Decision Science 2 – ORL-30306
Lecture 1 Introduction & Multi-Criteria Decision-Making
Weighted goal programming:
- Define targets for each goal
- Define deviational variables for each goal
- Min{weighted sum of unwanted deviations}
Assumes
- Knowledge of all targets
- Knowledge of all weights
- Constant and know trade-offs between the deviations
It offers support by decision making -> structure the problem
Pay-off matrix: optimize objective functions one by one and keep track of their values ->
Pareto set (set of efficient solutions) + Ideal point (best objective function values in Pareto
set) + Pessimistic point (estimation for worst objective function values in Pareto set) +
Range of objective function values in the Pareto set
Constraint method (modified feasible areas)
- Work with lower bounds
- Solution depends on the bounds you use
Weighting method (modified objective function)
- Optimize weighted sum of objective functions over original feasible area
- Solution depends on weights
- Only find corner points of the original feasible area
Lecture 2 Multi-Objective Programming
Compromise programming assumes that a decision maker seeks a solution as close as
possible to the ideal point, therefore we need a measure for distance
L1 difference is summing differences for coordinates (walking on a grid)
L infinity e.g. meters you have to jump, work with max (bottleneck approach), answer is only
the value of the largest one
With normalization you get rid of scale, dimension, and direction (min/max)
Normalized distance dj= distance from ideal / range of objective
The best is not unique, it depends on your distance measure
If stakeholders are cooperative, compensation is allowed, they aim for a good overall
performance
If stakeholders are competitive, compensation is not possible, they must negotiate, they
tend towards an alternative that is a good overall performer
Compromise programming -> alternatives are implicitly given
Compromise set is the most promising part of the solution space
, Lecture 3 Introduction to discrete-event simulation
To stimulate is to mimic a real system using a model for answering specific questions about
the system’s behavior under specific circumstances
Call center (performance measure): e.g., what if two call centers help each other
Production/transportation networks/supply chains: which process delays most = bottleneck
Static: time plays no role vs dynamic: state of system changes over time
Discrete event simulation (DES): event driven (state does not change during two
consecutive events, update state only after an event, precise timing of event is uncertain but
relevant (number of people in que changes only when one comes or goes)
Discrete-time (DT): update sate only at time ticks, precise timing is irrelevant, sample
number events in a time slot, faster than DES if time slot is not too small
Steps in simulation study: problem analysis + develop conceptual model -> collect data +
analyze data -> construct computer model -> verification & validation -> design of
experiments -> execute experiments -> analyze results + report
Conceptual model: objectives (what you want to do) + functionality (inputs: experimental
factors + outputs: performance measures) + model content (scope: system boundary / level
of detail: entities & processes) + data requirements
Flow charts show scope and level of detail -> diagram representing the product flow through
a system
Sojourn time: time in queue + time at server
Service time: time it takes to serve a client/product/job (cycle time)
Data is needed for exogenous variables (value is set outside of model/to be sampled)
Modelling exogenous variables:
1. Gather real data and plot histogram or line diagram -> gives an idea of the mean and
variability
2. Select and fit a similarly shaped probability distribution
3. Sample values from probability distribution
NegExp(labda) -> labda = rate = 1/mean e.g., arrival team = number of clients / min
Know the differences between the theoretical probability distributions (haha)
NegExp distribution -> to model duration of a single task
Erlang distribution -> to model total duration of k small tasks, each task NegExp(alpa)
Normal distribution -> to model total duration of many small tasks (bell-shaped)
LogNormal distribution -> to model higher/lower variability than NegExp (x>0)
Single task but potentially high variability in service duration as a few jobs take much
longer than others
Uniform distribution -> all values between a and b are equally likely
Triangular(a,b,c) distribution -> c = most likely a = most optimistic b = pessimistic
Beta (alpha, beta) -> has many shapes, symmetric is alpha = beta, can produce triangular
and uniform distribution
NegExp distribution is favorite to queueing theorists -> if time till next arrival independent
of time elapsed since last arrival -> IATs follow NegExp distribution + if time till service
completion independent of time elapsed since start service
Issues in modeling data
1. No/little real-life data available -> fit based on process characteristics + fit based on
rough estimates
2. Incorrect data -> biased, rounded, aggregated
