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CHAPTER VQUANTITATIVE TEC HNIQUES FOR FERTILIZER

MARRETING SYSTEMS

6.1 INTRODUCTION

Ferti lizer industry h as grown tremendously in the la st twenty years .T he inc rea ses in production capacities, utilization of th e installed capacitiesa s also th e increases in the consumption have been phenomenal since 1980.T h e dependence on imports has signif icantly decreased with t he steep growthin the indigenous production capacities although the consumption hasincreased. These are the basic requirements of developing an effectivem ark eti ng system and draw up a n optimization model for logistics. T heavailability of products from indigenous sources can be estimated and therequ irem ent ca n also be forecasted under this environm ent.

Quantitative technique in the area of product mix, consumptionforecasting, inventory control, logistics management can be adapted for costreduction and improved service to farmers.

In this chap ter qua ntitative techniques which can be adopted for saleses tim ati oq inventory control, transportation and warehousing are discussed.

Optimization is the act of obtaining th e best result und er a given se tof resource8 an d con strain ts. Th e goal of optimization is eithe r to minimize orto m axim ize a n objective function un de r a given s e t of conditions.

The objective function contains the variables and the associatedco8tsJprices which should be max imized or minimized.


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An Optimization problem can b e state d as:

Dete rmine X = ( XI., x2.., x3..., ,,) ,which m inimizes f(X)subject to: g (Xi) r 0 or i=1,2,3,4,.....

Li ne ar program ming (L.P) an d Transp ortation P roblem, (T.P) a reoptim ization me thods of Operations Research (O.R.)pplicable for th e so lutionin which th e objective function and the constraints app ear as linear functionsof th e decision variables.6% TRANSPORTATION PROBLEM

In t h e chapter on marketing costs it ha s been brought out th at over 30%of th e tota l m ark etin g cost is accounted for by tra nsp orta tion .

Th e optimization model adopted h as focused on th e cost oftran spo rtati on in moving the fertilizer produc ts from th e fertilizer pla nts tot h e consum ing centers. The objective of th is model i s tominimize th e aggregatecost of transportation.

Transportation problem is an important class of L.P. As the nameindicates th at the T.P minimizes the cost of transp ortation .

T.P. is widely adopted in developing transp orta tion plans for movem entof prod ucts from severa l sources of supply to sev eral consum ing centers a t theleast aggregate cost .C o n c e p t i o n a l Frame W o r k of t h e t r a n s p o r t a t i o n model

Transportation problem (T.P) is an important class of LinearPro gram m ing (L.P.). A trans porta tion problem is one in which t h e objective of


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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(Fertilize r pla nts ) a nd n destina tions (consuming points-centroids). Let beth e availability of product a t plant ai (i = 1 ....m) and bj th e requirement atdest inat ion j (1 ...n). L et Cii be th e cost of tran spo rtati on of fertilizer (u re a)from fertilizer plants (factoried i to centroid j,

T he problem ism nMinimize f = Z Z xiii= 1 j=1

Subject to Z:xu = aj, i = 1, ..... m, m.7 (fe rti liz er factories)j=1mI .. = b., j = 1, ..... n, n =7 1 (Districts)

U Ji = lTota l availability = Total requiremen t

Consistency condition.

In the illustrative example, seven fertilizer factories and seventy onedem and p oints (C entroids) have been chosen as a sample.

Th e purpo se of developing this model for south India is toill us tra te th e need for minimizing th e cost of trans port ation byrationalizing t h e movement. Th e objective is to minimize th e aggregatetra ns po rta tio n costs an d avoid th e crisscross movem ent of fertilizerproducts thro ugh a n rationalized allocation plan.


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Tran spo rtation plays a n important role in the fertil izer marketingaystem.In th e tota l m ark etin g cost transportation alone accounts for 40%'Making th e r ight product available to the farmers a t the r ight place andtim e will b e th e objective of fertilizer m ar ke tin g organizations. Sincetranspor ta t ion cost is quite significant in th e total cost of fertilizerma rketing. T he transportation cost can be minimized by allocating/ movingthe products according to a pre- determined pla n developed based ontransp ortation models.

