Concept explainers
A.
Interpretation: A network diagram representing the activities of the project is to be constructed.
Concept Introduction: Network diagram is a graphical representation of tasks and events happening in a project. It depicts the work flow and is used to compute the total duration of the project.
A.
Explanation of Solution
Given information: Theactivities to be taken up for the construction of a gas station and the time duration for each are given in the table.
Activity | Time |
A | 4 |
B | 2 |
C | 3 |
D | 1 |
E | 1 |
F | 2 |
G | 3 |
H | 1 |
I | 5 |
J | 3 |
K | 4 |
L | 2 |
M | 1 |
The activity times and the precedence relationship are shown in the table:
Activity | Time | Predecessors |
A | 4 | |
B | 2 | A |
C | 3 | B |
D | 1 | C |
E | 1 | D |
F | 2 | B |
G | 3 | F |
H | 1 | G |
I | 5 | B |
J | 3 | I |
K | 4 | C, F, I |
L | 2 | K |
M | 1 | L |
The network diagram showing the work flows is as follows:
B.
Interpretation: The critical path is to be identified by computing the earliest and the latest start and finish times.
Concept Introduction: Network diagram is a graphical representation of tasks and events happening in a project. It depicts the work flow and is used to compute the total duration of the project.
B.
Answer to Problem 26AP
The critical path is A − B − I − K − L − M with completion time as 18 weeks
Explanation of Solution
Given information:
Activity | Time |
A | 4 |
B | 2 |
C | 3 |
D | 1 |
E | 1 |
F | 2 |
G | 3 |
H | 1 |
I | 5 |
J | 3 |
K | 4 |
L | 2 |
M | 1 |
The earliest and latest start and finish times are calculated using the formulae:
Earliest Start (EST) = Maximum EFT of the predecessor activity
Latest Start (LST) = LFT - Duration
Earliest Finish (EFT) = EST + Duration
Latest Finish (LFT) = Minimum LST of the immediate successor
Slack = LFT − EFT (or) LST − EST
Activity | Time | EST | EFT | LST | LFT | Slack |
A | 4 | 0 | 4 | 0 | 4 | 0 |
B | 2 | 4 | 6 | 4 | 6 | 0 |
C | 3 | 6 | 9 | 8 | 11 | 2 |
D | 1 | 9 | 10 | 16 | 17 | 7 |
E | 1 | 10 | 11 | 17 | 18 | 7 |
F | 2 | 6 | 8 | 9 | 11 | 3 |
G | 3 | 8 | 11 | 14 | 17 | 6 |
H | 1 | 11 | 12 | 17 | 18 | 6 |
I | 5 | 6 | 11 | 6 | 11 | 0 |
J | 3 | 11 | 14 | 15 | 18 | 4 |
K | 4 | 11 | 15 | 11 | 15 | 0 |
L | 2 | 15 | 17 | 15 | 17 | 0 |
M | 1 | 17 | 18 | 17 | 18 | 0 |
The critical path includes the activities with zero slack. So, here the critical path is A − B− I − K − L − M. The total time taken to complete the project is 18 weeks.
C.
Interpretation: A Gantt chart of the
Concept Introduction: Gantt chart is a project management tool that is a type of bar chart. It depicts the project schedule and is used for resource allocation.
C.
Answer to Problem 26AP
A Gantt chart for the project has been drawn.
Explanation of Solution
Given information:
Activity | Time |
A | 4 |
B | 2 |
C | 3 |
D | 1 |
E | 1 |
F | 2 |
G | 3 |
H | 1 |
I | 5 |
J | 3 |
K | 4 |
L | 2 |
M | 1 |
Activity times and early start times:
Activity | EST | Time |
A | 0 | 4 |
B | 4 | 2 |
C | 6 | 3 |
D | 9 | 1 |
E | 10 | 1 |
F | 6 | 2 |
G | 8 | 3 |
H | 11 | 1 |
I | 6 | 5 |
J | 11 | 3 |
K | 11 | 4 |
L | 15 | 2 |
M | 17 | 1 |
The Gantt chart depicting the project based on the EST:
D.
Interpretation: The impact of replacement of the air compressor which takes two weeks on the completion of the project is to be determined.
Concept Introduction: Network diagram is a graphical representation of tasks and events happening in a project. It depicts the work flow and is used to compute the total duration of the project.
D.
Explanation of Solution
Given information:
Activity | Time |
A | 4 |
B | 2 |
C | 3 |
D | 1 |
E | 1 |
F | 2 |
G | 3 |
H | 1 |
I | 5 |
J | 3 |
K | 4 |
L | 2 |
M | 1 |
Installing the air compressor is represented by activity G.
