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Albany State University *
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Course
1101
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
Pages
4
Uploaded by MegaMoose3765
Operations - Lesson 3 Problem Set - Solution
Part 1
Consider the situation in Part B of the Senator Swift case.
1.
Recalling that rush hour ends at 9:30 AM, the system will clear of all rush hour traffic at __1__ AM/PM. (4 points)
2.
Due to an accident at 7:30 AM, the capacity of the exit ramp reduces to 30 cars per minute for a duration of two hours (between 7:30 and 9:30). How long will it take a driver arriving at 9:30 AM to leave the ramp (assume that the traffic inflow doesn’t change)? It will take the driver __67.5__ minutes (round to 1 decimal). (4 points)
3.
Disregarding 2., due to a union strike only 1 manual gate and 3 EZ-Pass gates are operational. How long would it take a car arriving at 9:30 AM to get through the system (assume that the traffic inflow doesn’t change)? It will take the car _225__ minutes. (4 points)
Explanation: In this case the bottleneck is the toll plaza with capacity of 20 cpm (2 + 3*6). Thus, the inventory buildup per minute between 7-9:30 AM is 50 – 20 = 30 cpm. So, by 9:30 the number of cars in the system is equal to 30 * 150 = 4500. By Little’s law,
a car arriving at 9:30 will take 4500 / 20 = 225 minutes.
4.
Disregarding 3., and assuming the toll is $5 per car, if Senator Swift’s proposal were to pass, approximately how much toll money would be lost per day? (5 points)
a.
$30,000
b.
$37,500
c.
$72,000
d.
$90,000
Explanation: As per the senator proposal, none of the cars during rush hour will have to pay toll. The number of cars during rush hour is 50 * 150 + 35 * 180 + 20 * 30 = 14,400. This amounts to a total of 14400 * 5 = $72,000 of lost toll revenue per day. Part 2
Consider a batch process with two stations. Each station can handle a batch size of up to 100 units. Station 1 has a processing time of 2 minutes per unit, and no setup time. Station 2 has a setup time of 20 minutes per batch, and a processing time of 1 minute per unit. Processing units
for a batch in Station 2 may only start when all the units in the same batch have been processed
in Station 1. In contrast, set up for a batch in Station 2 may being before that time.
1.
The flow time of an order of 100 units if it is processed as a single batch (of size 100 units) is __300__ minutes. (3 points)
2.
If instead, the same order is processed in 2 batches of size of 50 units each, the flow time would be __250__ minutes. (3 points)
3.
If instead, the same order is processed in 5 batches of size of 20 units each, the flow time would be _220__ minutes. (3 points)
4.
Finally, if instead, the same order is processed in 10 batches of size of 10 units each, its flow time would be _300___ minutes. (3 points)
5.
Of the above, what batch size is optimal in terms of minimizing the order flow time? (4 points)
a.
100 units
b.
50 units
c.
20 units
d.
10 units
Part 3
NYC Media is working on a new ad campaign for SuperUgg flipflops. They would like to make sure that the campaign is ready in time for spring. This project involves 7 steps described in the following table:
Activity
Description
Immediate Predecessors
Duration (weeks)
A
Determine campaign strategy
--
3
B
Pitch strategy to client
A
1
C
Choose advertising channels
B
3
D
Hire artists
A
3
E
Film campaign commercials
C, D
5
F
Schedule advertisement time slots
C
4
G
Launch campaign
E, F
3
1.
Draw a network that accurately describes the sequential relationships of this project. (4 points)
2.
The duration of the project is _15__ weeks, and the critical path is _ABCEG_. (3 points)
3.
What are the critical activities? What is the slack associated with the non-critical activities? The critical activities are A, B, C, E, G. The slack of activities D and F is 1 week each.
Part 4
Table from Part 3 describing the 7 steps for the new ad campaign for SuperUgg Flipflops:
Activity
Description
Immediate Predecessors
Duration (weeks)
A
Determine campaign strategy
--
3
B
Pitch strategy to client
A
1
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C
Choose advertising channels
B
3
D
Hire artists
A
3
E
Film campaign commercials
C, D
5
F
Schedule advertisement time slots
C
4
G
Launch campaign
E, F
3
Please refer to this table for the following questions. Activity
Normal Duration (weeks)
Minimum Duration (weeks)
Crash Cost per Week
A
3
3
-
B
1
1
-
C
3
1
$4,000
D
3
1
$2,000
E
5
4
$5,000
F
4
2
$2,000
G
3
3
-
1.
Suppose that due to the higher than usual March temperature, NYC Media would like to launch the campaign two weeks earlier than planned. It estimates that each week later than this new deadline will cost a penalty of $4,500. Therefore, it considers crashing the project. The table above provides details about crashing durations and costs. They should crash the project by _1___ week(s). (2 points)
2.
What is the total cost of crashing plus penalty? The total cost is $_4000 + 4500 = 8500__. (2 points)
3.
Ignoring question 1., suppose that their new goal is to complete the project within the minimum possible time. The minimum possible duration of the project is _12 weeks___ days.
(3 points)
4.
The minimum crashing cost required to complete this project within the minimal duration is $_15000___. (3 points)