MSCI432 Lecture Notes - Newsvendor Model, Msci, Toronto Star

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MSCI 432.001/633: Production and Service Operations Management, Winter 2010
Assignment # 4; Due: Monday, April 5
th
, by noon time in drop box on E2-CPH
There are 8 questions in this assignment. You can choose between Q2 and Q3 (i.e., you are required
to solve only one scheduling question). If we won’t manage to cover the required material for the
assignment, I will post an update on the scope of the assignment.
Q1. PK formula
Consider a setting with three identical servers, each with service rate of µ. Two alternatives are possible:
to have a single queue in front of all three servers, in which case, the arrival rate is 3λ, or three dedicated
queues, each with arrival rate of λ. Similar to what we did in the class, derive the ratio between the
inventory in a queue with a single queue over 3 dedicated queues, what are the extreme values of this
ratio, and plot your result for the relevant range.
Q2. Scheduling [Nahmias 8.9 (p.436)].
Jane Reed bakes breads and cakes in her home for parties and other affairs on a contract basis. One
particular Monday morning she finds that she has agreed to complete five jobs for that day. Her husband
John will make the deliveries, which require about 15 minutes each. Suppose that she begins baking at
8:00 am.
Job
Time required
Pro
mised time
1
1.2 hr
11:30 am
2
40 min
10:00 am
3
2.2 hr
11:00 am
4
30 min
5
3.1 hr
12:00 noon
6
25 min
Determine the sequence in which she should perform the jobs in order to minimize
a. Mean flow time
b. Number of tardy jobs
c. Maximum lateness
Q3. Scheduling [Nahmias 8.7 (p.435)]
On May 1, a lazy MBA student realizes that he has done nothing on seven different homework
assignments and projects that are due in various courses. He estimates the time required to complete each
project (in days) and also notes their due times:
Project
1
2
3
4
5
6
7
Time (days)
4
8
10
4
3
7
14
Due date
4/20
5/17
5/28
5/28
5/12
5/7
5/15
Because projects 1, 3, and 5 are from the same class, he decides to do those in the sequence that they are
due. Furthermore, project 7 requires results from projects 2 and 3, so 7 must be done after 2 and 3 are
completed. Determine the sequence in which he should do the projects in order to minimize the maximum
lateness.
(note the project 1 was due 10 days ago.)
Q4. Inventory management
Consider a newsvendor model with normally distributed demand arrival: mean =100 and SD=30. The
newsvendor sells fashion t-shirt which cost him $10 per unit. At the end of each period these t-shirts are
not attractive anymore so he donates them to a local charity. Each period he orders 123 t-shirts. What is
the selling price of each t-shirt? (round up)
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Document Summary

Msci 432. 001/633: production and service operations management, winter 2010. Assignment # 4; due: monday, april 5th, by noon time in drop box on e2-cph. You can choose between q2 and q3 (i. e. , you are required to solve only one scheduling question). If we won"t manage to cover the required material for the assignment, i will post an update on the scope of the assignment. Consider a setting with three identical servers, each with service rate of . Two alternatives are possible: to have a single queue in front of all three servers, in which case, the arrival rate is 3 , or three dedicated queues, each with arrival rate of . Jane reed bakes breads and cakes in her home for parties and other affairs on a contract basis. One particular monday morning she finds that she has agreed to complete five jobs for that day. John will make the deliveries, which require about 15 minutes each.

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