Volatility Forecasting of Market Demand as Aids for Planning Manufacturing Activities

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tainty over future market conditions, decide on its pro-

duction schedule? To keep on top of demand, a company

has to avoid shortages on one hand and too much invent-

tory on the other. This means that forecasting is a key

issue, whether the company builds its own products in its

own factories or outsources its production. Short of being

able to control market, demand planning and scheduling

manufacturing operations depend on an ability to predict

what will be the market demand and how it will fluctuate

during the execution of plans generally frozen over a

certain horizon.

Forecasting by extrapolating historical data (linear re-

gression, simple and double exponential smoothing, de-

composition of time-series in trends, cyclical variations

and randomness …..) [2] is a technique over-described in

textbooks and research papers. It is straightforward to

apply and could be justified in the postwar “fordist” era.

Today volatility is the key feature of the global economy:

the fluttering of a butterfly in Bejing can trigger a tor-

nado in Cuba.

The irreversibility of a decision and the possibility of

delaying its implementation are two important charac-

teristics when converting forecasts into scheduled

courses of action. A manufacturing company with an

opportunity to schedule production is holding an “op-

tion” analogous to a financial call option on a common

stock - it has the right and not the obligation, at some

future time of its choosing, to make an expenditure

(manufacturing a batch of products) and receive a

revenue (the proceeds of their sale) [3]. When such a

company decides on a schedule, it exercises, or “kills”,

its option to manufacture. It gives up the possibility of

waiting for complementary information to arrive that

might affect the desirability or timing of the expendi-

ture incurred by the scheduled production versus the

market value of the manufactured products, value

which fluctuates stochastically. The option can be “in

the money” meaning that when it is exercised it would

yield a positive payoff. It is said to be “out of the

money” if exercising yields a negative payoff. It cannot

disinvest2 that is get back the money already spent,

should market conditions change adversely.

An investment project, such as manufacturing a batch

of products, can be made more valuable if it gives the

manufacturer the option to expand when economic con-

ditions become favorable. That option to expand in the

future clearly has a value. The higher the volatility of the

underlying asset - the market demand - the higher value

is given to the option - the market value of the batch of

products manufactured to sell. Economists assume that

the selling price of a product depends on the market de-

mand expressed in terms of quantity of products so that

the proceeds of a sale increase along with market de-

mand.

3. Market Volatility and the Associated

Risks

3.1. Volatility

Volatility is the relative rate at which market demand

moves up and down. It is found by calculating, over a

period of time, the standard deviation of daily, weekly or

monthly change in market demand. The time intervals

considered are impelled to be chosen by the behavior of

market demand. If it moves up and down rapidly over

short periods of time, it is highly volatile. On the con-

trary if market demand is almost never changed it has

low volatility.

The risk that the scheduler of manufacturing activities

is exposed to, is based on the potential for the volatility

of the underlying market demand or the market’s percep-

tion of that volatility to change. It is generally assumed

that uncertainty in the future depends on the time span.

The longer the time interval, the greater is uncertainty

about the situation by the end of this time interval and, as

a consequence, the volatility of a variable z under con-

sideration. To match with this commonly accepted belief,

the time-dependent probability density function of the

variable z at a fixed time, when normally distributed, is

[4]

2

1

,exp

2

2.

z

fzt t

t

(1)

The mean value of at any time is

zt

,0Ezt

and the variance of at time is

zt

t t,zVar

.

In many contexts of business life changes in the values

of a variable are not measured in absolute terms but as

increments with respect to its values, that is in relative

terms. That is why volatility is calculated as the variance

of a log function representing the values of a variable at

different times.

Denoting the market demand as for the time

interval i, the volatility of this variable is defined as the

standard deviation of the function

Di

/ 1Di Diln

with 1in

.

3.2. Wiener Process

A Markov process is a particular type of stochastic proc-

ess where only the present value of a variable is relevant

for predicting the future. The past history of the variable

is supposed to be embedded in its present value. Predic-

tions for the future are uncertain and must be expressed

in terms of probability distribution. If the weak form of

market efficiency were not true, analysts could make

above-average returns on stocks by interpreting the cha-

rts of the past history.

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