CHAPTER QUANTITATIVE TECHNIQUES FOR FERTILIZER MARRETING...

CHAPTER V

QUANTITATIVE TECHNIQUES FOR FERTILIZER MARRETING SYSTEMS

6.1 INTRODUCTION

Fertilizer industry has grown tremendously in the last twenty years . The increases in production capacities, utilization of the installed capacities

as also the increases in the consumption have been phenomenal since 1980.

The dependence on imports has significantly decreased with the steep growth

in the indigenous production capacities although the consumption has

increased. These are the basic requirements of developing an effective

marketing system and draw up an optimization model for logistics. The

availability of products from indigenous sources can be estimated and the

requirement can also be forecasted under this environment.

Quantitative technique in the area of product mix, consumption

forecasting, inventory control, logistics management can be adapted for cost

reduction and improved service to farmers.

In this chapter quantitative techniques which can be adopted for sales

estimatioq inventory control, transportation and warehousing are discussed.

Optimization is the act of obtaining the best result under a given set

of resource8 and constraints. The goal of optimization is either to minimize or

to maximize an objective function under a given set of conditions.

The objective function contains the variables and the associated

co8tsJprices which should be maximized or minimized.

An Optimization problem can be stated as:

Determine X = ( XI., x2.., x3 ..., x,,) , which minimizes f(X)

subject to: g (Xi) r 0 for i=1,2,3,4 ,.....

Linear programming (L.P) and Transportation Problem, (T.P) are

optimization methods of Operations Research (O.R.) applicable for the solution

in which the objective function and the constraints appear as linear functions

of the decision variables.

6% TRANSPORTATION PROBLEM

In the chapter on marketing costs it has been brought out that over 30%

of the total marketing cost is accounted for by transportation.

The optimization model adopted has focused on the cost of

transportation in moving the fertilizer products from the fertilizer plants to

the consuming centers. The objective of this model is to minimize the aggregate

cost of transportation.

Transportation problem is an important class of L.P. As the name

indicates that the T.P minimizes the cost of transportation.

T.P. is widely adopted in developing transportation plans for movement

of products from several sources of supply to several consuming centers at the

least aggregate cost.

Conceptional Frame Work of t h e t ranspor ta t ion model

Transportation problem (T.P) is an important class of Linear

Programming (L.P.). A transportation problem is one in which the objective of

minimization of cost of transportation of products from a number of origins

(plants) to a member of destination is achieved. Suppose there are m origins

(Fertilizer plants) and n destinations (consuming points-centroids). Let be the availability of product a t plant ai (i = 1 .... m) and bj the requirement at

destination j (1 .... n). Let Cii be the cost of transportation of fertilizer (urea)

from fertilizer plants (factoried i to centroid j,

The problem is

m n Minimize f = Z Z xii

i=1 j=1

Subject to Z: xu = aj, i = 1, ..... m, m.7 (fertilizer factories) j=1

m I x.. = b., j = 1, ..... n, n=71 (Districts)

U J i = l

Total availability = Total requirement

Consistency condition.

In the illustrative example, seven fertilizer factories and seventy one

demand points (Centroids) have been chosen as a sample.

The purpose of developing this model for south India is to

illustrate the need for minimizing the cost of transportation by

rationalizing the movement. The objective is to minimize the aggregate

transportation costs and avoid the crisscross movement of fertilizer

products through an rationalized allocation plan.

Transportation plays an important role in the fertilizer marketing

aystem.In the total marketing cost transportation alone accounts for 40%'

Making the right product available to the farmers at the right place and

time will be the objective of fertilizer marketing organizations. Since

transportation cost is quite significant in the total cost of fertilizer

marketing. The transportation cost can be minimized by allocating / moving

the products according to a pre- determined plan developed based on

transportation models.

Transportation models deal with the transportation of products from

the source of production (fertilizer plant) or the source of supply ( warehouse/

port) to a number of consuming points/ retail outlets1 ultimate storage points.

The objective of the model is to satisfy the demands at final destinations,

given the supply constraints at minimum cost. The transportation model can

be formulated as a standard Linear Programming (LP) problem.

