LGT5102 Models for decision making

OR/MS Modeling (Scientific) Approach

Overlapping phases of the modeling approach

 1. Define problem and gather data

 2. Formulate mathematical model

 3. Develop a computer-based procedure for deriving
solutions from the model
 4. Test the model
 5. Prepare for the ongoing application of the model
 6. Implement

A case study: network design

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 Defining Problem and Gathering Data

Identify elements
 appropriate objectives, constraints, interrelationships with
other areas of the organization, alternative courses of
action, time constraints
OR/MS teams work in advisory capacity
Ascertain appropriate objectives from management
 Concerned with the entire organization
 Objectives need to be specific
 Example: maximum profit in the long run; minimum waiting
time
Data gathering
 Complete problem understanding
 Input to model 2
 Often challenging and time consuming
 Formulating a Mathematical Model

Decision variables:
 Represent the decisions to be made

 how many units to buy/sell

 how much time to spend on a task

Objective function
 Performance measure expressed as a function of the

decision variables
 Example: profit, P = 3x1 + 4x2 + 5x3

Constraints
 Restrictions of values of decision variables

 Often expressed as equalities and inequalities

 Example: x1 + 3x1x2 + 2x2 ≤ 10

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Parameters
 Constants in the equations called parameters of the

model
 Example: the number 10 in the above equation

 Determining parameter values: Often difficult; Done by

gathering data

Typical expression of the problem

 Choose values of decision variables

 so as to maximize the objective function,

 subject to the specified constraints

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 Deriving Solutions from the Model

Search for the optimal solution -- exact algorithm:

 Common theme in OR problems

 Keep in mind that the solution is optimal only with respect

to model being used

More common goal is to seek a satisfactory solution, rather
than the optimal -- heuristic procedures:
 Intuitively designed procedures that do not guarantee an

optimal solution

Postoptimality analysis (“what-if” analysis)

 Analysis done after finding an optimal solution

 What would happen if different assumptions were made?

 Determines which variables affect the solution the most

(Sensitivity analysis) 5
 Testing the Model (Model validation)

Must ‘debug’ the model as with a computer program

Process of testing/improving model is known as model
validation
How to?
 Check for dimensional consistency of units

 Vary values of parameters and/or decision variables,

and see if output behaves in a plausible way

 Retrospective test: Uses historical data to reconstruct

the past
 etc.

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 Preparing to Apply the Model

Install a well-documented system for applying the model

 Includes the model, solution procedure, and

implementation procedures
 May develop a decision support system (DSS)

Decision-support system
 Interactive, computer-based system

 MIS provides up-to-date model input

 Helps managers use data and models to support their

decision-making

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 Implementation

OR/MS team explains system to management

Develop procedures to put system into operation
 Responsibility of OR/MS team and management

Management trains the personnel and Initiate new course

of action

Important -- Success of implementation depends on

support from:
 Top management

 Operations management

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 Summary

Overlapping phases:
 Defining Problem and Gathering Data

 Formulating a Mathematical Model

 Deriving Solutions from the Model

 Testing the Model (Model validation)

 Preparing to Apply the Model

 Implementation

Subsequent chapters focus on constructing and solving

mathematical models:
 Linear programming, integer programming, queueing

models, among many others

 Require innovation and ingenuity

 Other phases are equally important

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 Case study:
Network design process

Note
 This “case study” aims to provide a concrete background for appreciating
the “modeling approach.”
 It is not required to fully understand the technical details.

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 Network design problem

 Single product
 Two plants p1 and p2: have same production costs
– Plant P1 has an annual capacity of 200,000 units.
– Plant p2 has an annual capacity of 60,000 units.
 Two warehouses w1 and w2: same handling costs.
 Three markets areas c1,c2 and c3 with demands of
50,000, 100,000 and 50,000, respectively.
 Distribution costs per unit

WH\Facility P1 P2 C1 C2 C3
W1 0 4 3 4 5
W2 5 2 2 1 2 11
 Problem: To find a distribution strategy that specifies the
flow of products from the suppliers through the warehouses
to the market areas without violating plant p2 production
capacity constraint, that satisfies market area demands,
and that minimizes total distribution costs.

