Operations Research:
Making More Out of
Information Systems
Dr Heng-Soon GAN
Department of Mathematics and Statistics
The University of Melbourne
This presentation has been made in accordance with the provisions of Part VB of the copyright
act for the teaching purposes of the University.
Copyright© 2005 by Heng-Soon Gan
Optimisation = Efficiency + Savings
• Kellogg’s
– 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
Mathematics in Operation
Real Practical Problem
Mathematical (Optimization) Problem
Mathematical Solution Method (Algorithm)
Computer Algorithm
Decision Support Software System
Human Decision-Maker
x2
Decision Support
Interface
Decision Support Tool
Information Systems
A Team Effort
Users
Interface
Ops Res
Decision Support Tool
Comp Sci
Information Systems
Biz Analyst
Info Sys
Staff Rostering
Allocating Staff to Work Shifts
A significant role for the “Team”
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)
…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
Problem Solving Stages
Real Practical Problem
Mathematical (Optimization) Problem
Mathematical Solution Method (Algorithm)
Staff Rostering at
Childcare Centre
Mathematical
Programming
CPLEX
XpressMP
Computer Algorithm
Decision Support Software System
Human Decision-Maker
LINGO
Excel with VBA
Childcare Centre
Manager
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.
Integer LP (just for show…)
10
7
 c x
Minimise
i 1 k 1
i ik
10
s.t.
1, if staff i works on day k
xik  
otherwise
0,

a
x

d
,

j

S
,
k

D
aij  
 ij ik jk
1, if staff i possesses skill j
otherwise
0,
i 1
5
2   xik  4, i  E
k 1
10
x
i 1
ik
 4, k  D
xik  0,1, i  E , k  D
ci  daily wage for staff i
d jk  requiremen ts for skill j on day k
Skill Demand
Equitability
Workplace Regulation
MP
Xpress
• Large-scale optimisation software developed
by Dash (http://www.dashoptimization.com)
• Xpress-IVE (Interactive Visual Environment)
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
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)
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.
Force Optimisation
A collaborative project between
Melbourne Operations Research (MORe)
&
Defence Science and
Technology Organisation (DSTO),
Department of Defence,
Australian Government
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)
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
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
The ForceOp Tool
• Before this tool,
– force design was carried out manually
– a lengthy and laborious process, based on intuitivereasoning (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.
Facility Location Decisions
LP as a “What-If” Tool
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.
Problem Statement
36km
Customer
10 000
W-3
180 000
C
W-4
D
220 000
180 000
B
W-5
E
W-2
10 000 units
A
F
W-1
36km
W-6
10 000
Warehouse
(W)
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.
The Mathematical Model
n
Minimise
n
d
 f x  W
i i
i 1
ij
i 1 j 1
s.t .
d
y
ij
j 1
n
y
ij
i 1
 Ci xi , i  1 n
 Dj ,
j  1 d
xi  0,1
yij is int eger
j
yij
i
xi
yij
Scenario 1
• Scenario 1:
Warehouse O/H
cost is very small
as compared to
transportation cost
10 000
W-3
180 000
C
W-4
D
220 000
180 000
– Warehouse O/H:
B
$6 000 000
– Transportation cost:
10 000 units
$20/km/unit
A
– proximity dominates
– operate the
W-1
warehouse closest
to each customer
W-5
E
W-2
F
W-6
10 000
Scenario 2
• Scenario 2: Warehouse
O/H cost is very large
as compared to
transportation cost
10 000
– Warehouse O/H:
180 000
$1 800 000 000
– Transportation cost:
B
$20/km/unit
– too expensive to
10 000 units
operate a warehouse
– hence, the most
A
centralised warehouse
selected (based on
W-1
demand & distance)
W-3
180 000
C
W-4
D
220 000
W-5
E
W-2
F
W-6
10 000
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
10 000
W-3
180 000
C
W-4
D
220 000
180 000
B
W-5
E
W-2
10 000 units
A
F
W-1
W-6
10 000
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
10 000
W-3
180 000
C
W-4
150 000
D
220 000
180 000
10 000
B
110 000
E
W-5
W-2
10 000 units
A
30 000
70 000
150 000
70 000
10 000
10 000
W-1
F
W-6
10 000
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
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.