Finish Slack 1 "--- 40 0 40 0 40 0 2 1 100 40 140 40 140 0 3 2 50 140 190 190 240 50 4 2 60 140 200 140 200 0 5 4 40 200 240 200 240 0 6 3,5 40 240 280 240 280 0 7 3 35 190 225 305 340 115 8 3 35 190 225 891 926 701 9 5,6 60 280 340 280 340 0 10 9 70 340 410 340 410 0 11 9 65 340 405 345 410 5 12 9 30 340 370 380 410 40 13 10,11,12 200 410 610 410 610 0 14 7,10,11 80 410 490 530 610 120 15 13,14 130 610 740 610 740 0 16 9 30 340 370 650 680 310 17 16 60 370 430 680 740 310 18 15,17 60 740 800 740 800 0 19 18 125 800 925 800 925 0 20 19 1 925 926 925 926 0 Critical path 1-2-4-5-6-9-10-13-15-17-18-19-20 and duration 926 days

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