This document discusses the application of operations research techniques for industrial engineers. It defines industrial engineering as focusing on designing integrated systems involving people, materials, equipment and energy. Operations research is defined as using mathematical modeling to help make optimal decisions. Some examples of operations research techniques discussed include linear programming applications like resource allocation, data envelopment analysis, and cutting stock problems. Other techniques covered are integer programming, network analysis, dynamic programming, and simulation. The document also lists relevant research journals, professional societies, and optimization/simulation software.

1. Application of Operations Research
Techniques for Industrial Engineers
Shanghai Jiao Tong University Hakeem-Ur-Rehman 1
Operations Research techniques for Industrial Engineers
“OR:THE SCIENCE OF BETTER”
Presented By:
Hakeem–Ur–Rehman
PhD (Scholar)–Management Science & Engineering
Major in (Logistics & Operations Management)
Antai College of Economics & Management, Shanghai Jiao
Tong University, Shanghai, China

2. Operations Research techniques for Industrial Engineers
Outline:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 2
 Defining Industrial Engineering (IE) & Operations Research (OR)
 Application of OR techniques (with few examples)
 Research Journals
 Societies & Professional Bodies
 Optimization / Simulation Software

3. Operations Research techniques for Industrial Engineers
What is Industrial Engineering:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 2
 Industrial Engineering is concerned with the design, improvement, and
installation of integrated systems of men, materials, equipment and energy. It
draws upon specialized knowledge and skill in the mathematical, physical
and social sciences together with the principles and methods of engineering
analysis and design to specify, predict, and evaluate the results to be obtained
from such systems. (American Institute of Industrial Engineers)
Industrial
Engineering
Operations
Research
Production &
Supply Chain
Manufacturing
Processes &
Systems
Ergonomics
Industrial Engineering at the Undergraduate Level is generally seen as a
composition of four areas.

4. Operations Research techniques for Industrial Engineers
What is Operations Research:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 4
 Optimal decision-making in, and modeling of, deterministic and probabilistic systems that
originate from real life. These applications, which occur in government, business,
engineering, economics, and the natural and social sciences, are largely characterized by
the need to allocate limited resources. In these situations, considerable insight can be
obtained from scientific analysis, such as that provided by Operations Research. (Hiller–
Lieberman)
TECHNIQUES
Deterministic
OR
Stochastic
OR
Heuristics
Meta-heuristics
(OR/MS)
o Linear Programming
o Integer Programming
o Network Analysis
o Dynamic Programming
o Non-linear
Programming
o …
o Queuing Theory
o Decision Theory
o Monte Carlo Markov
Chain
o Markov Decision Process
o Simulation
o …
o Problem Based o Simulated Annealing
o Neural Network
o Genetic Algorithms
o Ant Colony Optimization
o …
 OR: a new field which started in the late 1930's and has grown and expanded
tremendously in the last 30 years

5. Operations Research techniques for Industrial Engineers
Application O.R. Techniques:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 5
 LINEAR PROGRAMMING
o Resource Allocation Problems: Attempt to allocate a limited resource so as to
optimize the consequence of that allocation.
𝑴𝒂𝒙𝒊𝒎𝒊𝒛𝒆 Prof𝑖𝑡 =
𝑗=1
𝑛
𝑝𝑗 𝑥𝑗
Subject to:
𝑗=1
𝑛
𝑎𝑖𝑗 𝑥𝑗 ≤ 𝑏𝑖 𝑓𝑜𝑟 𝑖 = 1,2, . . . , 𝑚
𝑥𝑗 ≥ 0 𝑓𝑜𝑟 𝑗 = 1,2, . . . , 𝑛
General Resource Allocation Model: Parameters:
• n = # of activities (e.g.: products etc.)
• m = # of Resources (e.g. Machines etc.)
• 𝑝𝑗 = Profit for activity ‘𝑗’
• 𝑏𝑖 = Amount available of resource ‘𝑖’
• 𝑎𝑖𝑗 = Amount of resource ‘𝑖’ used by a unit of
activity ‘𝑗’
Decision Variables:
• 𝑥𝑗 = Amount of activity ‘𝑗’ selected
Machine Quantity Prodcut-1 Prodcut-2 Prodcut-3 Prodcut-4 Prodcut-5
M1 4 1.2 1.3 0.7 0.0 0.5
M2 5 0.7 2.2 1.6 0.5 1.0
M3 3 0.9 0.7 1.3 1.0 0.8
M4 7 1.4 2.8 0.5 1.2 0.6
Unit Profit ($) 18 25 10 12 15
EXAMPLE: Machine data and processing requirements (hrs./unit)
Number of hours available
on each machine type = 40

