Ik University Industrial Engineering Department
IE402 Operations Research III Spring 2011
Homework #1 Poisson Process
Answers
Question 1
a) 1.67minutes
b) 0.165
c) 9.17minutes
d) 0.354
Question 2
a) 0.050
b) 0.446
c) 0.302
d) 0.368 and 0.406
Question 3
P(
Name,Surname: ID: Signature: IE 232 Quiz # 2 1. (30 points) Use the following LP to find; max z = 40 x1 + 50 x2 Subject to x1 + 2 x2 40 x1 + x2 30 2 x1 + x2 40 x1, x2 0 a. b. (10 points)The optimum solution by using graphical method.
17 July 2009
(6 point
IE 232-Operations Research I
Homework#5
1. Each day, a news vendor must determine how many papers to order. She pays 42 for
each paper and sells each for 60. Any leftover papers are a total loss. From past
experience, she believes that the number of paper
IE 232-Operations Research I
Homework#4
1. Use the Wagner-Whitin and Silver-Meal methods to find production schedules
for the following dynamic lot-size problem: K=$30, h=$2, p=$4 d 1= 40, d2=
60, d3=10, d4=70, and d5=20.
2. A drug store sells 30 bottles
IE 232-Operations Research I
Homework#3
1. Use Dynamic programming to solve the knapsack problem shown below;
max z = 12 x1 + 25 x2 + 50 x3
s.to
3 x1 + 5 x2 + 7 x3 13
x1, x2, x3 0; x1, x2, x3 integer
2. The city of Smalltown consists of six subdivisions.
IE 232-Operations Research I Homework#2 KEY 1) Let Xi = number of units produced on machine i and Yi = 1 if machine i is used, Yi = 0 otherwise. n. min z= 1000 y1 + 920 y2 + 800 y3 + 700 y4 + 20 x1 + 24 x2 + 16 x3 + 28 x4 s.to - 900 y1 + x1 0 - 1000 y2 +
IE 232-Operations Research I
Homework#2
1. A product can be produced on four different machines. Each machine has a
fixed setup cost, variable production cost per-unit-processed, and a production
capacity given in the Table below. A total of 2000 units of
IE 232-Operations Research I
Homework#1
1. Sunco processes oil into aviation fuel and heating oil. It costs $40 to purchase each
1000 barrels of oil, which is then distilled and yields 500 barrels of aviation fuel and
500 barrels of heating oil. Output fr
Sample/Practice Problems for Midterm 2
1. True/False, Multiple choice, Fill-in-the-blank.
a. Multiple Choice. Which of the following inventory models should be used if demand is randomly distributed
and a one-time replenishment will be made?
a.
b.
c.
d.
e
Problem Set (Mini-Project) Part #1
Due: November 24, 2009
Note: If you are missing all In-Class Exercises due to a conflict in your course schedule, you
can work on the problem sets instead. There will be 3 problem sets throughout the semester.
Students w
IE 422
Homework #3
Due: November 17, 2009 (at the beginning of first lecture hour)
You can work alone or in groups of 2.
Important notes:
1. Show your work for all questions to receive partial credit.
2. Your homework should look professional and organize
The Multiple Items and Multiple
Locations
Previously:
Individual items
Single location
Next, we will focus on:
Different items at a single location
Single item in different locations
Need to coordinate!
2
Coordinated (Joint) Replenishments
at a Singl
file 06 (Nov 17)
14
Order-quantity, Order-point (Q,R) System
Continuous review system (RI=0)
A fixed quantity Q is ordered whenever the inventory
position drops to the reorder point R or lower.
Also called a two-bin system
Satisfy from the first bin
When
Inventory Control with Time-varying
(or Dynamic) Demand
Also known as lot sizing
Demand rate
Demand pattern:
1
2
3
4
5
6
7
8
Time period
2
Lot sizing approaches
1. Fixed Economic Order Quantity
Any time we produce, we produce the same
amount, Q.
Q is dete
Today
Lecture 4 plan:
Continue Chapter 5 : Basic EOQ model and its
extensions
Start Chapter 6: Lot sizing
Announcements:
Homework 2 (available on Course-Online by tomorrow
morning - due next week, October 27th).
Midterm 1 on November 3rd.
2-hour review ne
Chapter 5
Order Quantities
When Demand is
Approximately Level
1
Overview
Economic Order Quantity (EOQ)
Model and Its Extensions
Assumptions and Derivation (5.1, 5.2)
Sensitivity Analysis (5.3)
Quantity Discounts (5.5)
Limits on Order Sizes (5.7)
Economic
IE 422 Inventory Planning
Problems
Lecture 1 (last week)
Introduction: Class schedule and policies
In-class exercises will be given in the last hour
Alternative: Mini-project
File01 is uploaded on Course-Online.
Syllabus (updated) is uploaded on Course-On
1
IE 422 Inventory Planning Problems
Lecture 1
Introduction: Class schedule and policies
The Context and Importance of Inventory Management
Basic Concepts
The Importance of Inventory
Management
What is Inventory?
What is Inventory Management?
Why is it cr
Class Exercise 2
The demand for a product over six periods is 10, 40, 95, 70, 120, and 50 units. The ordering cost is $100
and the holding cost is $1 per unit per period. Consider a lot sizing method of your choice. Choose
among Fixed EOQ, Silver-Meal or