ENS 208
Introduction to Industrial Engineering
Aggregate Planning
by Blent atay and . lker Birbil Sabanci University
Aggregate Production Planning
n
n
n
Goal: To plan gross work force levels and set firm-wide
production plans
Aggregate Planning is essent

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
Introduction to Industrial Engineering
Linear Programming (LP)
by Blent atay and . lker Birbil Sabanci University
Introduction to Linear Programming
n
Many managerial decisions involve trying to make
the most effective use of an organizations
res

ENS 208 - Spring 2015
Exercises for Exam 1
Exercise 1:
Consider the following demand history over a 2-year horizon.
YEAR
PERIOD
1
2
3
4
2012
1700
2200
2300
1700
2013
1800
2100
2200
1900
Assuming that all necessary smoothing constants are equal to 0.1:
a)

ENS 208
Introduction to Industrial Engineering
Transportation & Assignment Problems
by Blent atay and . lker Birbil Sabanci University
Transportation Problem (TP)
Customers
n
A transportation problem
aims at finding the best
way to fulfill the demand of

ENS 208
Introduction to Industrial Engineering
Forecasting
by Blent atay and . lker Birbil Sabanc University
Forecasting
n
n
n
The art and science of predicting future events
A difficult task
It may involve
taking historical data and projecting them into

ENS 208 HW 5
A company owns a gas station in a local place. The demand for
gasoline is constant and 3,020 gallons per month. The company
purchases gasoline from a supplier for $8.7 per gallon . The company
estimates that the administrative cost associated

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

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

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,

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 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 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 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

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

Sales2
Example 2
Month
Jan 2012
Feb 2012
Mar 2012
Apr 2012
May 2012
Jun 2012
Jul 2012
Aug 2012
Sep 2012
Oct 2012
Nov 2012
Dec 2012
Jan 2013
Feb 2013
Mar 2013
Apr 2013
May 2013
Jun 2013
Jul 2013
Aug 2013
Sep 2013
Oct 2013
Nov 2013
Dec 2013
Jan 2014
Feb 201

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

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
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 (

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

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

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

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
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

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

A
1
2
3
4
5
6
B
Beginning Inventory
End of Inventory
Cost of a worker/day
Hiring cost/worker
Firing cost/worker
Holding cost/unit - month
C
500
750
50
500
1000
100
D
E
F
K = # of items /worker-day
Current# of workers for chase & level strategies
Current#

A
1
2
3
4
5
6
B
C
Beginning Inventory
End of Inventory
Cost of a worker/day
Hiring cost/worker
Firing cost/worker
Holding cost/unit - month
D
E
F
G
H
# of Units
Produced
B*D*K
500
750
50
500
1000
100
K = # of items /worker-day = 8000/(174*46)
Current# of

ENS 208
Introduction to Manufacturing
Systems
Linear Programming (LP)
by Blent atay and Gndz Ulusoy Sabanci University
Introduction
Linear Programming (LP) is a mathematical
optimization technique and belongs to the
mathematical programming tools in Oper

ENS 208 INTRODUCTION TO MANUFACTURING
SYSTEMS
INTRODUCTION
Spring 2014
2
Manufacturing - A Definition*
Manufacturing can be defined as a series of interrelated
activities and operations involving the design, material
selection, planning, manufacturing pro

ENS 208 - Fall 2014
Homework 1
Due on October 2, 2014 at 12:40
You have to carry this assignment out individually. You are supposed to submit your paperwork
to the ENS 208 box near FENS 1021. A map is provided in SUCourse.
SHORT QUESTIONS
#1)What is the a