Nick T. Thomopoulos,
Illinois Institute of Technology,
thomop@stuart.iit.edu
Abstract
When
traveling along the supply chain, the demands from n locations form an
aggregate demand for a part, here called the total demand. An example is a plant that serves as the
supplier to a collection of distribution centers where the sum of distribution
center demands is combined as one demand and directed to the supplier.
Sometimes the location demands are independent and sometimes they are
dependent. This paper explores the
statistical properties between the location demands and the total demand for
both situations -- dependent and independent.
Arvid C. Johnson, Dominican
University, 7900 W. Division St.,
River Forest, IL 60305 – ajohnson@dom.edu
Nick T. Thomopoulos, IIT Stuart School of Business,
Abstract
Left-truncated normal distributions – i.e., normal probability distributions in which values below a truncation point cannot be observed – have found great utility in a variety of disciplines within the purview of decision science. This paper provides a relation between the truncation point and the left-truncated normal distribution’s coefficient of variation. Through the introduction of a standardized truncated variable, a table of the partial expectation of the left-truncated normal distribution is developed and presented for reference.
Nick T. Thomopoulos
Stuart Graduate School of
Business
Illinois Institute of
Technology
Nick Z. Malham
Forecasting & Inventory
Consultants, Inc.
Abstract
The
monthly demands in three levels of the supply chain are measured using the
coefficient of variation. The supply
chain here includes the national, the distribution centers and the
dealers. One table compares the national
demands with distribution center demands, and another compares the national
demands with the dealer demands.
Robert B. Allen,
Nick T. Thomopoulos,
Abstract
This
paper shows how to estimate the optimal order quantity for unique batch
assemblies given that the component part quantity is a random variable. The population consists of customer
specified, dated assemblies with unique composition and application. The probability model assumes that the
quantity of the component parts is a random variable. This model uses four unknown parameters that
are needed to estimate the optimal order quantity. The results demonstrate methods of parametric
analysis for evaluation of management intervention effectiveness.
Nick T. Thomopoulos
Professor of Management
Sciences
Stuart Graduate School of
Business
Illinois Institute of
Technology
Abstract
This paper shows how to
estimate the population shape and size over time for a finished good item. The population consists of the units of the finished
good that are actively productive in their intended use. To accomplish, a
probability model is introduced to trace the active life for an individual
unit. The probability model is extended
so that the shape and size of the number of units that are actively productive
in the population can be measured over a wide span of years. The probability model has a pair of unknown
parameters that are needed to apply the model.
The paper shows how these parameters can be estimated for an individual
part and for a family of parts. The
results allow projection of service demands for any part that belongs to the
family.
Nick T. Thomopoulos
IIT Stuart Graduate School of Business
Illinois Institute of Technology
thomop@stuart.iit.edu
Abstract
In a typical inventory holding location along the supply chain, safety stock is needed to yield a desired service level of the type (demand filled)/(total demand). To determine the safety stock, the computations assume a planned lead time provided by the supplier. In reality, however, the actual delivery time may vary from the planned lead time and often is longer. The paper explores how the achieved service level is effected when the delivery time varies in this way. The paper also shows how to determine the safety time stock needed to offset the longer than expected lead times.
Nick T. Thomopoulos,
Nick Z. Malham, FIC Inc.
Mark J. Spieglan, FIC Inc.
Abstract
When
a company holds stock for sale to customers, a critical issue is the replenishment
of stock. The typical goals are to buy
the stock at the minimum cost, hold the least stock in inventory and maintain a
high service level. The most important function to achieve
these goals is the forecast of the future demands for each part and
location. The forecasts are key to many subsequent decisions concerning the buying and
replenishments of the parts. A FIC
white paper shows that a decrease in the forecast error of 10 % will decrease
the safety stock by 13 to 25% and at the same time, the decrease in forecast
error helps increase the service level.
Another white paper shows how the sales of the company will increase
when the service level increases. Clearly,
the forecast plays a key role in decreasing the costs and increasing the
profits of any company that holds inventory.
With the vast competition for customer satisfaction and sales, no
company can any longer afford forecasts that are not statistically sound.
FIC
understands how the forecast is a key player in the operation of the company
and -- because of this – the FIRM™ system uses much care in generating the
forecasts on each part. Sound and tested statistical
methods (many proprietary to FIC) are used throughout the computations. Below is a review on the features in FIRM
Forecasting.