5.3 THE MODEL

Allocation of urea from different urea manufacturing plants in south

India to the pre determined consuming centroids (Districts) in south by

minimizing the total transportation costs to illustrate.

Report of the high powered committee on Fertilizer prices.

Data base: Table No.60

Product availability urea

Source: Fertilizer Marketing News, May 1992.

Table No.61

r

S1.No.

1. 2. 3. 4. 5. 6. 7.

Source: Fertilizer Marketing News, May 1992.

Source of supply

MFL. Madras SPIC. Tutiwrin NLC. Neyveli FCI-Ram NFCL, Kakinada MCF Mangalore FACT. Cochin

Total availability

Requirement (in terms of NPK)

Andhra Pradesh Karnataka Tamil Nadu Kerala

Total

The details of the availability and requirement are received by the

Ministry of Agriculture GO1 , every season drawing up the distribution plan

under the essential Commodities Act (ECA).

Availability of urea OOOT

292 512 152 495 495 340 330

2616

(OOOT)

1432 509 583 92

2616

The Optimization model has considered

Seven fertilizer plants located in south (Andhra Pradesh, Karnataka,

Tamil Nadu and Kerala) and 71 centroids (demand points).

Distances from each one of the fertilizer factories (MFL, SPIC, NLC,

FCI-R, NFCL MCF and FAC) to each of the identified demand points

(Centroids), have been adopted as weights to obtain cost of transportation.

Since the cost of movement is directly proportional to the distances

between the supply points and the sources of supply. This is a balanced

transportation problem.

Let Xij represent the quantity of Urea transported from factory Pi to the

centroid Cj : i = 1, .... 71, j = 1 .... 7

The distance between plant pi to the centroid Ci be dij

Objective function; Z ( we aggregate cost of transportation) = ;I: Xij x dij must

be minimized

Subjected to;

Availability : P1 t P2 t P3t P4t P5t P6t P7 = 2616

Requirement : Cl+C2tC3+ ............... tC71 =2616

Table No.52

Solution of the Transportation Model

Optimum allocation plan - centroid wise

Tamil Nadu

Table No.65


Optimum allocation plan - Centroid wise

Table No. 54



Table No. 56



Table No.56

Av.1Lhlllty and requirement h~ been bmhnoed

Comparison of Optimum allocation p l an wi th ECA

Source of Supplies (factories)

Demand point wise allocation are given in the tables 48 to 52.

State

Tamil Nadu

Karnataka

Andhra Pradesh

Kerala

Source (1) ECA Plan for supply of fertilizer finalized for Kharif 92 under ECA, by GOI. Published in Fertilizer Marketing News May 92. p 3.

It is seen from the analysis and the model that the allocation under ECA

significantly differs from the optimization model. While the allocation under

ECA considers maximization of supplies to the state from the factories located

in the state, the optimization model has adopted the least transportation cost

to meet the requirement of the district (Centroids).

ECA (1)

FACT, MFC & SPIC

FACT,SPIC & MCF

FACT, FCI-R

FACT & SPIC

As p e r Model

MFL, SPIC, FCI-R & FACT

MFL, SPIC, FCI-R, MCF & FACT

MFL, SPIC, FCI-R, NFCL & FACI

FACT & MCF

The model has minimized the transportation cost and has made

complete allocation of the availability from the seven fertilizer factories considered for the model and the seventy one demand points in the four

southern states. The model has therefore significantly minimized the Logistics

cost.

This model can be adopted for making season wise allocation of products

from fertilizer factories on an all India basis for minimizing the logistics cost.

6.4 MODEL FOR MEASURING THE RELATIVE INFLUENCE OF SEVERAL FACTORS ON THE CONSUMPTION OF PHOSPHATES (P)

Demand for fertilizers depends on it's profitability. Among the msjor

factors which can influence farmers ' response to fertilizer use are ; prices of

fertilizer products and price of farm products (1). Other major determinant is

the availability of irrigation facility. Uncertainty of the profitability is reduced

under irrigated conditions availability of credit on time is another vital factor.