$0
$3 D = 50,000
Cap = 200,000
$4
$5
$5 D = 100,000
$4 $2
$2 $1
Cap = 60,000
$2
D = 50,000

Production costs are the same, warehousing costs are the same
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 Model formulation
– a linear programming model
Let: x ijpw = the flow from plant i to warehouse j
x wm
jk = the flow from warehouse j to market k

pw pw pw pw
min: 0x 1,1 + 5x1,2 + 4x 2,1 + 2x 2,2
wm
+ 3x1,1 + 4x wm
1,2 +5x wm
1,3 + 2x wm
2,1 +1x wm
2,2 +2x wm
2,3
pw pw
s.t . x 2,1 +x 2,2 ≤60 , 000
pw pw
x 1,1 +x 2,1 =x wm
1,1 +x wm
1,2 +x wm
1,3
pw pw
x 1,2 +x 2,2 =x wm
2,1 +x wm
2,2 +x wm
2,3
wm wm
x 1,1 +x 2,1 = 50 ,000
wm
x 1,2 +x wm
2,2 =100 , 000
wm
x 1,3 +x wm
2,2 = 50 ,000
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All flows non-negative

 Solving the model: Heuristics

A heuristic algorithm:
– Assign each market to closest WH. Then assign each plant based on cost.

D = 50,000
Cap = 200,000

$5 x 140,000 D = 100,000
$2 x 50,000

$2 x 60,000 $1 x 100,000
Cap = 60,000
$2 x 50,000
D = 50,000

Total Costs = $1,120,000 14

 Solving the model: Exact algorithm

Apply the simplex method

- an algorithm for linear programming model

Facility P1 P2 C1 C2 C3
Warehouse
W1 140000 0 50000 40000 50000
W2 0 60000 0 60000 0

The total cost for the optimal strategy is 740,000

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 How parameters are determined?
– Gathering data for network design

Data involved in a typical network configuration:

1. Location of customers, stocking points and sources
2. A listing of all products
3. Annual demand for each product by customer location
4. Transportation rates by mode
5. Warehousing costs
6. Shipment sizes and frequencies for customer delivery
7. Order processing costs
8. Customer service requirements and goals

Many challenges in practices! 16

 Too Much Data

In a large logistics network

 Too many customers
– Sales data typically collected on a by-customer basis
– E.g., a typical soft drink distribution system has between
10,000 to 120,000 accounts (customers).
 Too many products
– Variations in product models and style
– Same products are packaged in many sizes
– E.g., in a retail logistics network (e.g, Parknshop, Wal-Mart) the
number of different products that flow through the network is
in the thousands or even hundreds of thousands
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 Too Much Data (cont)

 Solution -- Data aggregation

– Customer aggregation
– Product aggregation
 Impacts:
– Loss of accuracy due to aggregation (bad)
– Reduction of complexity in data analysis (good)
– Forecast demand is more accurate (good)
 Challenge:
– The aggregation level must balances the above
impacts
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 Decision Support Systems (DSS)

 Why DSS?
– Some decisions are better made by computers
– Some decisions are better made by people
– DSS allow computers and people to work
together to make better decisions
 Components:
– Input data
– Analytical tools
– Output and Presentation tools
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 A DSS for Network Design
-- IBM ILOG LogicNet Plus

 Business Inputs and Data Requirements

– Customer demand by product and service level
requirements.
– Plant locations, number of lines, production
costs and capacities.
– Locations, costs, and sizes of warehouses
– Transportation modes and costs for each lane.
– Service level requirements for each customer.
– List of products and their attributes

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 IBM LogicNet Plus (cont)

 Optimization model includes features:

– Customer-specific service level requirements
– Existing warehouses
– Expansion of existing warehouses
– Specific flow patterns
– Warehouse-to-warehouse flow
– Bill of materials

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 IBM LogicNet Plus (cont)

 Typical Solution Outputs

– Total supply chain costs
– Landed cost per customer per product
– Optimal number, location, and size of plants, lines
and warehouses
– Best production quantity at each plant and line for
each product
– Appropriate assignment of customers to
warehouses
– Optimal flow of products through the network
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 Assignment

Review
 This slides

 Read the “6-step scientific approach” in the lecture notes,

“Introduction to Management Science” (incl. review

questions)
 Go through the “ExcelTips” tutorials.

Preview for next class: “Linear Programming:Basic

Concepts”

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 Assignment
– More about Excel

If you want more basic materials of Excel:

 Walk through Sections 1-14 of the Excel tutorial:
http://www.gcflearnfree.org/excel2010
 You may consult similar sections in recent versions of Excel (which
contain many features not used in our class and are not
preferable):
e.g., https://edu.gcfglobal.org/en/excel2016/

You can always refer to this tutorial (or a similar one) for the


basics of Excel in the future.

If you plan to work on your own computers, follow instructions on
how to install the Excel solver add-in
 https://support.microsoft.com/en-us/office/load-the-solver-add-in-in-excel-612926fc-d53b-46b4-872c-e24772f078ca
 Search “Excel solver add-in” in web browsers for other versions
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