Over. Pres. cour. Oper. rese. tech. Appl. exam.
Introduction
Operations Research Technologies
Master of Business Administration
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MBA 8419 – Decision Making Technology
1 Introduction – Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Overview of the presentation
Presentation of the course Content
Operations research technologies General definition
Operations research vs practical methods Origins of the field
Scientific approach
Application examples
Introduction – Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Eval. Cont. Presentation of the course
General themes :
Modeling decisional problems
Understanding the context in which decisional problems appear Define what constitutes a solution to the problems
What are the decisions to make ?
Define the criteria used to evaluate the possible solutions
What are the objectives pursued ? What goals need to be reached ?
Define the limits / restrictions that need to be enforced What defines a feasible versus infeasible solution ?
Important considerations
Quantitative elements ⇒ Objective measurements Qualitative elements ⇒ Subjective measurements
Introduction – Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Eval. Cont. Presentation of the course
General themes (cont’d) :
Solution algorithms
Prescriptive numerical tools Exact methods
Provide an optimal solution
Apply systematic search Heuristic methods
Provide a feasible solution
Exploit specific characteristics of the optimization model
Quality vs. effort Simulation methods
Descriptive numerical tools
Formulate and represent complex decisional contexts
Stochastic parameters
Introduction – Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
General definition
Operations research field :
Definition : Operations research, or operational research, is a discipline
that deals with the application of advanced analytical methods to help make better decisions.
It employs techniques from other mathematical sciences (i.e., mathematical modeling, statistical analysis, and mathematical optimization), to find opti- mal or near-optimal solutions to complex decision-making problems.
see “About Operations Research”, INFORMS.org
Problems addressed
Critical path analysis (project management)
Floor planning Network optimization Allocation problems Assignment problems Routing
Introduction – Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
Operations research vs practical methods
In practical settings :
Managers oftentimes apply intuition to solve problems Is it always a good idea ?
Intercity truck transportation
Problem 1 : Load assignments
Context : A company has seven trucks, which are currently located in seven different cities. Seven loads, each corresponding to a truck’s capacity and also located in a specific city, need to be collected and then delivered to a final terminal. Therefore, each load will be assigned to a single truck and each truck will be used to transport one of the loads to the final destination.
Objective :
The company is interested in minimizing the total distance travelled to bring the seven loads to the final terminal.
Introduction – Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
Operations research vs practical methods
Intercity truck transportation (cont’d)
Distances (km) :
Loads 1234567
1 Scranton 2 Honesdale 3 Y NY Dover Paterson 229 229 139 176 212 212 114 155 111 111 32 54
Newton 146 116 125 153 123 91 108 81 25
4Edison 62 62 69 68
5 Princeton 6 Warwick 7 Newark
Question :
92 92 84 95 116 116 62 69 54 54 43 26
88 89 111 44 101 76
How should the company proceed to solve this transportation problem ? → Exercise.
Introduction – Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
Operations research vs practical methods
Intercity truck transportation (cont’d) Intuitive solution approach :
1 Treat assignments one by one
2 For each assignment, identify, among all available options, the
one that minimizes the distance travelled
Heuristic method ⇒ Greedy algorithm
Question : Is this the best approach to solve the problem ?
Introduction – Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
Operations research vs practical methods
Intercity truck transportation (cont’d) Solution comparison
Greedy Solution Assignments Distance
Optimal Solution Assignments Distance
1→6 116 km 2→1 212 km 3→7 25 km 4→2 62 km 5→5 38 km 6→3 62 km 7→4 26 km
1→6 116 km 2→7 91 km 3→3 32 km 4→1 62 km 5→5 38 km 6→4 69 km 7→2 54 km
Total 541 km
Total 462 km
Introduction – Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
Operations research vs practical methods
Intercity truck transportation (cont’d)
Advantages of the greedy algorithm
Extremely fast
Easy to implement
Disadvantages of the greedy algorithm
Does not necessarily produce the best solution to the
Systematic search approach :
1 Enumerate all the possible solutions to the problem
2 Evaluate the total distance traveled for each possible
3 Choose the solution for which the total distance is minimum
Exact method ⇒ Complete Enumeration
Introduction – Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
Operations research vs practical methods
Intercity truck transportation (cont’d)
Assumption
Using a computer capable of treating (i.e., finding and evaluating) one billion solutions within one second of computation time.