A fertilizer demand function had been developed based on six key factors on

the data for 70-71 to 92-93,Consumption of P is crucial for crop productivity

among the Nutrients NPK , the price of P is the highest.

An analysis has been made to estimate the relationship between the

consumption of P and six variables: price ratio , rainfall , ratio of irrigated

area to cropped area 0(3),Area served by retail outlets, Disbursement of credit

Rslhect, ratio of area under HYV to total cropped area (X6).

Price ratio = wt. average price of P index of wholesale price of food

grains in the previous year. A time lag of one year has been adopted between

variation in price and the changes in demand, since most price changes have

happened after the fertilizer application is over in a season.

Regreasion Out put:

Constant -1.52

Standard error of Y Est 0.65

No, of observation 23

Degrees of Freedom 60

Y - Consumption of P (kghect)

XI - Price Ratio

& - Rainfall (mm)

X3 - % irrigated area to total cropped area

X4 - Area served by retail outlet

Xc, - Disbursement of Credit (Rs./hect)

X6 - % Area HYV to total cropped area

Consumption of P is given by the relationship:

Explanatory no te a n d Interpretation

In order to find out the relative significance of factors affecting the

consumption of Phosphatic Fertilizers, the Multiple Regression Model has

been developed for the data pertaining to the period 1970-71 to 93-94

(Compiled from Fertilizer News, March 93).

Since the co-efficient of determination, R~ is 0.99, the estimated

relationship between consumption of P and the identified factors X1 through X6 explains as high as 99% of the variation. Considering the

estimates of the parameters, irrigation, price, rainfall and HYV have

eignificant role to play in stimulating the demand for P.

Fertilizer use is inelastic to price when the procurement prices of the

produce ie considered. hundred percent increase in price ratio will decrease

the consumption only by 13.5%.

In order to increase the phosphate consumption, as per the Multiple

Regression Analysis, HYV have to be promoted, irrigation facilities

improved, the price ratio must be made high.

The above analysis suggests that fertilizer use is highly irrigation

elastic with positive coefficient.

This analysis indicates a significant bearing on policy decisions. Even

if fertilizer prices are raised, a corresponding increase in farm produce

prices/procurement prices to maintain the price-ratio will not significantly

result in decline in fertilizer demand.

6.5 SALES FORECASTING SYSTEM

Developing realistic sales estimates is the basic for an effective

marketing management, particularly the Logistics management.

In fertilizer industry large volumes of sales data are being

continuously generated, partly as for monitoring sales performance and

partly to provide monthly returns to Ministry of Agriculture GO1 and to

state govt under ECA statutory requirements. Further The fertilizer

Association of India compiles Fertilizer Statistics & annual reviews

annually. The regional ofice of the FA1 also publishes statistics

pertaining to district levels These valuable data on the fertilizer industry

has hardly been used for developing marketing strategies and

programs and any optimization cases.

These statistics are valuable inputs for developing trends,

relatiomhipa (correlations) and developing sales (consumption) forecasts at

micro & macro levels.

Experiences over the years indicate that auto-regression model for

short term forecasting of sales provides a good fit.

Projecting demand is an important aspect of fertilizer marketing

system. Realistic projection of demand is essential for developing

transportation and warehousing plans. Demand projection is also

required for other marketing efforts; promotion, pricing, product

development, etc,.

It is considered essential to develop simple models for

forecasting sales as reflected by the respondents when this topic was

discussed with Fertilizer Marketing Executives.

The concept of Auto-correlation (functional relationship auto-

regression) implies that for some products there exists a correlation

between the same variables at different points of time. This technique is

suited to the forecasting of fertilizers. The consumption of fertilizers

during the previous year(s) has a great impact on the immediate future

consumption pattern.

This technique is easy to understand and apply. It does not call for

elaborate data on several variables but relays on the recent past trends and

moving data. I t is important to normalize the data for any unusual

situations such as restriction of consumption due to non availability of

products etc . How ever if such occurrences are not unusual no

normalization is needed. The model will take care.

