3e Conférence Francophone de MOdélisation et SIMulation «Conception, Analyse et Gestion des Systèmes Industriels» MOSIM’01 – du 25 au 27 avril 2001 - Troyes (France)

STOCHASTIC SIMULATION MODELING IN STRATEGIC MARKETING PLANNING OF MANUFACTURING SYSTEMS Oleg ZAIKIN

Eduard PESIKOV

Institute of Computer Science & Information Systems Technical University of Szczecin 49, Zolnierska st., 71-210 Szczecin, Poland Ph: +4891 4876577, fax: +4891 4876439 E-mail: [email protected]

Department of Automized Systems of Processing and Management St. Petersburg State Electrotechnical University (LETI) 5, Professora Popova st., St. Petersburg, 197376, Russia Ph: +7 (812) 2342773 E-mail: [email protected]

Maxim FOMICHEV Department of Information Management Systems St. Petersburg Institute of Moscow State University of Print 13, Dszambula st., St. Petersburg, 191180, Russia Ph: +7 (812) 1649518 E-mail: [email protected] RESUME : The problems of construction of computer system of decision making support at strategic planning of the enterprise marketing are considered. The setting of a problem of simulation (statistical) modeling of functioning of the enterprise in conditions of market is reduced. In the work is offered the simulation model, based on use of the MonteCarlo method. The outcomes of computing experiments on modeling behaviour of the publishing enterprise in the market of printed production are resulted. KEYWORDS: decision making, marketing, simulation modeling, stochastic manufacturing system, strategy efficiency

1.

INTRODUCTION

One of the factors of successful activity of the enterprise in complicated competition is the effective application of computer systems and analytical toolkit of marketing for the analysis and choice of decisions at marketing management of the enterprise. The basic purpose of strategic marketing is the determination of the enterprise objective in a long-range period with allowance of varying environmental conditions and internal possibilities of the enterprise and shaping the marketing strategies providing reaching of firm objective. The problem of strategic marketing planning of the enterprise realizing the of mass demand production, has a number of features: the large nomenclature of made production; ramified manufacturing structure and distribution network; a plenty of influential factors in decision making; dependence on the environmental conditions exhibited in effect of random factors (oscillation of the market price of goods and materials, fast changing of demand, delayed materials delivery). The analysis of the listed features shows, that the shaping of marketing strategies of enterprise is a multifactor stochastic problem of large dimension. The

solution of a similar sort of problems with the help of heuristic methods can frequently result in essential commercial losses. There is an actual problem of development of the simulation model of enterprise functioning and methods of its analysis intended for strategic marketing planning. Now domestic and foreign firms - software developers offer a lot of computer systems of marketing decision making support. Such programs, as «Plan Magic Marketing» (production of the Plan Magic Corp., USA), «Business Inside» (yield of the Business Resource Software Inc., USA), «Market Pulse Analytics» (development of CCA (Computer Corporation of America) firm) and "Marketing Expert" (development of the "Pro-Invest Consulting" firm, Russia) concern to similar systems. The «Plan Magic Marketing» system is an automized manual on firm marketing planning. It allows to spend the analysis of a current position of the corporation in the market, and also to realize planning the marketing strategies on each components of «Marketing Mix». The operation of the program based on use of a set of MS Word and MS Excel templates.

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The «Business Inside» program concerns to the class of expert systems. In the system more than 500 questions, concerning various sides of business activity of firm, are incorporated. Because of processings of the user answers on offered questions the analysis of efficiency of the corporation marketing strategies is produced and the common strategic recommendations about possibilities of their productivity rising are formulated.

probability character of the influential factors in marketing decisions making. Exception is the marketing informational-analytical system "Marketing Expert". With the help of this tool it is obviously possible to spend the multialternative analysis of risk of profit short-reception at casual change in the given bounds of such metrics, as industrial and marketing costs, price for the goods. A disadvantage of this program is the boundedness of random factors number which are taken into account at the marketing planning.

The Market Pulse Analytics program is included into a set of software products Market Pulse. The Market Pulse Analytics system concerns to the class of intellectual marketing databases (information storages). The program allows the user to form manydimensional inquiries to the database (virtual metacubes) and to analyze the information in real time.

It is offering the approach, distinguished from used in system "Marketing Expert", by the universality. The universal character of the offered approach consists in possibility to make assumption at the simulation modeling that any parameter of the researched manufacturing system can be an aleatory variable.

