Operations Research: Making More Out of Information Systems

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Operations ResearchMaking More Out of
Information Systems
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Optimisation Efficiency Savings

• Kelloggs
• The largest cereal producer in the world.
• LP-based operational planning (production,
  inventory, distribution) system saved 4.5
  million in 1995.
• Procter and Gamble
• A large worldwide consumer goods company.
• Utilised integer programming and network
  optimization worked in concert with Geographical
  Information System (GIS) to re-engineering
  product sourcing and distribution system for
  North America.
• Saved over 200 million in cost per year.
• Hewlett-Packard
• Robust supply chain design based on advanced
  inventory optimization techniques.
• Realized savings of over 130 million in 2004
• Source Interfaces

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Mathematics in Operation
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Decision Support
Interface
Decision Support Tool
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A Team Effort
Users
Interface
Decision Support Tool
Comp Sci
Ops Res
Information Systems
Info Sys
Biz Analyst
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Staff Rostering

• Allocating Staff to Work Shifts
• A significant role for the Team

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The Staff Rostering Problem

• What is the optimal staff allocation?
• Consider a Childcare Centre
• The childcare centre is operating 5 days/week.
• There are 10 staff members.
• Each staff member is paid at an agreed daily
  rate, according to the skills they possess.
• One shift per day
• Skills can be categorised into 5 types.
• (Singing,Dancing)
• (Arts)
• (Sports)
• (Reading,Writing)
• (Moral Studies,Hygiene)

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other information

• CONSTRAINTS
• Skill Demand
• The daily skill demand is met.
• Equitability (breaks,salaries)
• Each staff member must at least work 2 days/week
  and can at most work 4 days/week.
• Workplace Regulation
• On any day, there must be at least 4 staff
  members working.
• OBJECTIVE
• Minimise Total Employment Cost/Week

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Problem Solving Stages
Staff Rostering at Childcare Centre
Real Practical Problem
Mathematical Programming
Mathematical (Optimization) Problem
Mathematical Solution Method (Algorithm)
CPLEX XpressMP LINGO
Computer Algorithm
Decision Support Software System
Excel with VBA
Childcare Centre Manager
Human Decision-Maker
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The Mathematical Problem

• Modelled as an Integer LP
• Decision variables are integers, i.e. variables
  can only take 0,1,2, not 0.2, 1.1, 2.4 etc.
• A binary variable a decision variable that can
  only take 0 or 1 as a solution.

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Integer LP (just for show)
Skill Demand
Equitability
Workplace Regulation
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XpressMP

• Large-scale optimisation software developed by
  Dash (http//www.dashoptimization.com)
• Xpress-IVE (Interactive Visual Environment)

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Decision Support Software System

• Excel Interface
• Database Management
• Staff Profile (Name, Category)
• Annual leave
• Shift preferences
• Reserve staff
• Roster
• etc.
• Information system installed to disseminate
  information (shift preference, roster etc.)
  effectively throughout the organisation

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Other Issues and Challenges

• Breaks
• scheduled breaks
• annual leave
• festive breaks (under-staffing issues)
• Fatigue
• limit to number of working hours per
  day/week/fortnight (Union Requirements)
• Equitable roster
• equitable weekend/night shifts
• Motivation
• skill utilisation (avoid monotonous job routine)
• Training
• training and development (scheduled)

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Other Industry Requiring Staff Rostering

• Airline (air crew and ground staff)
• Health (nurses and doctors)
• Manufacturing (operators)
• Transport (truck drivers)
• Entertainment and gaming
• Education (teachers, lecturers)
• MORe is currently involved in several (long-term)
  staff rostering projects for Australia-based
  companies in at least one of the industries
  mentioned above.