For ahort term forecast this method is found to be simple and

adequate. Aftar a great deal of checking and verification, this method

was adopted for estimating off take of warehouse-wise product-wise

volumes a t MFL. The technique has been found easy to understand and

apply. A five year moving data is used as the basis for the trends.

When the latest year data becomes available the earliest year data is

deleted so that a constant data for five years is available for trend

projections.

As a sample case the short term projection of consumption have

been made for each of the southern states for Urea, based on the five year

data. Department of agriculture of the state govt can use this simple

model for estimating the requirement for the seasons (Khar i fkbi ) . This

can form a very useful input for zonal conferences to draw up supply

plans. This model attempts to minimize the occasions of shortages and

excess availability. At the micro level manufacturing units adopt this for

district wise or warehouse-wise or dealer-wise estimates of

consumptiordoff take.

A Linear trend function is developed based on the auto

regression(time series) of the form Y=A+ Bt;

When the projection is made for the year it is split to months based

on the last five year monthly off take.

The following examples illustrates the method of developing short

term sales forecasts state wise.

Table No.67

Consumption tren* in South India

Source: Agricultural and Fertilizer Statistics 1993. FAI- Southern Region, Madras.

Year

1987-88 1988-89 1989-90 1990-91 1991-92

Tamil Nadu

Regression 0utput:for TN

Consumption Urea (000T)

Constant 594.95

Std Err of Y Est 25.71585

R~ 0.414453

No, of Observations 5


X Coefficient(s) 11.85

Std Err of Coef. 8.132066

TN

578.9 648.5 639.8 645.8 639.5

Consumption function based on time series (linear);

Y= 594.95+11.85)(, consumption forecast for the year

1992-93 can be obtained by substituting X=6 and so on ...

KN

395.2 590.4 539.7 583.1 509.8

kP

882.5 1231.8 1619.1 1676.1 1520.9

KE

64.6 94.9 88.5

106.7 113.3

Constant 417.07


R~ 0.589975

No. of Observations 5


X Coefticient(s) 42.19


Consumption function based on time series for Karnataka:

Andhra Pradesh

Regression 0utput:for AP

Constant 869.75


R~ 0.682560

No. of Observations 5 Degrees of Freedom 3

X Coeficient(s) 172.11


Consumption fundion for Andhra Pradesh :Y= 869.75 +172.11X

Constant 60.84

Std Err of Y Est 8.868220 R~ 0.834824

No. of Observations 5


X Coeficient(s) 10.92


Consumption function for Kerala:Y=60.84 + 10.92X

Developing short term (one year1 one season ) sales forecast based on

these functions will yield useful results for preparing marketing and

logistics plan by fertilizer organizations.

This concept can be applied for forecasting the demand for

warehouses b a e d on the past consumption / off take pattern . Such

estimates can be used for transportation and warehouse planning.

This technique was adopted by Madras Fertilizers Ltd, Madras (1986)

to draw up the logistics plan and significant saving was accrued.

6.6 INVENTORY MANAGEMENT IN FERTILIZER MARKETING

Inventory is one of the riskiest areas in logistical management.

Commitment to a particular inventory mix and subsequent allocation to

channels in anticipation of a future sales represent the vortex of logistical

operations. Without a proper inventory mix problems of customer service &

revenue generation would develop.

Inventory management is critical in marketing operations. Over

stocking and stock out situations should be minimized. Inventory control

seeks to achieve a balance between shortage and excess of stocks within a

planning period characterized by risk and uncertainty. Inventory

management considers the product mix, geographical spread of the

marketing territory, seasonality, the order size, safety stock levels, cost of

inventory carrying the self life of products etc. Utilizing the past

consumption pattern of specified market territory, the costs of storage, order

processing costs Economic Order Quantity (EOQ) for each storage location

can be determined, EOQ=Square root of twice the cost per order processing

multiplied by the sales volume in units divided by storage cost multiplied by

cost per unit (Price).