Disadvantage of the programs listed above is the impossibility of taking into account at planning a

The goal of the work is the development of methods of strategic planning of enterprise marketing based on

Supplier "Н 1 "

Supplier "Н w "

Supplier "Н n " W

ENTERPRISE

Structural subdividing "SP 1 "

Structural subdividing "SP i"

Territory "F i1 "

Territory "F is "

Structural subdividing "SP n I "

Territory "F in

S

"

Trade channel "CH is1 "

Trade channel "СН isс "

Trade channel "СН isn C "

Market segment "N isc1 "

Market segment "N isсa "

Market segment "N iscn "

Goods "Т iscа1 "

Goods "Т isсaj "

Goods "Т iscаn " J

Competitor "R 1 "

Competitor "R b "

Competitor "R n

A

Figure 1. Scheme of enterprise market infrastructure

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B

"

MOSIM’01 – du 25 au 27 avril 2001 - Troyes (France)

The researched manufacturing system consists of the following elements: "Structural subdividings", "Territories", "Trade channels", "Market segments", "Goods", "Competitors" and "Suppliers".

decision making simulation models, and modern software. The essence of a simulation modeling is construction of model for some business situation (manufacturing process), i.e. algorithm simulating with the help of computer operations the functioning of a manufacturing system with allowance of the casual revolting factors. Thus the elementary phenomena component process are imitated with preservation of their logical structure and sequence of course in time. The simulation modeling is the powerful tool for a solution complicated, poorly-structured problems providing multivariance of the substantiation of marketing solutions with allowance for of a plenty of random factors. The simulation models allow simply enough to take into account such factors, as numerous casual effects, availability of discrete and continuous elements, nonlinear performances of elements of a system. With the help of a simulation modeling it is possible to decide such problems of marketing planning of firm, as an estimation of the expected profit in a planned period, analysis of efficiency of trade channels, analysis of variants of behaviour of firm at various market situations. The application of the imitative approach allows before incarnation in life of a marketing solution originally to check up it on the simulation model, that increases efficiency and validity of accepted solutions.

For the enterprise the norms of a cost of materials per unit of the goods are considered given. The constant manufacturing costs are known.

In the basis of the analysis of the simulation model, offered in work, lays the method of statistical tests (Monte-Carlo method). The Monte-Carlo method consists in multiple realization of functioning system algorithm. In each realization of algorithm (test) the aleatory variables, represented in model, are generated with the help of gauges of pseudorandom numbers with the given laws of distribution. The outcomes of tests average. If the amount of tests is great enough, the obtained outcomes of simulation can with an adequate accuracy be accepted as estimations of researched parameters of manufacturing system. 2.

SETTING A PROBLEM

Let some enterprise plans entry into the market in a planned period with the given nomenclature of the goods. The scheme of a market infrastructure of the enterprise represented in a fig. 1. On the scheme the following conditional labels are entered: i - index of structural subdividing; I - set of indexes "i"; nI - potency of the set "I"; w - index of materials supplier; W - set of indexes "w"; nW - potency of the set "W"; s - index of territory; S - set of indexes "s"; nS - potency of the set "S"; c - index of a trade channel; C - set of indexes "c"; nC - potency of the set "C"; a - index of a segment of market; A - set of indexes "a"; nA - potency of the set "A"; b - index of the competitor; B - set of indexes "b"; nB - potency of the set "B"; j - index of the goods; J - set of indexes "j"; nJ - potency of the set "J".

The managers of enterprise select group of materials suppliers, with which intends to work in a planned period. Each supplier is characterized by the nomenclature of delivered materials, prices and volume of materials supply. The suppliers can execute the orders in complete volume, and can with some probability to default conditions of deliveries. The prices and volumes of materials supply are set by the way of aleatory variables, subordinated to the known laws of a probability distribution. The share of each supplier in maintenance of total need of the enterprise in materials is supposed known. Proceeding from total need in a material and share of the supplier in maintenance of this need, it is possible to determining the volume of the material order for the concrete supplier. The enterprise has some structural subdividings (departments, manufacturing platforms). The structural subdividings realizes production on several territories (regions, cities etc.). Within the framework of each territory the structural subdividing realizes production on several trade channels. Specialists of the enterprise defined the market segments, on which the enterprise gathers to work. For market segments, trade channels, territories, structural subdividings and the enterprises are as a whole characteristic the marketing costs. Marketing costs we shall understand as an all costs which are not relating directly the technology of goods production. The marketing costs are divided into nine items of expenses: administrative; infrastructural; warehouse; trade; transport; advertising; on sales promotion; on public relation and on marketing researches. The nomenclature of production sold by the enterprise on each segment of the market is given. The prices of units of the goods and capacity of the market segments in previous period are known. The income of the consumers on segments in the previous period is given. The prices per unit of production and income of the consumers in a planned period has casual character. In the market the competitors realizing goods of a similar kind. The prices of the goods of the competitors in the previous period are assumed given. The prices of the goods of the competitors in a planned period can carry casual character. The significances of coefficients of consumers income elasticity of demand and enterprise goods price elasticity of demand have defined by specialists of the enterprise. The significances of cross-elasticity coefficients of demand at the price of competitors are determined. It is possible to evaluate shares of market segments taken by enterprise, with the help of market competitiveness analysis of the enterprise (SWOTanalysis) or to set by the way of aleatory variables. The