Computation time as a function of the size of the problem, where n represents the number of trucks / loads
n n! Computation time
≈ 1, 307674 × 1012 ≈ 2, 432902 × 1018
6 nanoseconds 120 nanoseconds ≈ 22 minutes ≈ 77 years
11 Introduction – Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
Operations research vs practical methods
Intercity truck transportation (cont’d)
Advantages of complete enumeration
Finds an optimal solution to the problem
Disadvantages of complete enumeration
Extremely long search process in the case of larger problems
Operations Research proposes technological tools to solve these types of problems (i.e., Assignment Problems)
These tools are much more efficient than either the greedy method or the complete enumeration procedure
Introduction – Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
Operations research vs practical methods
Intercity truck transportation (cont’d)
Using such technological tools, the computation time as a
function of the size of the problem n are as follows
n Assignment Problem
50 100 200
< 1 seconds 1 seconds 2 seconds 10 seconds
13 Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
Operations research vs practical methods
Managing human ressources
Problem 2 : Planning schedules
Context : A company needs to plan its needs for a cer- tain type of staff for the next day of operations. The follo- wing table provides the mini- mum numbers of staff mem- bers that need to be present to perform operations throughout the next day.
Objectives :
Minimize the number of staff that are scheduled for the day, or, minimize the number of hours they work
Periods 06:00 07:00 08 :00 09:00 10:00 11 :00 12:00 13:00 14 :00 15:00 16:00 17:00 18 :00 19:00 20 :00 21:00 22:00 23 :00 24:00 01:00
:00 à :15 -
:15 à :30 -
:30 à :45 2
:45 à :60 2
Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
Operations research vs practical methods
Managing human ressources (cont’d)
Considered staff are unionized and their collective agreement specifies the following conditions :
A staffer must work at least 4 hours on a day shift A staffer can work at most 10 hours on a day shift
Greedy algorithm :
Establish the next scheduled shifts at the earliest non-covered period of the day
Number of required staff ⇒ required number of staff to cover the identified period
Shifts are prolonged as far as possible without exceeding the required minimum number of staff of subsequent non-covered periods, while enforcing union requirements
Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
Operations research vs practical methods
Managing human ressources (cont’d) Solution comparison
Greedy Solution Number Shift
2 06:30à13:00 1 07:15à12:30 1 08:45à13:30 1 09:15à13:15 2 13:30à23:30 1 15:30à21:15 1 17:30à01:15 1 21:15à01:15
Optimal Solution Number Shift
2 06:30à10:30 1 07:15à12:30 1 08:45à13:00 1 09:15à19:15 1 13:30à21:00 1 15:30à24:00 1 17:30à22:15 1 20:15à01:15
In terms of the objectives
Greedy solution ⇒ 10 employees who will work 64.5 hours Optimal solution ⇒ 9 employees who will work 53.25 hours
Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
Origins of the field
The Industrial Revolution
Description : transition to new manufacturing processes in the period from about 1760 to sometime between 1820 and 1840
manual/hand production methods ⇒ machines new processes (manufacturing and iron production) ⇑ steam power and factory systems
Development of machine tools
Managing projects of ever increasing complexity
Hydroelectric Dams Interstate highway systems
Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Def. OR vs. PM Operations Research Technologies
Origins of the field
Description : theory of management that analyzes and synthesizes work- flows and whose main objective is improving economic efficiency and labour productivity
measuring and evaluating simple operations use measurements for better management
Description : standardization of mass production processes and the deve- lopment of more efficient production chains
Taylorism applied on more complex operations
Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam.
Def. OR vs. PM
Operations Research Technologies Scientific Approach
1. A problem is detected
2. Formulate the problem
3. Model the problem
4. Collect data
Figure – A general 7 step process
5. Solve or apply the model
7. Make decisions
6. Validate the model
19 Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam.
