Application of or for industrial engineers

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–RehmanPhD (Scholar)–Management Science & EngineeringMajor in (Logistics & Operations Management)Antai College of Economics & Management, Shanghai Jiao Tong University, Shanghai, China


Outline:


Defining Industrial Engineering (IE) & Operations Research (OR)

Application of OR techniques (with few examples)

Research Journals

Societies & Professional Bodies

Optimization / Simulation Software


What is Industrial Engineering:


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

OperationsResearch

Production & Supply Chain

Manufacturing Processes &

SystemsErgonomics

Industrial Engineering at the Undergraduate Level is generally seen as a composition of four areas.


What is Operations Research:


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

HeuristicsMeta-heuristics

(OR/MS)

o Linear Programmingo Integer Programmingo Network Analysiso Dynamic Programmingo Non-linear

Programmingo …

o Queuing Theoryo Decision Theoryo Monte Carlo Markov

Chaino Markov Decision Processo Simulationo …

o Problem Based o Simulated Annealing o Neural Networko Genetic Algorithmso Ant Colony Optimizationo …

OR: a new field which started in the late 1930's and has grown and expanded tremendously in the last 30 years


Application O.R. Techniques:


LINEAR PROGRAMMINGo Resource Allocation Problems: Attempt to allocate a limited resource so as to

optimize the consequence of that allocation.

𝑴𝒂𝒙𝒊𝒎𝒊𝒛𝒆 Prof 𝑖𝑡=∑𝑗=1

𝑛

𝑝 𝑗 𝑥 𝑗Subject to:

∑𝑗=1

𝑛

𝑎𝑖𝑗 𝑥 𝑗 ≤𝑏𝑖 𝑓𝑜𝑟 𝑖=1,2, ... ,𝑚

𝑥 𝑗≥ 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.)• = Profit for activity ‘’• = Amount available of resource ‘’• = Amount of resource ‘’ used by a unit of

activity ‘’Decision Variables:• = Amount of activity ‘’ 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




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:

𝑀𝑎𝑥𝑣 ,𝑢

𝜃=∑𝑟=1

𝑠

𝑢𝑟 𝑦𝑟𝑝

∑𝑖=1

𝑚

𝑣 𝑖𝑥 𝑖𝑝

∀𝑝=1,2 ,... ,𝑛

Subject to:∑𝑟=1

𝑠

𝑢𝑟 𝑦𝑟𝑗

∑𝑖=1

𝑚

𝑣 𝑖𝑥 𝑖𝑗

≤1 ∀ 𝑗=1,2 ,... ,𝑛

𝑢𝑟 ,𝑣𝑖≥ 0

Examples: DMU: Banks, schools, … Input: Labor, Capital, … Output: Revenues, Profit …

DEA Vs Regression line




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 .¿For Factory-1:

S.t.:

¿¿Similarly do it for factory-2 & factory-3; then compare the objective function values




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.




LINEAR PROGRAMMING…(Cutting Stock Problems)Parameters:o ‘’ available lengths for which there are

supplies of ‘’, ‘’o ‘’ desired lengths for which demands are

‘’, ‘’o ‘’ distinct cutting patterns (‘’)o = # of desired lengths ‘k’ according to

pattern ‘j’o = A set of all patterns ‘j’ that use the

available length ‘’o = cost of cutting pattern ‘j’o = cost per unit of length ‘k’ General Model:

Subject to:

Decision Variables:o Number of time we cut the jth

patterno Number of desired length ‘k’

purchased




LINEAR PROGRAMMING…(Cutting Stock Problems)…EXAMPLEEXAMPLE: 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…




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…




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:

Subject to:

o Few Examples:o Cargo loading Problemo Flyaway kit problemo Project Selection Problem




Integer Programming: …

o Capacitated Lot Sizing Problem: Minimize Setup & Holding cost subject to Capacity Constraint.

CLSP Model: Minimization

Subject to: = + Inventory Balances Const. Production of Item ‘j’ if machine is setup Const. Capacity Const. ;




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…




Network Analysis:o Maximum Flow Problem, Shortest Path Problem & Minimum Spanning Tree:

o Many Many More…

NODES ARCS FLOW

Communicationsystems

phone exchanges,computers, Transmission facilities, Satellites

Cables, fiber optic links, microwave relay links

Voice messages, Data, Video transmissions

Hydraulic systems

Pumping stationsReservoirs, Lakes

Pipelines Water, Gas, Oil,Hydraulic fluids

Mechanical systems

Joints Rods, Beams, Springs

Heat, Energy

Integrated computer circuits

Gates, registers,processors

Wires Electrical current

Transportationsystems

Intersections, Airports,Rail yards

Highways,Airline routes Rail birds

Passengers, cargo,vehicles,




Dynamic Programmingo Knapsack Problemo Shortest Path Problem (Stage Coach Problem)o Assembly line balancing Problemo Flow Shop Problemo Many Many More…

Simulation:o Waiting Line Management / Queuing Systems:o Inventory Systemo Many Many More…

…


Research Journals:


Few Important Research Journals:o Operations Researcho Management Scienceo Mathematics of Operations Researcho IIE Transactionso Mathematical Programmingo European Journal of Operational Researcho Journal of the Operational Research Societyo Naval Research Logisticso Operations Research Letterso Interfaces (applications oriented)o Production & Operations Managemento International Journal of Production Economicso International Journal of Production Research


Some Societies & Professional Bodies:


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/

http://www.iienet2.org/

https://www.informs.org/

http://www.poms.org/



http://www.apics.org/

http://www.apics.org/


Optimization / Simulation Software:


Optimization Software o CPlex, Gurabi, AIMMS, Matlab, etc.

Simulation Softwareo Arena, Simlu8, Simio, Flexsim, etc.

Computer Programming o C++, Java, Python etc.



ANY QUESTION?

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