In the future we will divide incoming supply of goods and supplies goods which already were serviced. (by analogy with the concepts of the theory of mass service [2.1] the offered load and. the carried out load).
Incoming supply of goods in the time interval (t1, t2) denoted by Ainc. (t1, t2), it is represents the sum of the quantities of goods handled by this consumer group during the period (t1, t2).
Supplies of goods which already were serviced. over a period of time (t1, t2) is called such the supply of goods if each incoming goods will immediately purchased by the consumer in moment. (t1, t2). Sometimes this supply will be called a potential supply.
The difference between the incoming supply of goods and supplies goods which already were serviced will be called a the losses supplies of goods :
Alost (t1, t2)=A income (t1,t2) Aserved.. (t1, t2)
1.4. Numerical characteristics of flows supplies of goods
1.4.1. The intensity of the supplies of goods
By analogy with the concepts of instantaneous and average intensities of random flow may to considered instantaneous and the average intensity of the supply of goods. However, in the theory and practice of calculation of the capacity of the market it is advisable to use the average intensity of the flows offers supply of goods. The intensity the incoming supply of goods means the offer of goods per unit of time. As a unit of measurement of the intensity of the supply of goods adopted the value a=1, i.e. the maximum volume of the supply of goods the (Preal= Pmax).
The following theorem facilitates the determination of intensity of the supply goods
It shows that this value has the property of ergodicity, which is that
Average at the time is equal to the average of the ensemble.
In this case, monitoring the arrival of shipments on time can be replaced by monitoring the number of simultaneously incoming groups of consumers.
The theorem on the quantification of the intensity incoming supply of goods:
The intensity of incoming supply of goods, which is expressed in units o relative consumption, quantitatively equal to the average number of simultaneously busy consumer groups serving this load.
Suppose that during the T hours continuously recorded the number of simultaneously busy groups of consumers market, which receives steady flow of supplies for consumer groups. Let the result of the observations was that during the time t1 was busy υ1 consumer groups, during the time t2. was busy v2 consumer groups, etc. (Fig.1.1). In General can imagine that during the time ti was busy υi consumer groups,
Σni=1 ti= T
and where n is the number, the value of v which is taken, within T hours.
Total time, when busy all consumers of the market at time ti expressed by the product of υit. In the time interval T total time when all users busy of the market will be expressed by amount. This amount, it is supplies of goods all consumers of the market at the time T.
The supplies of goods what, all consumers acquired of the market per unit time are equal to:
Aserv = (1/T) Σni=1vi ti
On the other hand, the average number of simultaneously consumer groups occupied during the time T can be defined as a weighted average of ti:
v= (v1t1 + v2t2 ++ vntn) / (t1 + t2 + tn) =
= (1/T) Σ ni=1 (vi ti)
therefore Aserv= v
A theorem about the quantitative assessment of the intensity of the incoming floe supplies of goods.
To quantify the intensity of the incoming flow supply of goods you can use the following theorem:
The intensity of the incoming flow supplies of goods, which expressed in terms of relative consumption, creates a simplest flow of goods, which quantitatively equal to the mathematical expectation of the number of goods (c), received for a time equal to the average duration of one consumption of one batch products (tcons)
Figure 1.1. The moments of arrives of goods
Let the inputs of the market comes a simple flow of goods with the intensity μ. We assume that the duration of consumption T is a finite random variable
0T Tmax is independent of the stream type of the incoming supplies goods with the average value t, Consider the time interval [t1, t2) such that t2 t1> T max. The mathematical expectation of the number of supplies placed on the market in the time interval [t1, t2) denoted by Λ (t1, t2) =μ (t1.t2).
Part of these supplies is consumed to the moment t2 (Fig. 1.1 a), and the other part does not end in this time (Fig. 1.1 b). Denote the mathematical expectation of the number of goods received in the time interval [t1, t2) and what not purchased to the time t2, denote ρ. In addition to products that arriving to market in the time interval [t1, t2), it is necessary to take into account products that have arrived up to time t1 and the time t2 are not yet purchased. We denote the expected number of goods that began before the time t1 and are ended in the time interval [t1, t2), denote ε (Fig. 1.1), and the expected number of calls that started before t1 and ended after the time t2, denote ζ (Fig. 1.1 g). Since t2 t1> Tmax, then ζ=0. For the simplest flow ρ=ε.
By definition, the mathematical expectation of entering the market supply of goods during a time interval [t1, t2),
a (t1,t2) = [μ (t2t1) ρ +ε] t ̅=μ tconsum (t2t1)
and the intensity of the inbound supplies:
a= [a (t1,t2)] / (t2t1) = μ tcosum
The mathematical product (multiplication) is the mathematical expectation of the number of goods received over the average duration of consumption. The theorem is proved.
For example, suppose that one day (between t1=0 and t2=24 hours) enters Nc=1004=400 items of goods.
Let the average duration of a consumption equal per day. Therefore, for time will receive 400 1/40 =10 items of goods.
At the same time, the number of the mathematical expectation of the number of proposals received per day is equal to:
For example, suppose that one day (between t1=0 and t2=24 hours) enters Nc=1004=400 items of goods.