Tra nsp orta tion models deal with the transportation of products fromth e sou rce of production (fertilizer pl an t) or th e source of supply ( warehouse/port) to a nu m be r of consuming points/ retail outlets1 ultim ate stora ge points.Th e objective of th e model is to satisfy th e dem ands a t f inal destinations,given th e supply constraints a t minimum cost. Th e transportation model canbe formulated as a stan da rd Linear Programming (LP) problem.5.3 THE MODEL

Allocation of ure a from different urea ma nufacturing plants in southIndia to th e pre determ ined consuming centroids (Districts) in south bymin imizing the total transportation costs to illustrate.

Report of the high powered committee on Fertilizer prices.


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Data base: Table No.60Pro duc t ava il abi li ty urea

Source: Fertilizer Marketing News, May 1992.

Ta ble No.61

r

S1.No.

1.2.3.4.5.6.7.

Source: Fertilizer Marketing News, May 1992.

So urc e of supplyMFL. MadrasSPIC. TutiwrinNLC. NeyveliFCI-RamNFCL, KakinadaMCF MangaloreFACT. CochinTotal availability

Requ i remen t( in terms of NPK)Andhra PradeshKarnatakaTamil NaduKeralaTo t a l

The details of the availability and requirement are received by theMinistry of Agriculture GO1 , every season drawing up th e distribution planunder th e essential Commodities Act (ECA).

Availabili ty of ur e aOOOT2925121524954953403302616

(OOOT)143250958392

2616


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The Optimization model has considered

Se ven fert il izer plan ts located in south (Andhra Pradesh, Ka rnata ka,Tam il N adu a nd Kerala) and 71 centroids (demand points).Distan ces from each one of th e fertilizer factories (MFL, SP IC, NLC,

FCI-R, NFCL MC F an d FAC) to each of th e identified de m an d points(Centroids), ha ve been adopted a s weights to obtain cost of tran spor tation.

Sin ce t h e cost of movem ent is directly proportional to th e distancesbetw een th e supply points an d th e sources of supply. This is a balancedtransportation problem.

L et Xij rep res en t th e quan tity of Urea tran sported from factory Pi to th ecentroid Cj : i = 1, .... 71, j = 1 .... 7

T he dista nce between p lant pi to th e centroid Ci be dijObjective function ; Z ( we aggre gate cost of transp ort atio n) = ;I: Xij x dij m ustbe m inimizedSubjected to;Availability : P1 t P2 t P 3 t P 4 t P 5 t P 6 t P 7 = 2616Requi rement : C l + C 2 t C 3 + .............. t C 7 1 =2616


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Table No.65Solution of the Transportation Model

Optimum allocation plan - Centroid wise


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Table No. 54

Solution of the Transportation ModelOptimum allocation plan - Centroid wise


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Table No. 56Solution of the Transportation Model

Optimum allocation plan - Centroid wise


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Table No.56Av.1Lhlllty and requirementh~ been bmhnoed

C o m p a r i s o n o f O p t i m u m a l lo c a ti o n p l a n w i t h E CAS ou r c e of S upp l i e s ( f a c to r i e s )

Dem and point wise allocation ar e given in th e tabl es 48 to 52.

StateTamil NaduKarna takaAndhra PradeshKerala

Source (1)ECA Plan for supply of fertilizer finalized for Kharif 92 underECA, by G OI. Published in Fertilizer Marketing News M ay 92. p 3.

It i s seen from t he analysis and the model th at th e allocation und er ECAsignificantly differs from the optimization model. While the allocation underECA consid ers maximization of supplie s to the s ta te from th e factories locatedin t h e s tate, th e optimization model h as adopted th e least transportation costto mee t th e requirem ent of th e district (Centroids).

ECA (1)FACT, MFC & SPICFACT,SPIC & MCFFACT, FCI-RFACT & SPIC

As p e r M odelMFL, SPIC , FCI-R & FACTMFL, SPIC, FC I-R, MCF & FACTMFL, SPIC, FCI-R, NFCL & FACIFACT & MCF


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The model has minimized the transportat ion cost and has madecomplete allocation of th e availability from t h e seven fertilizer factoriesconsidered for the model and the seventy one demand points in the fourso uth ern sta tes . The model ha s therefore significantly minimized th e Logisticscost.

Thi s model can be adopted for maki ng season wise allocation of pro duc tsfrom fe rtiliz er factories on an all India basis for minimizing th e logistics cost.

