M. Consider the following the House Construction Project:TaskLabelDuration Prerequisite(weeks) TasksA7BCDEFGHIJTaskMasonryCarpentry for roofRoofPipe and Electrical InstallationsFront of HouseWindowsGardenCeilingPaintingMoving Ina. Draw the AOA network.318211321ABAD, CD, CD, CFHE, G, Ib. Calculate the Early Event Time and Late Event Time for every node in the resulting AOAnetwork.c. Determine Total Float and Free Float for every activity (arc) in the resulting AOA network.d. Determine a Critical path in the resulting AOA networ

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Answered: a. Draw the AOA network. b. Calculate…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 100P

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The Advanced Tech Company has a project to design an integrated information data base for a major bank. Data for the project are given in the following table. Indirect project costs amount to $250 per day. The company will incur a $200 per day penalty for each day the project lasts beyond day 12. Activity Normal Time (days) Normal Cost ($) Crash Time (days) Crash Cost ($) Immediate Predecessor(s) A 5 800 4 1,000 − B 5 1,100 2 2,900 − C 2 600 1 900 A, B D 3 1,200 2 2,000 B E 3 1,500 2 1,700 C, D F 2 1,300 1 1,400 E G 3 900 3 900 E H 5 500 2 800 G a. What is the project's duration if only normal times are used? The project duration is nothing day(s). (Enter your response as an integer.)…
Two law students, John and Marsha, are planning an all-nighter to prepare for theirlaw boards the following day. Between them they have one set of materials in thefollowing five subjects: contracts, torts, civil law, corporate law, and patents.Based on their previous experience, they estimate that they will need the following amount of time (in hours) with each set of materials:Contracts Torts Civil Corporate PatentsJohn 1.2 2.2 0.7 0.5 1.5Marsha 1.8 0.8 3.1 1.1 2.3They agree that Marsha will get the opportunity to see each set of notes beforeJohn. Assume that they start their studying at 8:00 P.M. Determine the exact timesthat each will begin and end studying each subject in order to minimize the totaltime required for both to complete studying all five subjects
Maximize profit = 4X + 4Y Subject to: 3X +5Y ≤ 150 X – 2Y ≤ 10 5X + 3Y ≤ 150 X, Y ≥ 0 Required: a- The corner point method to obtain the optimal point. b- Specify the profit value. c- Calculate the Slack for each constraint and state its formula.
Consider the network in the following figure. Edges that are not pictured have a length of ∞. Image attatched (a) What is the optimal TSP tour on this network, and what is its total length, z*? What is the optimal 1-tree Tˆ* on this network (“rooted” at node 1), and what is its total length, z(Tˆ*)? (b) Find the best Held-Karp lower bound you can. That is, find weights to add to one or more nodes so that z* and the right-hand side of the following formula are as close as possible. z* ≥ z(Tˆ*) + SUM{i∈N} λi(di(Tˆ*) − 2) Image attatched Here Tˆ* is the optimal 1-tree under the revised distance matrix, z(Tˆ*) is its cost and di(Tˆ*) is the degree of node i in 1-tree Tˆ*.
Patel and Associates, Inc., is an accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader-client assignments differ in terms of projected completion times. The possible assignments and the estimated completion times in days are as follows. Project Leader Client 1 Client 2 Client 3 Jackson 10 16 32 Ellis 14 22 14 Smith 22 24 34 Formulate the problem as a linear program. (Express your answers in the form xij where xij is 1 if leader i is assigned to client j and 0 otherwise.) Then solve: Relationship Value Time (Days) x11 x12 x13 x21 x22 x23 x31 x32 x33
I need help in formulating the constraints for this problem. So, help with part (a) is all I need.
The Monroe Logistics Company would like to schedule its drivers to minimize the number of drivers used to cover the requirements over all seven days of the week. The company has 6 cabs but needs all six of them on duty only on Fridays. The estimated requirements are as follows: Day Mon Tue Wed Thu Fri Sat Sun Requirements 6 4 4 4 6 3 3 Prepare a schedule that minimizes the total number of drivers needed and minimizes the amount of slack capacity. In case of ties for assignment, it is preferred to give weekend days off. Identify the slack capacity for each day of the week. In addition, please identify the number of people working less than full-time (i, e., working less than five days a week. This is employee scheduling program. No employee can be off on Friday and please do not change the requirement in the question. Thank you.
What is the minimum cost of crashing the following project that James Walters manages at Athabasca University by 4 days Activity Normal Time (days) Crash Time (days) Normal Cost Crash Cost Immediate Predecessor(s) A 5 4 $800 $1,000 — B 8 6 $200 $600 — C 5 4 $600 $650 — D 7 4 $750 $1,500 A E 6 4 $1,200 $1,650 C A. By how many days should each activity be crashed to reduce the project completion time by 4 days? Fill in the table below. (Enter your responses as whole numbers.) Activity Each Activity Should be Reduced BY (days) A 1 B 0 C 1 D 3 E 2 B. The total cost of crashing the project by 4 days is _____ (Enter your response as a whole number.) Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You…
Solve the following problems using Excel Solver or R Studio. 1. Scott and Associates is an accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader-client assignments differ in terms of projected completion times. The possible assignments and estimated completion times in days are given below. Find the optimal assignment of leaders to clients. 2. Suppose in problem 1, an additional employee, Joanne, is available for possible assignment, and that Joanne will take 14, 18and 36 days with clients 1, 2, and 3, respectively. What is now the optimal assignment of project leaders to clients?
The JPC Company has five different production jobs to complete next week. Five multipurpose machines, each with somewhat different characteristics are available. The estimated costs of completing each job on each of the five machines are as follows: Allocate each job to each machine for minimum cost: Job 2 was assigned to? what is total assignment cost?
Every project is constrained in different ways.These limitations are often denoted as the “triple constraints”. Using an appropriate diagram, describe these constraints.
As the project manager you have been asked by AstraZeneca to assess the viability of two (2) subprojects based on their net present value (NPV). Based on the information below which project would be selected and why? Projects 1 has an initial investment of $50,000 and a net cash inflow of $27,000 for a period of 2 years. Project 2 has an initial investment of $150,000 and a net cash inflow of $59,000 in year 1 and $120,000 in year 2. The discount rate to be used is 5%

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a. Draw the AOA network. b. Calculate the Early Event Time and Late Event Time for every node in the resulting AOA network. c. Determine Total Float and Free Float for every activity (arc) in the result@ling AOA network.