Let the average duration of a consumption equal per day. Therefore, for time will receive 400 1/40 =10 items of goods.
At the same time, the number of the mathematical expectation of the number of proposals received per day is equal to:
A= N c(T) /T=400 (1/40) =10 items of goods per day
1.5. The demand and its fluctuations
1.5.1. The basic definitions. The time of greatest demand
The intensity of demand called the demand of goods per unit of time. For measuring the size of demand is applied relative consumption. A unit of measurement of the intensity of demand of the goods sometimes may make the value a=1, i.e. equal to the maximum consumption (Preal= Pmax) per unit time.
The intensity of demand in a general case can vary in different hours of the day, days of the week and months of the year. Observations have revealed that, along with random fluctuations of demand, there are exist, relatively regular fluctuations that must be considered when predicting the quantity demanded.
The most significant fluctuations with the seasons.
For some goods the greatest demand falls on a holiday, (e.g. New Year).
Largely they depend on level of life in this area and structural composition of consumers, which serves the market.
Regular fluctuations in demand may depend on the days of the week. On Saturday and Sunday, the demand for goods of mass consumption can be higher than in the other days of the week. Regular fluctuations in demand are observed for the months of the year. The minimum load on the mass consumer goods, excluding resort towns, is observed in the summer months: June, July, and August. The maximum load on the goods of mass demand occurs in February, March and November, December; should be measured demand in these months.
For strategic goods, such as oil, weapons and etc. plays role of the political situation, global and local conflicts.
For the satisfactory quality of customer service at any time, the calculation of the offer you must perform on the basis of the intensity of demand at a time when he is the greatest.
This time will be called the time of greatest demand TGD (similar to the Busy-Hour of Greatest Traffic HGT in theory queueing).
The time of greatest demand TGD it is a continuous time interval during which the average intensity of the demand is the greatest.
The degree of concentration of demand in the TGD estimated coefficient of concentration
kTGD=ATGD/Aobs,
where A TGD. the demand value for TDG;
Aobs. the demand value during the observation.
1.5.2. Main parameters and calculation of the intensity of demand
The main parameters of the demand are:
· the number of consumer groups -n;
· the average number of requests for goods received from one group of consumers per unit time ;
· the average duration of consumption for maintenance of a single application of t.
Consider the possible composition of consumers, which differ in the average intensity and average duration of consumption:
individual consumers;
intermediaries (e.g., agencies for the purchase and sale of apartments);
Firms and government agencies.
By lowering the prices of the goods the number of consumers may increase. The lengthy existence of the product on the market the number of consumers can be stabilized, and they are not changing or changing insignificantly.. A similar reaction may be in case overproduction when the relative consumption is close to 1(unit).Real consumption is stable.
1.5.3. The average number of requests from one consumer per unit of time
In accordance with the categories source of requests average number of request for goods per unit of time respectively
from one group of individual consumers;
intermediaries (e.g., agencies for the purchase and sale of apartments);
firms and government agencies.
We denote in a general way the average number of applications from groups of consumers from sources of the i th category,
ni the number of sources i th category.
Then if on the market have k groups of consumers the average number of applications from one group of consumers will be determined from the expression.
c= (Σ Ki=1 ci ni) / Σkini
The average duration of consumption (t).
The duration of one consumption it is to the period of time from the date of acquisition until the moment you start searching the same product.
Time of consumption is always less time of possession of the goods.
For example, the owner of the car bought it 3 years ago. If he started looking for a new car without selling the old, the time of consumption will be 3 years.
The duration of consumption of food products is determined by the physical needs of the person also by the allowable time storage.
The duration of consumption of clothing is determined by its wear resistance, but now mainly accordance to fashion.
The duration of consumption of control automates, computing machines of cars is limited by their reliability and by their main indicators.
Therefore, the duration of consumption, is a random value and its the mean value can be determined only on the basis of observations of existing markets and statistical studies. The impact of advertising and managing consumer behavior in this book is not considered. Therefore, the duration of consumption, is a random value and its the mean value can be determined only on the basis of observations of existing markets and statistical studies.
Sometimes you must take into account the characteristics of the purchase process that affect time of consumption.
It is possible to allocate
1. Immediate purchase as the initial moment of consumption.
2. Purchases when were refunded or replaced
3. Remote buying (online) with delayed time of consumption.
4. The purchase requisition, which is not satisfied at the lack of product.
5. The purchase requisition, which is not satisfied at the lack of goods acceptable to the buyer.
6. The purchase requisition, which is not satisfied by reason of the expiration of the release of goods etc.
In determining the parameters of the market should be taken into account that the duration of consumption of most goods (except commodities first needs) and the number of users significantly to effects on the demand the stage when the market is not saturated and it very much to depend on the prices.
For example, at higher prices on televisions the number purchases decreases, the time of consumption increases (less likely to alter the old model).
However, as we will see later, when the market is saturated demand growth in consumption (purchases) stops regardless of price.
1.5.4. Characteristics of quality of service of goods
Quality of service of suggestion on the market of goods is characterized by the number of unsold within a certain time of the goods or length of expectation of sale.
There are two basic approaches, the two disciplines of servicing coming to market goods: apparent losses and conditional losses.