6.4 MODEL FOR MEASURING THE RELATIVE INFLUENCE OFSEVERAL FACTORS ON THE CONSUMPTION OFPHOSPHATES (P)

Demand for fertilizers depends on it 's profitability. Among the msjorfactors which can influence farm ers ' response to fertilizer use ar e ; prices offertilizer produ cts a nd price of farm products (1).Other major determ inant ist h e ava ilab ility of irrigat ion facility. Uncertainty of th e profitability is reducedun de r irrigate d conditions availability of credit on tim e is another vital factor.A fertilizer d em an d function had been developed based on six key factors ont h e d a t a for 70-71 to 92-93,Con sumption of P is cruc ial for crop produc tivityamong the Nut r i en t s NPK , h e price of P is the highest.

An analysis ha s been made to est imate th e relat ionship between theconsum ption of P an d six variables: price ratio , rainfall , ratio of irrigateda re a to cropped are a 0(3),Area served by retail outlets , Disb ursem ent of creditRslhect, ratio of are a under HYV o total cropped a re a (X6).

Price rat io = wt. average price of P index of wholesale price of foodgrain s in the previous year . A tim e lag of one year h a s been adopted betw eenvari ation i n price an d th e changes in demand, since most price chan ges havehap pen ed a fter t he fertil izer application is over in a season.


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Regreasion O ut put:

Cons tan t -1.52Sta n d a rd e r ro r of Y Est 0.65No, of observ ation 23De grees of Freedom 60Y - Consumption of P (kghec t )XI - Pric e Ratio& - Rainfall (mm)X3 - % irrigated area to total cropped areaX4 - Are a served by retail outletXc, - Disbursement of Credit (Rs./hect)X6 - % Area HYV to total cropped are aConsum ption of P is given by th e relationship:

E x p l a n a t o r y n o t e a n d I n t e rp r e ta t io n

In order to find out th e relative significance of fac tors affecting th econsu mp tion of Phosp hatic Fertilizers, the Multiple Regression Model h a sbe en developed for th e da ta pertaining to th e period 1970-71 to 93-94(Compiled from Fertilizer News, March 93).

Sin ce th e co-efficient of dete rm inatio n, R~ s 0.99, th e estimatedrelationship betw een consumption of P and th e identified factors X1through X6 explains as high as 99% of th e variation. Con sidering th eestim ates of th e para m eters, irrigation, price, rainfall an d HYV haveeignificant role to play in st imulating the dem and for P.


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Fertilizer use is inelastic to price when the procurement prices of theproduce ie considered. hundred percent increase in price ratio will decreasethe consumption only by 13.5%.

In order to increase the phosphate consumption, as per the MultipleRegression Analysis, HYV have to be promoted, irrigation facilitiesimproved, the price ratio must be made high.

The above analysis suggests that fertilizer use is highly irrigationelastic with positive coefficient.This analysis indicates a significant bearing on policy decisions. Even

if fertilizer prices are raised, a corresponding increase in farm produceprices/procurement prices to maintain the price-ratio will not significantlyresult in decline in fertilizer demand.6.5 SALES FORECASTING SYSTEM

Developing realistic sales estimates is the basic for an effectivemarketing management, particularly the Logistics management.

In fertilizer industry large volumes of sales data are beingcontinuously generated, partly as for monitoring sales performance andpartly to provide monthly returns to Ministry of Agriculture GO1 and tostate govt under ECA statutory requirements. Further The fertilizerAssociation of India compiles Fertilizer Statistics & annual reviewsannually. The regional ofice of the FA1 also publishes statisticspertaining to district levels These valuable data on the fertilizer industryhas hardly been used for developing marketing strategies andprograms and any optimization cases.


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These stati stics ar e valuable inp uts for developing tren ds,rel atiom hipa (correlations) and developing sales (consumption) forecasts a tmicro & mac ro levels.

Experiences over the yea rs indicate th at auto-regression model forshor t term forecasting of sal es provides a good fit.

Projecting demand is an important aspect of fertilizer ma rke tingsystem . Realis tic projection of dem and is essential for developingtranspo rtatio n an d warehousing plans. Demand projection is alsorequired for other marketing efforts; promotion, pricing, productdevelopm ent, etc,.

