ENS 208 - Spring 2015
Homework 5
Due on May 11, 2015 @ 23:00
This homework will be carried out individually. You must submit the homework online as 1
single .pdf file. Otherwise, it will not be graded!
Name your file as yourSUuserID_yourID.pdf (e.g. catay

ENS 208 - Spring 2015
Homework 4
Due on April 27, 2015 @ 23:00
This homework will be carried out individually. You must submit the homework online as 1
single .pdf file. Otherwise, it will not be graded!
Name your file as yourSUuserID_yourID.pdf (e.g. cat

ENS 208 - Spring 2015
Exercises for Final Exam
Exercise 1:
Problem #9 from Nahmias (2013) on p. 436.
+d) Assume that for baking the breads 3 and 5 she uses the same dough she prepares for bread 2.
Calculate a schedule so as to minimize maximum tardiness (

ENS 208
Introduction to
Manufacturing Systems
Introduction to Integer Programming
by Blent atay and . lker Birbil Sabanci University
Integer Programming
n
An Integer Programming (IP) problem is a Linear
Programming (LP) problem in which some or all of th

ENS 208
Introduction to
Manufacturing Systems
Project Scheduling
by Blent atay and . lker Birbil Sabanci University
Introduction
n
A project is a collection of tasks that must be completed
in minimum time or at minimal cost.
n
Objectives of Project Sched

ENS 208
Introduction to
Manufacturing Systems
Inventory Control Subject to
Known Demand
by Blent atay and . lker Birbil Sabanci University
Types of Inventories
n
Raw materials
n
Components
n
Resources required in production or processing activity
Items t

ENS208 - 2014-2015 Spring
Recitation 8 Solution
Problem 4.10 on page 201, Nahmias 5th Ed.
A specialty coffeehouse sells Columbian coffee at a fairly steady rate of 280 pounds annually.
The beans are purchased from a local supplier for $2.40 per pound. The

ENS 208
Introduction to
Manufacturing Systems
Scheduling & Assembly Line Balancing
by Blent atay and . lker Birbil Sabanci University
Introduction
n
Operations Scheduling
Scheduling
of jobs in a manufacturing shop
Personnel scheduling
Facilities sched

Solutions to Sample Problems for Chapter 8
8.4
Four trucks, 1, 2, 3, and 4, are waiting
FCFS
Sequence
Completion Time
1
2
3
4
Flow Time
1:20
1:34
2:09
2:19
Total
20
34
69
79
202
Tardiness
0
0
19
49
68
Mean flow time = 202/4 = 50.5
Average tardiness = 68/4

Solutions to Sample Problems for Chapter 9
9.3
A project consisting of eight activities
a)
3
E
B
1
A
Dummy
2
F
6
3
G
H
C
D
4
b) Activity
Time
A
B
C
D
E
F
G
H
3
5
1
4
3
3
2
4
8
Immed.
Pred.
ES
A
A
B,C
B
E,D
F
E,D
EF
3
8
4
12
11
15
17
16
0
3
3
8
8
12
15
12

ENS 208 - Spring 2015
Exercises for Final Exam
Exercise 1:
Problem #9 from Nahmias (2013) on p. 436.
+d) Assume that for baking the breads 3 and 5 she uses the same dough she prepares for bread 2.
Calculate a schedule so as to minimize maximum tardiness (

Sample LP Problems
Problem 1
Solution 1
Decision variables:
C1 = # of acres of Farm 1 planted in corn
W1 = # of acres of Farm 1 planted in wheat
C2 = # of acres of Farm 2 planted in corn
W2 = # of acres of Farm 2 planted in wheat
Objective:
Min 90 C1 + 11

h a n g e Vi
e
w
N
y
bu
to
k
w
.c
FORECASTING
Error -> et = Ft Dt
Mean Absolute Deviation =
=1
Mean Squared Error =
=1
2
=1
Mean Absolute Percentage Error = 100
Root Mean Squared Error =
=1
2
Moving Average
MAt = (Dt + Dt-1 + Dt-2 +.Dt-k+1)/k
Exponential

ENS 208
Homework 1
Fall 2012
Due on November 7, 2011, 15.30
This assignment will be carried out individually. You are supposed to submit your paperwork
to the box near FENS 1021. As the due date coincides with semester break, you can also
upload the scann

ENS 208 - Fall 2012
Homework 2,
Due on November 25, 2012, 17.00
This assignment will be carried out individually. It is required that your assignment be done
in Excel and you are expected to submit the Excel sheet through SUCourse. Name your Excel
file as

ENS 208
Fall 2015-2016
Recitation 1 Question
Taking the following 6-month 2014 data, calculate the forecasts for the first
three months of 2015 using both moving average (3 months) and simple
exponential smoothing (smoothing constant is 0.4). Also compare

ENS208 - 2014-2015 Spring
Recitation 5 Solutions
Question 1. You have decided to enter the candy business. You are considering producing
two types of candies: Slugger Candy and Easy Out Candy, both of which consist solely of
sugar, nuts and chocolate. At

Solutions to Sample Problems for Chapter 3
3.14.
A local semiconductor firm, Superchip,
k = $60,000/250 = $240 per worker per day
#Units
Working /Worker
Mo Days
($000)
1
2
3
4
5
6
7
8
9
10
11
12
22
16
21
19
23
20
24
12
19
22
20
16
(A)
Cum
#Units
/Worker

ENS208 2014-2015 Spring
Recitation 6 Solution
Question
Solve the following LP model with the graphical method. Find the optimal solution, optimal
OFV, reduced costs of decision variables and shadow prices of constraints.
Maximize z = 6 x1 + 6 x2
Subject t

Solutions to Sample Problems for Chapter 4
4.4
I Carry rents trucks for moving and hauling
a)
Sum total of ending inventories is 26 + 38 + 31 + 22 + 13 + 9 + 16 + 5 = 160.
Monthly holding cost h = Ic where I = monthly interest rate and c = value
of item.

ENS208 2014-2015 Spring
Recitation 7 Question
Question
Write the LP model of the question below.
Shoemakers of America forecasts the following demand for each of the next six months:
month 1, 5000 pairs; month 2, 6000 pairs; month 3, 5000 pairs; month 4,

ENS 208 - Spring 2015
Homework 3
Due on March 31, 2015 @ 23:00
Problem 1
A gourmet cook bakes two types of cakes (chocolate and vanilla) to supplement her income.
Each chocolate cake can be sold for 12 YTL, and each vanilla cake can be sold for 9 YTL.
Eac

Question 1
Solve the following problem by using IBM ILOG CPLEX Optimization Studio. You have to submit the
mathematical model (as we did in recitations) and you should submit the model and data files
electronically over SUCourse(.dat and .mod files).
A mo