Download cost minimization in press distribution in a final sales point

COST MINIMIZATION IN PRESS
DISTRIBUTION IN A FINAL SALES POINT
José M. Caridad y Ocerin [email protected]
Dpt. of Statistics and Econometrics Córdoba
ETEA, Centro Andaluz de Prospectiva Spain
Francisco J. Rodríguez Aragón
Dpt. of Distribution GELESA1
[email protected]
ABSTRACT
Press distribution is done trough a network of selling points, and it can be compared to the
commercialisation of non durable goods. The companies in charge of the distribution generally
use heuristic methods, based on their market knowledge and of past experiences. Demand is a
random variable that should be analyzed to minimize the distribution costs: the over and
undersupply of journals. The random demand in a final selling point is modelled, and the effects
of deviation in the offer function are studied, including a sensibility analysis dependent of the
relative value of both types of costs involved. The obtained results are applied to the distribution
process of a well known journal, proving that the proposed methodology improve the
distribution costs over the usual approach.
Keywords: press distribution, demand simulation, sensibility analysis, cost minimization
INTRODUCTION
To supply a market of a perishable good, as it happens with a daily or weekly
publication, the distribution process should aim to provide enough goods to comply
with the existing demand in each point, avoiding an excess in the number of items
provided. These two goals are in conflict, as both deviation involve costs that would
lower the overall profit. In case demand outstrip supply, consumer may switch to
another journal, or just do not buy ours, implying no only a financial loss, but also a
dent in the image or opinion about the publication. On the other side, an excess in the
number, s, of the journals put one day on a selling point, produces additional costs, not
only of the goods produced, but also in the process of having to collect the non sold
journals. In Spain, it is the distributor, that is the press company that has to pay for
collecting the non sold items, without any penalty for the owner of the sales point, that
has, thus, no incentive in trying to estimate the daily demand.
The local demand in a particular outlet should be considered a random variable, X,
which is not a priori known. Its distribution should be either estimated or established on
1
GELESA company (www.Gelesa.es) has given support and data for this paper
market knowledge suppositions. Of course it is a discrete variable, and if its probability
function is fX(x), the expected cost function is
s 1
C ( s )  Pd  ( s  x) f X ( x)  Pa
x 0

 ( x  s) f
x  s 1
X
( x)
In case demand outstrip the number s of journals supplied, Pa is the unitary cost
associated to the loss of image or just to the fact that there are a loss of sales. If the
contrary occurs, Pd is the unitary cost associated to the production, distribution and
recall of a non sold item.
In the expected cost function, it is clear that the second part has a finite number of
terms, but as the probability function should decrease in a very fast rate, the
approximation, as stated, should be acceptable. In a point of sale with a high level of
sales, even a continuous random variable could be used to model the demand. Here we
focus on the situation on most points of sales of a network, where the daily demand is
quite low for a particular journal, that is in situations where the sales would be between
0 and 50 items.
The decision about the overall production is easiest to analyse than the supply to each
particular point. Usually press companies decide this number, and then des-aggregate,
sending to each outlet a number of journals. As stated, here we treat the problem of
calculating this number for a particular point in the network. An optimality criteria has
to be stated, based upon the demand statistical distribution. Some a priori assumptions
have to be made about it, and thus, these have to be checked with sampling data.
Historical data can be used for this purpose. It can be seen that in many cases, simply a
Poisson distribution will do, in the case of sales on a press distribution point. It is not
unusual to have some a priori information, that would leads to a bayesian approach: for
example, a sport or political event, that it is known to influence demand, or a
commercial promotion associated with a newspaper sales on a particular day. An
alternative is to build a model using the corresponding intervention variables. In the
Spanish case, the week end sales are often enhanced with some gifts or add-ons to the
journal, usually with an additional token price. Here we do not consider this case,
although there are precedents in the economic literature (T.M. Heskes, 2002), where the
approach has been more general: it is the whole distribution process that is been
modelled, using past sales data, and a neural network based model. In this case, the
distribution to a particular point of sale has been calculated using a the neural network,
without attempting to characterize the statistical distribution of the desaggregated
demand.