6. Operations Research techniques for Industrial Engineers
Application O.R. Techniques:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 6
 LINEAR PROGRAMMING …
o Data Envelopment Analysis: (developed by Charles, Cooper and Rhodes (1978)) is
an application of linear programming that deals with the comparison of different decision
making units (DMUs), with respect to their efficiencies such as branches of a fast-food
chain, automobile dealerships selling the same brand, etc.
General Basic DEA (CCR) Model:
𝑀𝑎𝑥
𝑣,𝑢
𝜃 = 𝑟=1
𝑠
𝑢 𝑟 𝑦𝑟𝑝
𝑖=1
𝑚
𝑣𝑖 𝑥𝑖𝑝
∀ 𝑝 = 1,2, . . . , 𝑛
Subject to:
𝑟=1
𝑠
𝑢 𝑟 𝑦 𝑟𝑗
𝑖=1
𝑚
𝑣𝑖 𝑥𝑖𝑗
≤ 1∀𝑗 = 1,2, . . . , 𝑛
𝑢 𝑟, 𝑣𝑖 ≥ 0
 Examples:
DMU: Banks, schools, …
Input: Labor, Capital, …
Output: Revenues, Profit …
DEA Vs Regression line

7. Operations Research techniques for Industrial Engineers
Application O.R. Techniques:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 6
 LINEAR PROGRAMMING …
o Data Envelopment Analysis: …
Example: DMU Output
(Units/day)
Inputs
Material
(cost ‘$’)
Labor
(Hours)
Factory-1 100 10 2
Factory-2 80 8 4
Factory-3 120 12 1.5
Max. 𝜃 = (𝑢1 ∗ 100 ( 𝑣1 ∗ 10 + 𝑣2 ∗ 2
For Factory-1:
S.t.: (𝑢1 ∗ 100 ( 𝑣1 ∗ 10 + 𝑣2 ∗ 2 ≤ 1
(𝑢1 ∗ 120 ( 𝑣1 ∗ 12 + 𝑣2 ∗ 1.5 ≤ 1
(𝑢1 ∗ 80 ( 𝑣1 ∗ 8 + 𝑣2 ∗ 4 ≤ 1
Similarly do it for factory-2 & factory-3; then compare the
objective function values

8. Operations Research techniques for Industrial Engineers
Application O.R. Techniques:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 7
 LINEAR PROGRAMMING…
o Cutting Stock Problems: Cutting the material in certain shapes and sizes, in order
to generate certain desired shapes and sizes, so as to minimize cost etc.
o One–dimensional, Two–dimensional & Three–dimensional cutting stock
problem
o Example: A stock roll is cut into given sizes so that demand of each product is satisfied.
o A solution is specified by
o Cutting Patterns: a pattern is a set of products whose total length is not more than ‘L’
o Frequency: the number of times each cutting pattern is applied.