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modification of a market capacity of a segment in a planned period is defined, how an increment of demand caused by modification of the consumers income level, prices of enterprise goods and prices of competitors. Sales volume of the enterprise on a market segment settles up proportionally to its market share. The enterprise managers consider a possibility of realization in a planned period of advertising campaign directed on increase of sales volume. For an estimation of expediency of realization of advertising campaign it is necessary to evaluate an economic efficiency of advertising. An economic efficiency of advertising we shall expect as the relation of the additional profit obtained as a result of effect of advertising, to total advertising costs. Advertising campaign of the enterprise is planned to conduct in some stages, on each of which the advertising of specific goods is made. It is offered to determine magnitude of a modification of sales volume caused by effect of advertising, with the help of VidalWolf model. The Vidal-Wolf equation looks like:

∆S M −S =r×A −b×S , ∆t M where

∆S - modification of sales volume of the goods ∆t

in a planned period caused by effect of advertising; S sales volume of the goods in planned period disregarding influences of advertising; A - advertising costs in a planned period; r - response of sales volume on advertising; M - market capacity on the given goods; b rate of a diminution of sales volume for want of advertising. Factor of response of sales volume on advertising is defined as a modification of sales volume of the goods caused by each rouble, expended on advertising, in conditions, when sales volume is equal to zero. The rate of a diminution of sales volume for want of advertising calculates as a share of sales volume, on which this volume will decrease in a planned period for want of advertising costs. It is required to construct the simulation model of activity of the enterprise in the market. With the help of the simulation model it is necessary to conduct the profitability and yield analysis of manufacturing system elements and to evaluate economic efficiency of advertising. For realization of the purposes of simulation it is necessary for any element of considered manufacturing system to determine the laws of probability distribution for such parameters, as total amount of the proceeds and profit on realization of production; total manufacturing and marketing costs; cost-effectiveness of production for a planned period and to define their average value expected as a result of realization of two variants of marketing strategy: without advertising (variant 1) and with realization of advertising campaign (variant 2).

3. CONSTRUCTION OF MATHEMATIC MODEL The offered simulation model of functioning of the enterprise is based on application of a Monte-Carlo method. From qualitative setting of problem follows, that the model is oriented basically on imitation of marketing activity of enterprise. The production process in model is considered as a "black box". All connections between elements of model are determined, since the market infrastructure of the enterprise in a planned period is supposed constant. At determination of target parameters of manufacturing system as whole for a planned period the model is used in a static mode. For an estimation of a modification of output parameters of a system in dynamics inside the planned period, it is necessary for each time pitch (quarter, month or week) to set the gang of input datas and to conduct an appropriate series of tests. At construction of model such types of elements, as "Enterprise", "Structural subdividing", "Supplier", "Territory", "Trade channel", " Market segment", "Goods" and "Competitor" are used. For each element of manufacturing system the typical procedure of account of such parameters, as the income and profit of products realization, total manufacturing and marketing costs, cost-effectiveness of production and sales volume in natural expression will be realizing. Let's show a technique of account of these parameters on example of the typical unit. In a fig.2 the "Mβ" unit on a level "ν" of hierarchic structure represented. The knot "Uαβ", were on a level of hierarchy "ν", is connected by information connections to a knot "Uα", located on a level "ν-1", and knots "Uαβ1", …, "Uαβγ", …, " UαβnΓ ", were on a level "ν+1", where "α" - index of a knot located at a level "ν1"; "β" - index of a knot were at a level "ν"; "γ" - index of a knot were at a level "ν+1"; "Γ" - set of indexes "γ"; "nΓ" - potency of a set "Γ". Data-ins for a knot "Uβ" are the parameters designed for knots, were on a level "ν+1". To these parameters concern: total marketing costs for the items of expenses (TMCmαβγ), total fixed manufacturing costs (TFCαβγ), total variable manufacturing costs (TVCαβγ), income (Dαβγ), profit (PRαβγ), sales volume of the goods "j" in natural expression (Vαβγj). On an input of a knot the own fixed and variable marketing costs (FMCmαβ and VMCmαβj) arrive. On an output of the "Uαβ" unit the following parameters settle up: Sales volume of the goods: Vαβj =