Activity | Time | EST | EFT | LST | LFT | Slack |
A | 4 | 0 | 4 | 0 | 4 | 0 |
B | 2 | 4 | 6 | 4 | 6 | 0 |
C | 3 | 6 | 9 | 8 | 11 | 2 |
D | 1 | 9 | 10 | 16 | 17 | 7 |
E | 1 | 10 | 11 | 17 | 18 | 7 |
F | 2 | 6 | 8 | 9 | 11 | 3 |
G | 3 | 8 | 11 | 14 | 17 | 6 |
H | 1 | 11 | 12 | 17 | 18 | 6 |
I | 5 | 6 | 11 | 6 | 11 | 0 |
J | 3 | 11 | 14 | 15 | 18 | 4 |
K | 4 | 11 | 15 | 11 | 15 | 0 |
L | 2 | 15 | 17 | 15 | 17 | 0 |
M | 1 | 17 | 18 | 17 | 18 | 0 |
The latest start time of the activity G is 14th week. If the failure is identified before installation, the project will not be delayed as the replacement time (2 weeks) is less than the slack (6 weeks).
If the failure is found during testing of the air compressor, represented by activity H, still the project would not be delayed, as again there is a slack of 6 weeks.
E.
Interpretation: The activities that can be completed by the end of the 15th week without delaying the project completion are to be determined.
Concept Introduction: Network diagram is a graphical representation of tasks and events happening in a project. It depicts the work flow and is used to compute the total duration of the project.
E.
Answer to Problem 26AP
The activities A, B, C, F and I have to be completed by the end of the 15th week to guarantee project completion without delay.
Explanation of Solution
Given information:
Activity | Time |
A | 4 |
B | 2 |
C | 3 |
D | 1 |
E | 1 |
F | 2 |
G | 3 |
H | 1 |
I | 5 |
J | 3 |
K | 4 |
L | 2 |
M | 1 |
The table shows the Earliest and Latest times of the activities
Activity | Time | EST | EFT | LST | LFT | Slack |
A | 4 | 0 | 4 | 0 | 4 | 0 |
B | 2 | 4 | 6 | 4 | 6 | 0 |
C | 3 | 6 | 9 | 8 | 11 | 2 |
D | 1 | 9 | 10 | 16 | 17 | 7 |
E | 1 | 10 | 11 | 17 | 18 | 7 |
F | 2 | 6 | 8 | 9 | 11 | 3 |
G | 3 | 8 | 11 | 14 | 17 | 6 |
H | 1 | 11 | 12 | 17 | 18 | 6 |
I | 5 | 6 | 11 | 6 | 11 | 0 |
J | 3 | 11 | 14 | 15 | 18 | 4 |
K | 4 | 11 | 15 | 11 | 15 | 0 |
L | 2 | 15 | 17 | 15 | 17 | 0 |
M | 1 | 17 | 18 | 17 | 18 | 0 |
The latest finish times of the activities A, B, C, F and Iam less than 15 weeks. Therefore, these activities have to be completed by the end of the 15th weeks to guarantee project completion without any delay.
F.
Interpretation: The optimal solution for the problem is to be determined using linear programming.
Concept Introduction: Linear programming is a mathematical technique used to achieve the best outcome, given a list of parameters usually restrictions on the resources.
F.
Answer to Problem 26AP
The optimal solution for the problem is obtained using linear programming.
Explanation of Solution
Given information:
Activity | Time |
A | 4 |
B | 2 |
C | 3 |
D | 1 |
E | 1 |
F | 2 |
G | 3 |
H | 1 |
I | 5 |
J | 3 |
K | 4 |
L | 2 |
M | 1 |
The various paths of the project and the durations are:
The critical path is A − B − I − K − L − M with the completion time of 18 weeks.
Using linear programming, the EST is calculated.
Objective function = =SUM (B2:M2)
Nodes | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
EST |
The constraints
Activity | Time | ||
A | 0 | > | 4 |
B | 0 | > | 2 |
C | 0 | > | 3 |
D | 0 | > | 1 |
E | 0 | > | 1 |
F | 0 | > | 2 |
G | 0 | > | 3 |
H | 0 | > | 1 |
I | 0 | > | 5 |
J | 0 | > | 3 |
K | 0 | > | 4 |
L | 0 | > | 2 |
M | 0 | > | 1 |
P1 | 0 | > | 0 |
P2 | 0 | > | 0 |
P3 | 0 | > | 0 |
Solver Solution:
Objective Function |
120 |
EST for the nodes:
Nodes | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
EST | 0 | 4 | 6 | 9 | 8 | 11 | 11 | 11 | 10 | 15 | 17 | 18 |
Want to see more full solutions like this?