9. Operations Research techniques for Industrial Engineers
Application O.R. Techniques:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 9
 LINEAR PROGRAMMING…(Cutting Stock Problems)
Parameters:
o ‘𝑚’ available lengths for which there are
supplies of ‘𝑠𝑖’, ‘𝑖 = 1,2, … , 𝑚’
o ‘𝑝’ desired lengths for which demands
are ‘𝑑 𝑘’, ‘k = 1,2, … , 𝑝’
o ‘ 𝑛 ’ distinct cutting patterns (‘ j =
1,2, … , 𝑛’)
o 𝑎 𝑘𝑗 = # of desired lengths ‘k’ according
to pattern ‘j’
o 𝑇𝑖 = A set of all patterns ‘j’ that use the
available length ‘𝑖’
o 𝑐𝑗 = cost of cutting pattern ‘j’
o 𝑐 𝑘
∗
= cost per unit of length ‘k’
General Model:
𝑀𝑖𝑛. 𝑍 = 𝑗 𝑐𝑗 𝑥𝑗 + 𝑘 𝑐 𝑘
∗
𝑦 𝑘
Subject to:
𝑗∈𝑇𝑖
𝑥𝑗 ≤ 𝑠𝑖 ∀ 𝑖 = 1,2, … , 𝑚
𝑗 𝑎 𝑘𝑗 𝑥𝑗 + 𝑦 𝑘 ≥ 𝑑 𝑘 ∀ 𝑘 = 1,2, … , 𝑝
𝑥𝑗, 𝑦 𝑘 ≥ 0; ∀ 𝑗 = 1,2, … , 𝑛 ; 𝑘 = 1,2, … , 𝑝
Decision Variables:
o 𝑥𝑗 = Number of time we cut the
jth pattern
o 𝑦 𝑘 = Number of desired length
‘k’ purchased

10. Operations Research techniques for Industrial Engineers
Application O.R. Techniques:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 10
 LINEAR PROGRAMMING…(Cutting Stock Problems)…EXAMPLE
EXAMPLE: A firm has
an inventory of one
hundred and twenty
(120), 20-ft rods, one
hundred and sixty (160),
15ft rods, and forty (40),
8-ft rods. Their customers
demand two hundred 10-
ft rods, and two hundred
and fifty 6-ft rods. Each
cut costs 30¢, while
buying the rods costs 50¢
and 25¢, respectively, for
the 10-ft and 6-ft rods.
Given the above
information, we can now
determine the cutting
plan shown in figure…

11. Operations Research techniques for Industrial Engineers
Application O.R. Techniques:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 11
 LINEAR PROGRAMMING…
o Production & Inventory Planning: minimizing production & inventory holding
cost subject to meeting the customer demand & Take care of Capacity constraint.
o Employee Scheduling Problems: Scheduling problem that assigns employees to
shifts
o Transportation & Transshipment Problems
o Assignment Problem
o Many Many More…

12. Operations Research techniques for Industrial Engineers
Application O.R. Techniques:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 12
 Integer Programming:
o Knapsack Problem: Given a set of items, each with a mass and a value,
determine the number of each item to include in a collection so that the total
weight is less than or equal to a given limit and the total value is as large as
possible.
Maximize: 𝑖=1
𝑛
𝑣𝑖 𝑥𝑖
Subject to: 𝑖=1
𝑛
𝑤𝑖 𝑥𝑖 ≤ 𝑊, 𝑥𝑖 ∈ {0,1}
o Few Examples:
o Cargo loading Problem
o Flyaway kit problem
o Project Selection Problem

13. Operations Research techniques for Industrial Engineers
Application O.R. Techniques:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 13
 Integer Programming: …
o Capacitated Lot Sizing Problem: Minimize Setup & Holding cost subject to
Capacity Constraint.
 CLSP Model:
Minimization 𝑗=1
𝐽
𝑡=1
𝑇
(𝑠𝑗 𝑥𝑗𝑡 + ℎ𝑗 𝐼𝑗𝑡
Subject to: 𝐼𝑗𝑡 = 𝐼𝑗(𝑡−1 + 𝑞 𝑗𝑡 − 𝑑𝑗𝑡 Inventory Balances Const.
𝑝𝑗 𝑞 𝑗𝑡 ≤ 𝐶𝑡 𝑥𝑗𝑡 Production of Item ‘j’ if machine is setup Const.
𝑗=1
𝐽
𝑝𝑗 𝑞 𝑗𝑡 ≤ 𝐶𝑡 Capacity Const.
𝑥𝑗𝑡 ∈ {0, 1}; 𝐼𝑗𝑡, 𝑞 𝑗𝑡 ≥ 0

