Queuing Systems and Forecasting Methods

Why do customers have to wait?

Variations in arrival rates and service rates

What is the managerial trade-off? Explain queuing system tradeoff?

Utilization of servers v.s. customer wait times
you want to find the intersection between cost of waiting and cost of service. if there is low cost of service people wait a long time. if there is high cost of service than there is no wait time.

We can avoid drawbacks of waiting by:

changing prices so that supply equals demand
scheduling using reservations
make waiting fun

Maister's First Law of Service

Customers compare expectations with perceptions

Maister's Second Law of Service

It is hard to play catch-up; i.e., first impressions are critical

Unoccupied time goes slowly; what's the strategy

That Old Empty Feeling

Pre-service waits seem longer than in-service waits; what's the strategy

A foot in the door

Reduce anxiety with attention; what's the strategy

The light at the end of the tunnel

First come first serve queue discipline is often perceived as most fair; what's the strategy

excuse me, but i was first

Average time in the system

Ws

Average # of customers in the system

Ls

Average customer arrival rate

λ (throughput)

Little's Law Formula

Ls = λ * Ws
average # of customers in the system = average time in system * average customer arrival rate

What does TRUE mean in the excel exponential distribution formula?

P(≤ t)

If interarrival times are exponentially distributed then...

# of arrivals follow a poisson distribution

What are the strengths in calculating an N-period moving average forecast?

Only need N observations to make a forecast
Very inexpensive and easy to understand

What are the drawbacks in calculating an N-period moving average forecast?

Does not consider observations older than N periods
Gives equal weight to last N observations

What are the advantages of exponential smoothing?

Old data are never dropped but have progressively less influence
Don't need to keep any historical information; only need most recent smoothed value

When alpha is ___________, ______ data points have _____ weight in determining the forecast.

small (i.e. closer to 0)
older
more

Cumulative Forecast Error (CFE) purpose

Should be close to zero. Otherwise, forecast is biased.

Mean Absolute Deviation (MAD) purpose

Common measure of error. Gives equal weight to all errors.

Mean Squared Error (MSE) purpose

Gives extra penalty to large error values

Mean Absolute Percentage Error (MAPE

Use percentages to prevent large forecast values from dominating the accuracy measure.

Overfitting

An overly complex model that tells you more about the idiosyncrasies of historical data without having value for future predictions.

How do we avoid overfitting to pick among various candidate models?

Divide our data into training and testing datasets (50/50, 80/20, 99/1)
Fit our candidate models based on the training dataset.
see how they perform on the testing dataset.

Historical Analogy (type, data required, relative cost, horizon)

Type: Subjective
Data Required: Experience
Relative Cost: High
Horizon: Medium-to-long

Regression (type, data required, relative cost, horizon)

Type: Casual
Data Required: All past data
Relative Cost: Medium
Horizon: Medium

Moving Average (type, data required, relative cost, horizon)

Type: Time Series
Data Required: Recent data
Relative Cost: Very low
Horizon: Short

Exponential Smoothing (type, data required, relative cost, horizon)

Type: Time Series
Data Required: Last forecast and smoothed value
Relative Cost: Very low
Horizon: Short

Arrival (explanation, example accommodation, example reduction)

Explanation: customer arrivals are independent decisions not evenly spaced

Example Accommodation: provide generous staffing or hold high inventory

Example Reduction: require reservations

Capability (explanation, example accommodation, example reduction)

Explanation: level of knowledge and skills vary, resulting in some hand-holding

Example Accommodation: adapt to customer skill level

Example Reduction: target customers based on their capability

Request (explanation, example accommodation, example reduction)

Explanation: uneven service times result from unique demands

Example Accommodation: cross-train employees

Example Reduction: limit service breadth

Effort (explanation, example accommodation, example reduction)

Explanation: level of commitment to coproduction or self-service varies

Example Accommodation: do work for customers

Example Reduction: reward increased effort

Subjective Performance (explanation, example accommodation, example reduction)

Explanation: personal preferences introduce unpredictability

Example Accommodation: diagnose expectations and adapt

Example Reduction: persuade customers to adjust expectations

Some random variable that we are guessing (often demand, could be # of no-shows

d

Our decision variable (e.g. amount of inventory to choose)

x

unit cost of being too low (underestimating d)

Cu

unit cost of being too high (overestimating d)

Co

Strategies to manage demand

offering price incentives and dynamic pricing

promoting off-peak demand

developing complementary services

reservations systems

overbooking

How to manage capacity

scheduling to a forecast

increasing customer participation

creating adjustable capacity

sharing capacity

cross-training employees

using part-time employees

Yield Management

a variable pricing strategy to maximize revenue from a fixed, perishable resource

When is yield management most useful?

relatively fixed capacity

perishable inventory

product sold in advance

fluctuating demand

low marginal sales costs and high capacity change costs

What are possible benefits of simulation for a business?

Try out scenarios that would be expensive/impossible to test in real life

Account for uncertainty/randomness/risk

Develop a deeper understanding of the process because you:

--> have to model it quantitatively

---> can visualize it in a new way

Estimate the performance of lots of different configurations or policies

Find the optimal solution for some problem

What is a Monte Carlo experiment?

Use random numbers and operational rules to estimate performance

What are the steps to a Monte Carlo experiment?

(Optional) If testing a decision, create a decision variable

Generate random number inputs

Insert inputs into some system and apply operational logic

Aggregate results

Excel function to get a value on the interval between 0 and 1

rand()

Excel function between a and b (including a and b as possibilities)

randbetween(a,b)

An expert guesses that Establishment dining times are between 45 min - 180 min. Which strategy to create random numbers is this? How do you simulate this?

Expert Opinion. We simulate dining duration as Randbetween(45,180).

Expert Opinion

Useful if no data exists about the random variable

Use very simple distributions (e.g. uniform)

Resample Existing Data

Useful if a large amount of data exists about the random variable

Establishment has duration data from 1,000 recent visits. Which strategy to create random numbers is this? How do you simulate this?

Resample Existing Data. To build our simulation, each simulated customer's dining duration is picked at random from those 1,000 data points.

Fit to Distribution

Useful if we have limited data

Simpler way to describe a random number distribution

We calculate that dining duration has a mean of 100.8 minutes and a SD of 26.2 min. Which strategy to create random numbers is this? How do you simulate this?

Fit to Distribution. We simulate dining duration for each customer as Norm.Inv(Rand(), 100.8, 26.2).

Probability Mass Function

probability that a discrete random variable takes some value

Probability Density Function

relative likelihood of some instantaneous value (continuous)

Cumulative Distribution Function

probability that a random variable is less than or equal to some value