Chapter 10 Solutions
Production and Operations Analysis, Seventh Edition
- Grocers Inc. is considering offering a purified water service through a contract company that would locate a machine on the inside of the market store. There are two contract companies Grocers Inc. is considering, ClearWater and PureVida. ClearWater would charge an annual lease fee of $800 for set-up of the machine and for this machine, there is a utility cost of $0.10 for every gallon of water dispensed and ClearWater charges $0.05 for maintenance. For PureVida, the annual lease fee is $700, the utility cost is $0.12 for every gallon and PureVida charges $0.06 for maintenance. Grocers Inc. customers would purchase refilled gallons of water for $0.97.a. What is the annual break-even point for each option?b. At what volume in number of gallons would the two options have the same cost?c. At what forecasted volume should Grocers Inc. select ClearWater and what volume should they select PureVida and why?arrow_forwardA council has a brown-field sites designated for social housing. After allowing for roads and parks it has an area of 150000 m² for social housing. The housing association intends to build a mixture of flats, two-bedroom houses, three-bedroom houses, and shops (which include a living space) on this site. The housing association wishes to maximise the number of people that can be housed but has strict housing requirements: • there must be at least twice as many two-bedroom houses as three-bedroom houses; • at least 10% of the total housing units excluding shops (i.e. flats and houses) must be flats; • buildings containing the flats (i.e a "block") must have two storeys and every flat must have the same floor space; • shops must be provided at a rate of at least one per 1500 inhabitants. The average number of inhabitants per housing unit and the ground floor area of each are given in the following table. Housing type Flat Two-bedroom house Three-bedroom house Shop Average number of…arrow_forwardTwo brothers have purchased a small lot, in the center of town, where they intend to build a gas station. The station will have two pumps, a service area for water and tire maintenance, and a main building with restrooms, office, and cash register area. Before they begin excavating the site, the local authorities must approve the location for a gasoline station and be certain that the placement of the storage tanks will not interfere with water, gas, and electric lines that are already in place.Once the site has been approved, the excavation can begin. After excavation, the three primary parts of the construction can begin: laying in the gasoline tanks, building the water and tire service area (including installation of the air compressor), and constructing the main building. The surfacing can begin after all building is completed. After surfacing, the site must be cleaned and the station’s signs erected. However, before the station can open for business, the air compressor must be…arrow_forward
- James Lawson's Bed and Breakfast, in a small historicMississippi town, must decide how to subdivide (remodel) the largeold home that will become its inn . There are three alternatives:Option A would modernize all baths and combine rooms, leavingthe inn with four suites, each suitable for two to four adults.Option B would modernize only the second floor; the results wouldbe six suites, four for two to four adults, two for two adults only.Option C (the status quo option) leaves all walls intact. In this case,there are eight rooms available, but only two are suitable for fouradults, and four rooms will not have private baths. The details ofprofit and demand patterns that will accompany each option are: Which option has the highest expected monetary value?arrow_forwardJoel Deaine, CEO of Deaine Enterprises Incorporated (DEI), is considering a special offer to manufacture a new line of women’s clothing for a large department store chain. DEI has specialized in designer women’s clothing sold in small, upscale retail clothing stores throughout the country. To protect the very elite brand image, DEI has not sold clothing to large department stores. The current offer, however, might be too good to turn down. The department store is willing to commit to a large order, which would be very profitable to DEI, and the order would be renewed automatically for two more years, presumably to continue after that point. Required: Explain two of the implementation tools covered in this chapter that Joel can use to implement his strategy.arrow_forwardJoel Deaine, CEO of Deaine Enterprises Incorporated (DEI), is considering a special offer to manufacture a new line of women’s clothing for a large department store chain. DEI has specialized in designer women’s clothing sold in small, upscale retail clothing stores throughout the country. To protect the very elite brand image, DEI has not sold clothing to large department stores. The current offer, however, might be too good to turn down. The department store is willing to commit to a large order, which would be very profitable to DEI, and the order would be renewed automatically for two more years, presumably to continue after that point. Required: Determine Joel’s competitive strategy (cost leadership or differentiation) and use this strategy to analyze the choice Joel faces.arrow_forward