Def. OR vs. PM
Operations Research Technologies Scientific Approach : Abstraction of reality and the model
Figure – The optimization model is based on the abstraction of the real-world
20 Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Application examples
Figure – Supply chain management
Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Application examples
Logistics (cont’d)
Vehicle routing problems
Context : Considering a fleet of vehicles, determine an optimal set of routes for them to traverse overtime in order to deliver (or pickup) a set of products to a given set of customers.
Different variants : Capacity constraints
Time windows
Periodicity of deliveries
Multiple depots
Multiple trips
Simultaneous pickups and deliveries etc.
Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Application examples
Logistics (cont’d)
Vehicle routing problems (cont’d)
Note : Even in its simplest form, this type of problem is extremely complex to solve.
Travelling salesman problem
Context : Given a list of cities (or customers) and the distances bet- ween each pair of cities, find the shortest possible route that visits each city once.
Consider the case where there are 3 cities to visit, how many pos- sibleroutes?→ 3×2×1=6.
n! Number of solutions
10! 3 628 800
20! 2 432 902 008 176 640 000
Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Application examples
Enterprise-wide risk management
Context : Strategy that aligns a firm’s business with risk factors of its envi- ronment in the pursuit of strategic objectives.
see Managing Risk, Reaping Rewards, Changing financial world turns to Operations Research, OR/MS Today, 2001, S. A. Zenios.
4 key functions :
Pricing ⇒ models to measure risks
Securitization ⇒ design financial products that are adjusted to an organization’s needs
Asset and liability management ⇒ portfolio optimization Indexation ⇒ design of market benchmarks (i.e., indices)
Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Application examples
Media selection and promotional effort Context :
Set of markets that need to be reached Set of media outlets that are available Promotional impact (outlet → market) Promotional budget
Question :
How to design a marketing plan (i.e., a set of outlets to be applied through time) to max impact over considered markets ?
Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Application examples
Marketing (cont’d)
Sales Territory Design Context :
Set of potential (or recurring) clients Set of salespersons
Workload per client
Value per client
Question :
How to assign salespersons → clients to ensure that either the overall workload (or client value) per salesperson is uniform and to min costs ?
Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Application examples
Information technology
Data mining
Context : computing process of discovering patterns in large data sets involving me- thods at the intersection of machine learning, statistics, and database systems
Objective :
extract information from a data set and transform it into an understandable structure for further use (i.e., organizational decision making)
Common tasks :
Anomaly detection ⇒ outlier, change and deviation detection
Association rule learning ⇒ dependency modelling (relationships between variables)
Clustering⇒discovering similar groups and structures in the data
Classification⇒ generalizing known structures to apply to new data
Regression⇒ formulate models to estimate the relationships between different data, or datasets, with the least error
Summarization⇒ compact representation of the data set (visualization and report generation)
Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Application examples
Managing human ressources
Scheduling Context :
Schedule ⇒ list of times at which possible tasks, events, or actions are intended to take place
Scheduling ⇒ deciding how to order the tasks and how to commit the necessary resources to perform them
Scheduling problem
Scheduling a number of employees with typical constraints such as rotation of shifts, limits on overtime, etc. to cover the demands for treatment and care for a set of patients
Introduction - Operations Research Technologies
Over. Pres. cour. Oper. rese. tech. Appl. exam. Application examples
Managing human ressources (cont’d)
Scheduling problem (cont’d) Specific components :
Hard constraints ⇒ a constraint that absolutely needs to be enforced (otherwise, the schedule is invalid)
Examples :
specification of shifts (e.g., morning, afternoon, and night)
a nurse should be assigned to no more than one shift per day all patients be covered
Soft constraints ⇒ a constraint that should preferably be enforced (however, not meeting them does not make the schedule invalid) Examples :
min and max numbers of shifts assigned to a given nurse in a given week
min and max days worked consecutively
shift preferences of individual nurses
Introduction - Operations Research Technologies
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