14. Operations Research techniques for Industrial Engineers
Application O.R. Techniques:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 14
 Integer Programming: …
o Workload Balancing Problem: Allocation of tasks to employees, so as to
ensure that none of the employees is overworked, while others are partially idle.
o Facility Location Problem: ‘n’ sites in a region require a product; manufactured
by plants in the same region at most ‘m’ sites (of ‘n’ sites) can be selected; How
to locate the manufacturing facilities?
o Traveling Salesman Problem: Given a list of cities and the distances between
each pair of cities, what is the shortest possible route that visits each city exactly
once and returns to the origin city?
o Vehicle Routing Problem:
o Many Many More…

15. Operations Research techniques for Industrial Engineers
Application O.R. Techniques:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 15
 Network Analysis:
o Maximum Flow Problem, Shortest Path Problem & Minimum Spanning Tree:
o Many Many More…
NODES ARCS FLOW
Communication
systems
phone exchanges,
computers,
Transmission facilities,
Satellites
Cables,
fiber optic links,
microwave relay
links
Voice messages,
Data,
Video transmissions
Hydraulic systems Pumping stations
Reservoirs, Lakes
Pipelines Water, Gas, Oil,
Hydraulic fluids
Mechanical
systems
Joints Rods, Beams,
Springs
Heat, Energy
Integrated
computer circuits
Gates, registers,
processors
Wires Electrical current
Transportation
systems
Intersections,
Airports,
Rail yards
Highways,
Airline routes
Rail birds
Passengers,
cargo,
vehicles,

16. Operations Research techniques for Industrial Engineers
Application O.R. Techniques:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 16
 Dynamic Programming
o Knapsack Problem
o Shortest Path Problem (Stage Coach Problem)
o Assembly line balancing Problem
o Flow Shop Problem
o Many Many More…
 Simulation:
o Waiting Line Management / Queuing Systems:
o Inventory System
o Many Many More…
 …

17. Operations Research techniques for Industrial Engineers
Research Journals:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 17
 Few Important Research Journals:
o Operations Research
o Management Science
o Mathematics of Operations Research
o IIE Transactions
o Mathematical Programming
o European Journal of Operational Research
o Journal of the Operational Research Society
o Naval Research Logistics
o Operations Research Letters
o Interfaces (applications oriented)
o Production & Operations Management
o International Journal of Production Economics
o International Journal of Production Research

18. Operations Research techniques for Industrial Engineers
Some Societies & Professional Bodies:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 18
 IIE (Institute of Industrial Engineering): http://www.iienet2.org/
 INFORMS (Institute for Operations Research and the Management
Sciences): https://www.informs.org/
 POMS (Production & Operations Management Society:
http://www.poms.org/
o APICS (Professional association for supply chain and operations
management) :http://www.apics.org/

19. Operations Research techniques for Industrial Engineers
Optimization / Simulation Software:
Shanghai Jiao Tong University Hakeem-Ur-Rehman 19
 Optimization Software
o CPlex, Gurabi, AIMMS, Matlab, etc.
 Simulation Software
o Arena, Simlu8, Simio, Flexsim, etc.
 Computer Programming
o C++, Java, Python etc.

20. Operations Research techniques for Industrial Engineers
Shanghai Jiao Tong University Hakeem-Ur-Rehman 20
ANY QUESTION?
THANKS FOR LISTENING ()
Questions & Answers:
E-mail: Hakeem.rehman@gmail.com