- On January 1, Jack signed a contract with AT &T for his mobile phone services. The contract includes three lines with a $120 fixed payment each month plus $15 per gigabit if the data usage is more than 9 gigabits. On March 1, Jack wants to add one more phone line to the existed contract, and the payment becomes $150 fixed payment each month plus $15 per gigabit if the data usage is more than 12 gigabits. Is this change a contract modification? Please use one sentence to explain why?arrow_forwardOne definition of risk is that it is the possibility that an event will occur and adversely affect the achievement of an objective. An illustrative objective and event are presented below: Objective: To safeguard the city’s citizens and resources Event: An accident at a four-way intersection a. Identify three potential adverse consequences of the event occurring. b. Identify three inherent risk factors that make the event more or less probable. c. The city’s management must decide how to respond to this risk. Two of its choices are to 1) avoid the risk or 2) reduce the risk to an acceptable level. 1. Explain how the city can avoid the risk. 2. Identify two ways the city can reduce the risk.arrow_forwardSarah has a startup business that makes two distinct bird feeders that she has designed. Sarah is planning on operating a small factory to build the bird feeders. She is looking at two possible locations, A and B. If she chooses location A, the lease on the building will be higher than location B, thus leading to higher fixed costs than what she would have with location B. However, if she makes more than 20,000 units, both locations will likely have to be expanded, both the physical buildings and the manufacturing equipment. Variable costs to produce each unit will vary by location as well as by product. For example, the first design will have variable costs of $10 and $15 in locations A and B respectively, while the second bird feeder design will have variable costs of $20 and $25 respectively depending on location. However, she thinks that variable costs will decrease if she sells more than 5,000 units, as she will receive discounts from her suppliers at that point. She is unsure of…arrow_forward
- Three commercial properties are located adjacent to Highway 21 and there are twoentrances to each property. The entrances do not meet MTOD requirements and can bedeemed illegal entrances as they were constructed without MTO approval.For a GWP Project, one entrance to each property must be removed. However, theproperty owners have decided to file a lawsuit against the ministry and have also writtento the premier’s office citing that MTO is being unreasonable with their request toremove the second entrance to their property as without the second entrance Truckswould be backing onto the Highway creating unsafe conditions for the motorist. Theproperty owners have been using their respective properties and dual entrances formore than 30 years before this GWP project. 1. As a Corridor Management Officer, to further the GWP Project, what steps will you take to remove ormodify an entrance from each property?2. How would you resolve any potential conflicts with the property owner?arrow_forwardThe city of Winnipeg is considering whether to build a new public ice rink. This rink would have a capacity of 800 ice skaters per day, and the proposed admission fee is $6 per individual per day. The estimated cost of the ice rink, averaged over the life of the rink, is $4 per ice skater per day. The city of Winnipeg has hired you to assess this project. Fortunately, Ottawa already has an ice rink, and the city of Ottawa has randomly varied the price of that rink to find how price affects usage. The results from their study follow: Ice rink price Number of ice skaters per day $8 $10 $4 $6 $2 per day 500 200 1100 800 1400 a. If the ice rink is built as planned, what would be the net benefit per day from the ice rink? What is the consumer surplus for ice skaters? b. Given this information, is an 800-ice rink the optimally sized ice rink for Winnipeg to build? Explain.arrow_forwardA circus is scheduled to appear in a city on a given date. The profits obtained are heavily dependent on the weather which can be classified as "good" or" bad". The circus owners may choose to setup operations in a large open field that is centrally located or rent a small building to stage a small version of the circus. The small building is not expected to be adversely affected by bad weather – thus will not affect the circus for it is well secure and has covered parking for the guests. The following shows the profits of the options and states of nature: States of nature Decision alternatives Set up in field Rent small building | Probability Good Bad $14,500 $5,000 -$15,000 $4,000 P(G)=0.5 P(B)=0.5 The circus owners may choose to delay the decision until the day before the event is due. At this time they can obtain the one-day weather report (free) which is usually reliable. This delay will however increase their set up cost by $1000.00 or if they choose to rent, the rental cost will…arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,Operations ManagementOperations ManagementISBN:9781259667473Author:William J StevensonPublisher:McGraw-Hill EducationOperations and Supply Chain Management (Mcgraw-hi...Operations ManagementISBN:9781259666100Author:F. Robert Jacobs, Richard B ChasePublisher:McGraw-Hill Education
- Purchasing and Supply Chain ManagementOperations ManagementISBN:9781285869681Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. PattersonPublisher:Cengage LearningProduction and Operations Analysis, Seventh Editi...Operations ManagementISBN:9781478623069Author:Steven Nahmias, Tava Lennon OlsenPublisher:Waveland Press, Inc.