Random variable
Not what you're looking for?
Using the martingale method of forecast evolution (MMFE) of heath and Jackson and obtain a formula for the mean and variance of the lead time demand and apply these formulas to specific demand models.
The Martingale Method of Forecast Evolutions (MMFE) can be represented as follows:
(SEE ATTACHMENT)
Using the martingale method of forecast evolution (MMFE) of heath and Jackson and obtain a formula for the mean and variance of the lead time demand and apply these formulas to specific demand models.
The Martingale Method of Forecast Evolutions (MMFE) can be represented as follows:
At the beginning of the first period, there is an initial forecast for the demand to prevail
in period s for each s >= 1 in the planning horizon. Forecasts are updated at the beginning
of every period as follows: For all s >= t
+
where is the forecast at the beginning of period t for the demand to prevail during
period s >= t and is a mean zero, variance ,random variable that becomes known
at the end of period t. The actual demand seen during period s is Ds = .Thus, for
1 =< t =< s + 1 we can write the actual demand for period s as
Ds =
Ds at the beginning of period t1.
Let Et[Ds] and Vart[Ds] denote the expectation and the variance of Ds given what is
known at the beginning of period t.
Thus,
is just the unbiased forecast
is a measure of the forecast error
Questions?
If we apply (MMFE) to Autoregressive Integrated Moving Average (ARIMA) Demand Model.
D1 = µ + for s >=2
Ds = µ +
where 's are zero mean random variables with variance . is constant and is between 0 and 1.
- For (ARIMA), knowing that for all s > t, and , how can I prove that this model (ARIMA) can be fit into the framework of (MMFE)?
- In the formula Ds = µ + does each , , ....and are independent of each other and all have the same variance of ?
I need to find the variance.
What is the variance (if it is too much work to find the variance, it is okay to leave it)?
Purchase this Solution
Solution Summary
The martingale method of forecast evolutions of health are determined. The mean and variance of the lead time demands are given.
Solution Preview
See the attached sheet. I hope you understand the arguments.
Using the martingale method of forecast evolution (MMFE) of heath and Jackson and obtain a formula for the mean and variance of the lead time demand and apply these formulas to specific demand models.
The Martingale Method of Forecast Evolutions (MMFE) can be represented as follows:
At the beginning of the first period, there is an initial forecast for the demand to prevail
in period s for each s >= 1 in the planning horizon. Forecasts are updated at the beginning
of every period as follows: For all s >= t
+
where is the forecast at the beginning of period t for the demand to prevail ...
Purchase this Solution
Free BrainMass Quizzes
Managing the Older Worker
This quiz will let you know some of the basics of dealing with older workers. This is increasingly important for managers and human resource workers as many countries are facing an increase in older people in the workforce
Six Sigma for Process Improvement
A high level understanding of Six Sigma and what it is all about. This just gives you a glimpse of Six Sigma which entails more in-depth knowledge of processes and techniques.
Income Streams
In our ever changing world, developing secondary income streams is becoming more important. This quiz provides a brief overview of income sources.
Team Development Strategies
This quiz will assess your knowledge of team-building processes, learning styles, and leadership methods. Team development is essential to creating and maintaining high performing teams.
Marketing Management Philosophies Quiz
A test on how well a student understands the basic assumptions of marketers on buyers that will form a basis of their marketing strategies.