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Force Optimisation

• A collaborative project between
• Melbourne Operations Research (MORe)
• Defence Science and
• Technology Organisation (DSTO),
• Department of Defence,
• Australian Government

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Project Background

• DSTO LOD working with Melbourne Operations
  Research (MORe), The University of Melbourne
• Project aim support the Army (Force Design
  Group) with their capability options development
  and analysis, seeking
• What types of forces should be maintained?
• What force strength is required?
• to ensure forces are effective in achieving
  defence objectives
• Project started in mid-2004 and successfully
  completed its modelling, interface design and
  testing phases in the beginning of year 2005
• The model will be presented at the Australian
  Society for Operations Research 2005 Conference
  (26-28th September)

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General Aim of Project
Forces wishlist
Choose forces (STRATEGIC)
? budget




Force configuration
Deploy forces (TACTICAL)
e
e
e
e
e
e
e
max effectiveness
Objectives
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The Mathematical Model

• An integer LP-based prototype decision support
  tool has been developed.
• The support tool, ForceOp, has an Excel
  interface, written with VBA and optimised using
  XpressMP.
• Future directions
• database management
• integrated military systems Military
  Information System

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The ForceOp Tool

• Before this tool,
• force design was carried out manually
• a lengthy and laborious process, based on
  intuitive-reasoning (no quantitative basis).
• difficult to assess effectiveness or compare
  quality of solutions
• With this tool,
• solutions can be obtained fast.
• quality of solutions can be quantified.
• many sets of objectives can be tested within a
  short period of time.
• many different force configurations can be tested
  against a given set of objectives.

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Facility Location Decisions

• LP as a What-If Tool

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The Facility Location Problem

• LP-based techniques can be used to locate
• manufacturing facilities,
• distribution centres,
• warehouse/storage facilities etc.
• taking into consideration factors such as
• facility/distribution capacities,
• customer demand,
• budget constraints,
• quality of service to customers etc.
• using Operations Research techniques such as
• linear programming,
• integer linear programming, and
• stochastic programming.
• With OR techniques, solutions for the facility
  location problem can be obtained fast, and hence,
  we are able to perform a large range of what-if
  scenarios.

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Problem Statement
36km
Customer
W-3
10 000
36km
180 000
Warehouse (W)
W-4
D
C

• Assume
• Transportation cost 20/km/unit
• Warehouses have the same O/H cost
• Warehouse has very large capacity
• Problem modelled as an integer linear program,
  and solved using XpressMP.

220 000
180 000
B
E
W-5
W-2
10 000 units
A
F
W-1
W-6
10 000
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The Mathematical Model
j
i
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Scenario 1

• Scenario 1 Warehouse O/H cost is very small as
  compared to transportation cost
• Warehouse O/H
• 6 000 000
• Transportation cost 20/km/unit
• proximity dominates
• operate the warehouse closest to each customer

W-3
10 000
180 000
W-4
D
C
220 000
180 000
B
E
W-5
W-2
10 000 units
A
F
W-1
W-6
10 000
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Scenario 2

• Scenario 2 Warehouse O/H cost is very large as
  compared to transportation cost
• Warehouse O/H
• 1 800 000 000
• Transportation cost 20/km/unit
• too expensive to operate a warehouse
• hence, the most centralised warehouse selected
  (based on demand distance)

W-3
10 000
180 000
W-4
D
C
220 000
180 000
B
E
W-5
W-2
10 000 units
A
F
W-1
W-6
10 000
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Scenario 3

• Scenario 3 Both warehouse O/H and transportation
  costs are competing
• Warehouse O/H
• 60 000 000
• Transportation cost 20/km/unit
• solution is not obvious too many possibilities

W-3
10 000
180 000
W-4
D
C
220 000
180 000
B
E
W-5
W-2
10 000 units
A
F
W-1
W-6
10 000
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Scenario 4

• Scenario 4 Both warehouse O/H and transportation
  costs are competing AND warehouse capacity
  limited
• Warehouse O/H
• 60 000 000
• Transportation cost 20/km/unit
• Warehouse capacity 150 000 units

W-3
10 000
180 000
W-4
D
C
150 000
220 000
180 000
10 000
30 000
B
E
110 000
W-5
150 000
W-2
10 000 units
70 000
70 000
A
F
10 000
10 000
W-1
W-6
10 000
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Facility Location

• Possible variants
• closure decisions
• acquisition decisions
• Possible extensions
• limitations to the number of distribution centres
• warehouse-customer distance constraint
• complex cost functions
• uncertain demand

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Other OR Applications

• Other areas where OR techniques have been proven
  to be useful include
• Inventory control
• Warehouse design, storage and retrieval, order
  picking
• Vehicle routing
• Delivery transport mode selection
• Capacity and manpower planning
• Production scheduling
• and other resource usage and allocation
  decisions.