I t is considered essential to develop simple models forforecasting sa les as reflected by th e respond ents when th is topic w asdiscussedwit h Fertilizer Marketing Executives.

T h e concept of Auto-correlation (functional relation ship auto-regression) implies th at for some products the re exists a correlationbe twe en th e sa m e variables a t different points of time. Th is technique issuited to th e forecas ting of fertilizers. The consumption of fert ilize rsdu rin g th e previous year(s) ha s a great impact on the immediate futureconsumption pattern.

Th is technique is easy to unde rsta nd and apply. It does not call forelabo rate da ta on several variables bu t relays on the recent past trends andmoving d ata. I t is important to normalize the d ata for any un usua lsitu ations such a s restriction of consumption due to non availability ofproducts etc . How ever if such occurrences a re not un usu al nonorma lization is needed. The model will take care.


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For ahort term forecast this method is found to be simple an dad eq ua te. Aftar a gre at deal of checking an d verification, th is me thodwas adopte d for es tim ati ng off ta ke of warehouse-wise product-wisevolumes a t MFL. Th e technique ha s been found eas y to understand andapply. A five year moving da ta is used as th e basis for th e t rends.When th e la test year da ta becomes available the ear l iest year da ta i sdeleted so th a t a constant da ta for five yea rs is available for tren dprojections.

As a sam ple case th e short term projection of consum ption hav ebee n m ad e for each of the southern s ta te s for U rea, based on th e five yea rd at a. D epa rtm ent of agriculture of th e st at e govt can use th is simplemodel for est imat ing th e requirement for th e seasons (K h a ri fk b i ) . Thisca n form a very useful inp ut for zonal conferences to dra w up supplyplans. Th is model at temp ts to minimize th e occasions of shortag es a ndexcess availability. At th e micro level manu facturing un its adopt thi s fordistr ict wise or warehouse-wise or dealer-wise estim ates ofconsumptiordoff take.

A Linear trend function is developed based on th e au toregres sion(tim e serie s) of the form Y=A+ Bt;

When th e projection is made for th e yea r it is split to m onth s basedon the last five year monthly off take.Th e following examples i l lust rates th e m ethod of developing s hort

term sales forecasts sta te wise.


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Table No.67Consumption tren* in South India

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

Year

1987-881988-891989-901990-911991-92

Tamil Nadu

Regression 0utput:for TN

Consumption Urea (000T)

Constant 594.95Std Err of Y Est 25.71585R~ 0.414453No, of Observations 5Degrees of Freedom 3X Coefficient(s) 11.85Std Err of Coef. 8.132066

TN578.9648.5639.8645.8639.5

Consumption function based on time series (linear);Y= 94.95+11.85)(, consumption forecast for the year1992-93 can be obtained by substituting X=6 nd so on ...

KN395.2590.4539.7583.1509.8

kP882.51231.81619.11676.11520.9

KE64.694.988.5106.7113.3


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Constant 417.07Std Err of Y Est 64.21508R~ 0.589975No. of Observations 5Degrees of Freedom 3

X Coefticient(s) 42.19Std Err of Coef. 20.30659

Consumption function based on time series for Karnataka:

Andhra Pradesh

Regression 0utput:for APConstant 869.75Std Err of Y Est 214.2918R~ 0.682560No. of Observations 5Degrees of Freedom 3X Coeficient(s) 172.11St d Err of Coef. 67.76 502

Consumption f un di on for Andhra Pradesh :Y= 869.7 5 +1 72.11 X


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Constant 60.84S t d Err of Y Est 8.868220R~ 0.834824No. of Observations 5Degrees of Freedom 3X Coeficient(s) 10.92S t d E rr of Coef. 2.804377

Consumption function for Kerala:Y=60.84 +10.92XDeveloping sh or t term (one year1 one season ) sal es forecast based on

the se functions will yield useful resu lts for prep aring m arke ting andlogistics pl an by fertilizer organizations.

T hi s concept can be applied for forecasting th e dema nd forwarehouses b a e d on the pas t consumption / off take pattern . Suc hes tim ate s can be used for transportation and w arehouse planning.

Th is technique was adopted by M adras Ferti l izers Ltd, Ma dras (1986)to d raw u p t h e logistics plan and signif icant savin g was accrued.