Lecture 1 Introduction & Multi-Criteria Decision-Making
Weighted goal programming:
- Define targets for each goal
- Define deviational variables for each goal
- Min{weighted sum of unwanted deviations}
Assumes
- Knowledge of all targets
- Knowledge of all weights
- Constant and know trade-offs between the deviations
It offers support by decision making -> structure the problem
Pay-off matrix: optimize objective functions one by one and keep track of their values ->
Pareto set (set of efficient solutions) + Ideal point (best objective function values in Pareto
set) + Pessimistic point (estimation for worst objective function values in Pareto set) +
Range of objective function values in the Pareto set
Constraint method (modified feasible areas)
- Work with lower bounds
- Solution depends on the bounds you use
Weighting method (modified objective function)
- Optimize weighted sum of objective functions over original feasible area
- Solution depends on weights
- Only find corner points of the original feasible area
Lecture 2 Multi-Objective Programming
Compromise programming assumes that a decision maker seeks a solution as close as
possible to the ideal point, therefore we need a measure for distance
L1 difference is summing differences for coordinates (walking on a grid)
L infinity e.g. meters you have to jump, work with max (bottleneck approach), answer is only
the value of the largest one
With normalization you get rid of scale, dimension, and direction (min/max)
Normalized distance dj= distance from ideal / range of objective
The best is not unique, it depends on your distance measure
If stakeholders are cooperative, compensation is allowed, they aim for a good overall
performance
If stakeholders are competitive, compensation is not possible, they must negotiate, they
tend towards an alternative that is a good overall performer
Compromise programming -> alternatives are implicitly given
Compromise set is the most promising part of the solution space
, Lecture 3 Introduction to discrete-event simulation
To stimulate is to mimic a real system using a model for answering specific questions about
the system’s behavior under specific circumstances
Call center (performance measure): e.g., what if two call centers help each other
Production/transportation networks/supply chains: which process delays most = bottleneck
Static: time plays no role vs dynamic: state of system changes over time
Discrete event simulation (DES): event driven (state does not change during two
consecutive events, update state only after an event, precise timing of event is uncertain but
relevant (number of people in que changes only when one comes or goes)
Discrete-time (DT): update sate only at time ticks, precise timing is irrelevant, sample
number events in a time slot, faster than DES if time slot is not too small
Steps in simulation study: problem analysis + develop conceptual model -> collect data +
analyze data -> construct computer model -> verification & validation -> design of
experiments -> execute experiments -> analyze results + report
Conceptual model: objectives (what you want to do) + functionality (inputs: experimental
factors + outputs: performance measures) + model content (scope: system boundary / level
of detail: entities & processes) + data requirements
Flow charts show scope and level of detail -> diagram representing the product flow through
a system
Sojourn time: time in queue + time at server
Service time: time it takes to serve a client/product/job (cycle time)
Data is needed for exogenous variables (value is set outside of model/to be sampled)
Modelling exogenous variables:
1. Gather real data and plot histogram or line diagram -> gives an idea of the mean and
variability
2. Select and fit a similarly shaped probability distribution
3. Sample values from probability distribution
NegExp(labda) -> labda = rate = 1/mean e.g., arrival team = number of clients / min
Know the differences between the theoretical probability distributions (haha)
NegExp distribution -> to model duration of a single task
Erlang distribution -> to model total duration of k small tasks, each task NegExp(alpa)
Normal distribution -> to model total duration of many small tasks (bell-shaped)
LogNormal distribution -> to model higher/lower variability than NegExp (x>0)
Single task but potentially high variability in service duration as a few jobs take much
longer than others
Uniform distribution -> all values between a and b are equally likely
Triangular(a,b,c) distribution -> c = most likely a = most optimistic b = pessimistic
Beta (alpha, beta) -> has many shapes, symmetric is alpha = beta, can produce triangular
and uniform distribution
NegExp distribution is favorite to queueing theorists -> if time till next arrival independent
of time elapsed since last arrival -> IATs follow NegExp distribution + if time till service
completion independent of time elapsed since start service
Issues in modeling data
1. No/little real-life data available -> fit based on process characteristics + fit based on
rough estimates
2. Incorrect data -> biased, rounded, aggregated