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∑ Vαβγj , j∈J; γ ∈Γ

(1)

MOSIM’01 – du 25 au 27 avril 2001 - Troyes (France)

Profit on products realization:

Total marketing costs for the items of expenses: TMC mαβ = ϕ × + FMC mαβ +

∑ VMC mαβj × Vαβj +

j∈ J

∑ TMC mαβγ , m ∈ M ,

PRαβ = Dαβ − ( SMCαβ + TVCαβ + TFCαβ ) ; (7) (2)

γ ∈Γ

RN αβ =

0 , for " Market segments" ,  where ϕ =   1, in other situation;

∑ TMC mαβ ; m∈M

(5)

(6)

At the mathematical description of aleatory variables in models of manufacturing systems most such laws of distribution frequently are used, as normal, uniform, exponential, Weibull and beta-distribution.

(3)

Total variable manufacturing costs: TVCαβ =

∑ TVCαβγ ; γ ∈Γ

(4)

Total fixed manufacturing costs: TFCαβ =

∑ TFCαβγ ; γ ∈Γ

The income of production realization: Dαβ =

∑ Dαβ γ ; γ ∈Γ

Dαβ − ( SMCαβ + TVCαβ + TFCαβ ) . (8) SMCαβ + TVCαβ + TFCαβ

From the formulas (1)-(8) follows, that the account profitability and yield of an element of manufacturing system is made on all outline laying below of a considered element. It means, that in the beginning is settled an invoice profitability and yield for all elements were below investigated element in an outline. The outcomes of accounts for the lower elements are lifted upward to more high level, up to a considered element and summarized with outcomes for elements. After that to outcomes of accounts the own costs of an investigated element are added and are determined it profitability and yield. Except for the settlement formulas used in the typical unit, in elements of a system the expressions, characteristic only to elements of the given type can be applied. These formulas are not resulted because of limitations on volume of the paper.

Total marketing costs: SMCαβ =

Cost-effectiveness of production:

Unit Mβ Uα {TMCmαβ, TVCαβ, TFCαβ, PRαβ, Dαβ, Vαβj}

{VMCmαβj,

FMCmαβ}

Level "ν −1"

{SMCαβ, TMCmαβ,

Uαβ

TVCαβ, TFCαβ, PRαβ, Dαβ, RNαβ} Level "ν" {TMCmαβγ, TVCαβγ, TFCαβγ, PRαβγ, Dαβγ, Vαβγj}

Uαβ1

Uαβγ

Uαβn

Γ

Level "ν+1"

Figure 2. Unit of manufacturing system

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4. OUTCOMES OF COMPUTING EXPERIMENTS Within the framework of realization of the offered simulation model on the PC the computing experiments on simulation of market behaviour of the publishing enterprise were conducted. The experiments were conducted within the framework of a numerical example which carries conditional character. For calculations used the ARENA program. The researched business situation consist in the following: some publishing enterprise works in the St. Petersburg market of the computer literature; the realization of production is made on two trade channels. The firm sells production on two market segments. On these segments the firm competes to three competitors. The deliveries of expendable materials for firm are carried out three enterprisessuppliers. The enterprise realizes six products. Within the framework of simulation the following target parameters of elements of manufacturing system were determined: the income and profit on realization of production for a planned period; fixed and variable manufacturing costs; marketing costs; total costs and cost-effectiveness of production. For each variant of the marketing strategy (without application of advertising (variant 1) and with realization of advertising campaign (variant 2) series of 5000 tests were conducted. At simulation of the first variant of the marketing strategy the time of accounts has made 2 min. 37 sec. The time of accounts at simulation of the second variant of the strategy has made 2 min. 45 sec. Outcomes of accounts are: the histograms of relative frequencies of distributions; cumulative probability curves; confidence intervals and tables of average values of output parameters of model.