For a seasonal product like fertilizer Statistical Probability can be

adopted. This involves analysing a sample data of lifting of a specific

products during tile past similar seasons in for a given warehouse point to

obtain the average and standard deviation (s.d) values. Average plus or

minus 1.96 times the s.d. divided by the square root of the number of

samples considered. This provides the best estimates of the possible sales . The other parameters of the EOQ formula are constants for a given period.

This helps in managing the inventory levels on a warehouse to warehouse

basis and assures 95% level of confidence of adequacy of stocks and the

inventory level is minimum.

Some simple but effective inventory management techniques which

can be adopted in inventory management at in field warehouses are

discussed here. This technique was adopted in a Fertilizer manufacturing

unit in South for inventory control systems in 186 field storage points (1)

Discussion of some inventory models:

Model I

The objective of this model is to help maintain adequate inventory

levels a t warehouses to service the retailers, cooperatives and farmers;

The data required for this model is a five year month wise product

wise lifting statistics for the ware house. The statistics should be updated

every adopting a 5 point moving average technique; adding the latest data

and eliminating the earliest data and maintaining the constant sample size

of 5.

The level of safety stock can be obtained by adopting the following the

statistical formula:

MODEL FOR OPTIMUM WAREHOUSE STOCK

The model can be adopted for determining the safety stock of

Fertilizer products at warehouses. The level of stock necessary to meet the

sales requirement a t warehouse location can be estimated by the statistical

formula:

= JR (o,~) + s ~ ( ~ ~ ~ )

where

a, : Inventory requirement for the month.

R : Average time lag (days) between the order placed by

warehouselstock point, and the delivery of products at the

warehouse.

a~ : The Standard deviation 6 . D ) of time lag.

S : Average Sales/month

0, : S.D. of Sales

AN ILLUSTRATION

Month : April '93 Warehouse : ... A. Product: Urea

Time Lag (days): Time elapsed between the order placing by

warehouse/stock point and actual delivery of product at the warehouse: 10,

12, 10, 8, 10.

Year

88 89 90 91 92

Total

Sales(s) t000T)

12 15 12 10 11

60

s-s*

0 3 0 -2 - 1

(s-s')~

0 9 0 4 1

14

For 85% of service level the estimated maximum stock for April '93 should

be 17,900T.

This is a very simple and effective model which can be easily adopted

for stock management at field warehouses. This mode was adopted by

fertilizers manufacturing unit2 operating 210 warehouses. Substantial

savings in terms of warehouse space reservation and inventory control was

obtained.

Model I1

1. Warehouses should be classified in to A,B and C category depending

on the through put on the basis of the turnover cumulating to 80% for

415% for B and 5% for C categories.

2. Data pertaining to the lifting pattern ( Tonnes of each product

drawn by fertilizer dealers) during each month of the season be

maintained.

3. Average liftings (X) be calculated for each product and warehouse

locations based on five sample data pertaining to the same month

during the preceding five years.

' Madras Fertilizers Ltd. (1986). Lakshman Rao H.K.

4. Standard deviation s.d. of the data for which the average has been

obtained must me calculated.

The minimum and Maximum inventory levels to be maintained at the

warehouse for the product during the month is given by :

Lower limit: X - s.d multiplied by 1.141

Upper limit: X+ 8.d multiplied by 1.141

5.7 CONCLUSION

In order to make the fertilizer marketing system effective and to

reduce the cost of marketing operations there is scope to adopt quantitative

techniques in the area of planning implementation and control. Marketing

programs and strategies can be evaluated and their relative impacts can be

measured utilizing optimization tools and techniques. Software computer

packages are available in all the areas discussed. In this chapter detailed

discussions of the various quantitative and optimization techniques that can

be adopted for fertilizer marketing system have been made with illustrative

examples.

In this chapter a Transportation model based on L.P. technique has

been discussed. A logistics plan based on least transportation cost for seven

fertilizer factories located in South India has been developed. The advantage

of adopting this plan for minimizing the logistics cost has been brought out.

CHAPTER QUANTITATIVE TECHNIQUES FOR FERTILIZER MARRETING...

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