In a fig. 3 the histogram of relative frequencies of distribution of a settlement parameter of the simulation model constructed with the help of the "Arena" program is represented. In the table 1 the average value and factors of variation of manufacturing system functioning parameters at "Enterprise" level appropriate to two variants of marketing strategy showed. In a fig. 4 the diagram of the parameter profit received at realization of each of two variants of marketing strategy at the "Enterprise" level represented. The analysis of outcomes of simulation allows to evaluate an economic efficiency of advertising. Advertising costs in volume 10.37 millions rbl. appropriate to magnification of total costs on 17%, allow to increase the enterprise income by 13.6%, and profit of the enterprise on 7.1%. The economic efficiency of advertising, defined as the relation of additional advertising, received as a result of effect, of the profit to advertising costs, makes 37.1%. The analysis of efficiency of advertising allows to make a conclusion about expediency of realization of variant of the marketing strategy providing the advertising campaign Models and the methods of strategic planning of marketing, offered in work, have universal character and can be used in various branches (for example, in consumer goods production, food production, in orb of tourism etc). The outcomes of computing experiments have shown high performance of the offered approach application at strategic marketing planning of enterprise in conditions of incompleteness of the information.

Enterprise income

(thousand rbl.)

Figure 3. Histogram of parameter income at "Enterprise" level

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Name of output parameter

Without advertising Average Coefficient of value variation 159246 0.00880

With advertising Average Coefficient of value variation 180970 0.02020

Income of realization of production (thousand rbl.) Variable manufacturing costs (thousand rbl.) 48620 0.01900 54933 Fixed manufacturing costs (thousand rbl.) 164 0.00000 164 Marketing costs (thousand rbl.) 56297 0.00459 67852 Administrative costs (thousand rbl.) 5700 0.51441 5700 Infrastructural costs (thousand rbl.) 4594.9 0.49855 4594.9 Warehouse costs (thousand rbl.) 664.51 0.00144 664.51 Trade costs (thousand rbl.) 609.48 0.00112 609.48 Transport costs (thousand rbl.) 555.98 0.00256 555.98 Costs on public relation (thousand rbl.) 34400 0.11185 34400 Costs on sales promoting (thousand rbl.) 8890.3 0.02906 8890.3 Costs on marketing researches (thousand rbl.) 881.95 0.00169 881.95 Advertising costs (thousand rbl.) 0 0 10371 Total costs (thousand rbl.) 105080 0.00966 122950 Profit on realization of production 54167 0.02259 58015 (thousand rbl.) Cost-effectiveness of production (%) 51.55 0.02635 47.18 Table 1. Significances of output parameters of model at "Enterprise" level 5. CONCLUSION The simulation model of firm operation in conditions of the competitive environment, permitting to form the marketing strategies and to spend the analysis of their efficiency and degrees of risk, is developed. The analysis of the spended computing experiments on PC has shown legitimacy and efficiency of the offered approach to construction of the simulation model of the manufacturing system. The simulation model can be used as the unit at construction of more powerful on functionalities marketing decision making system, for example expert system. REFERENCES Bove C.L. and Arens W.F., 1986. Contemporary

0.02536 0.00000 0.00782 0.51441 0.49855 0.00144 0.00112 0.00256 0.11185 0.02906 0.00169 0.00002 0.01360 0.04446 0.04020

advertising. Homewood, Ill.: Irwin. Hahn G. and Shapiro S., 1967. Statistical models in engineering. John Wiley & Sons, Inc., New York – London – Sydney Kartishev S.V. and Smirnov B.V., 1998. Technique of the analysis of risk and indeterminacy and problems of variants of goods group prices account from the given profit in the program "Marketing Expert". Marketing and marketing researches in Russia, No.1, p.44-52. Kelton W.D., Sadowski R. and Sadowski D., 1998. Simulation with Arena. WCB/McGraw-Hill, New York, N.Y. Kotler P., 1991. Marketing Management, 7th Edition, Englewood Cliffs, NJ, Prentice – Hall. Lambin J.J., 1994. Le Marketing Strategique. Une perspective europeenne. Ediscience International, Paris. Shannon R.E., 1975. Systems simulation: the art and science. Englewood Cliffs, N.J.: Prentice-Hall.

59 58

W ithout advertising

57 W ith advertising

56 P ro fit (m illions. rbl.) 55 54 53 52 Enterp rise

Figure 4. Diagram of parameter profit at "Enterprise" level

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