6.6 INVENTORYMANAGEMENT IN FERTILIZER MARKETING

Inventory is one of th e r iskiest a rea s in logistical ma nag em ent.Com mitment to a particular inventory mix and sub sequ ent allocation toch an ne ls in anticipation of a futu re sales rep res en t th e vortex of logisticaloperation s. W ithout a proper inventory mix problem s of custom er service &rev en ue gene ration would develop.


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Inventory management is critical in marketing operations. Overstocking and stock out situations should be minimized. Inventory controlseeks to achieve a balance between shortage and excess of stocks within aplanning period characterized by risk and uncertainty. Inventorymanagement considers the product mix, geographical spread of themarke tin g territory, seasonality, the order size, safety stock levels, cost ofinventory carrying the self life of products etc. Utilizing the pastconsum ption patte rn of specified market territory, th e costs of storage, orderprocessing costs Economic Order Quantity (EOQ) for each storage locationcan be determined, EOQ =Square root of twice the cost per order processingmultiplied by th e sales volume in units divided by storage cost multiplied bycost per unit (Price).

For a seasonal product like fertilizer Statistical Probability can beadopted. This involves analysing a sample data of lifting of a specificproducts during tile pas t similar seasons in for a given warehouse point toobtain th e average and standard deviation (s.d) values. Average plus orminus 1.96 times the s.d. divided by the square root of the number ofsam ples considered. This provides the best estimates of the possible sales .The other parameters of the EOQ ormula are constants for a given period.This helps in managing the inventory levels on a warehouse to warehousebasis and assures 95% level of confidence of adequacy of stocks and theinventory level is minimum.

Some simple but effective inventory management techniques whichcan be adopted in inventory management at in field warehouses ar ediscussed here. This technique was adopted in a Fertilizer m anufacturingun it in South for inventory control systems in 186 field storage points (1)


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D i s c u s s i o n of s o m e inventory models :

Model I

T h e objective of thi s model is to help main tain ade qua te inventorylevels a t warehouses to service the retailers, cooperatives and farmers;

T h e da ta required for this model is a five yea r m onth wise productwise lifting statistics for th e ware house. The statistics should be updatedevery adopt ing a 5 point moving average technique; add ing th e latest da taan d el iminating th e earl iest da ta and m aintaining the constant sample sizeof 5.T h e level of safety stock can be obtained by ado pting th e following th estatistica l formula:

MODEL FOR OPTIMUM WAREHOUSE STOCKThe model can be adopted for determining the safety stock of

Fertilizer produ cts a t warehouses. Th e level of stock necessary to m eet t hesa les requirem ent a t warehouse location can be estimated by the statisticalformula:

= J R o,~) s ~ ( ~ ~ ~ )where

a, : Inventory requirement for the m onth.R : Average time lag (days) between th e order placed by

warehouselstock point, and th e delivery of produ cts a t th ewarehouse.

a~ : Th e Sta nd ard deviation 6 . D ) of time lag.


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S : Average Sales/month0, : S.D. f Sales

AN ILLUSTRATIONMonth :April '93 Warehouse : ...A.

Product: UreaTime Lag (day s): Time elapsed between the order placing bywarehouse/stock point and actual delivery of product at the warehouse: 10,12,10,8, 0.

Year8889909192

Total

Sales(s)t000T)121512101160

s-s*030-2-1

(s-s')~0904114


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For 85%of service level th e es tim ated max imum stock for April '93 shouldbe 17,900T.

Th is is a very simp le and effective model which can be easily adoptedfor stock man agem ent a t field warehouses. This mode wa s adopted byfertilizers manufa cturing u nit2 operating 210 warehouses. Su bstantialsavings in te rm s of wareh ouse space reservation an d inventory control w asobtained.Model I1

1. W areh ous es should be classified in to A,B and C category dependingon the throug h p ut on the basis of th e turnove r cum ulating to 80% for4 1 5% for B and 5% for C categories.

2. Da ta per ta ining to the l if ting pattern ( Tonnes of each productdra w n by fertilizer dealers) du rin g each m onth of th e season bemaintained.

3. Average liftings (X) be calculated for each product and warehouselocations based on f ive sample da ta pertaining to the same monthdurin g t h e preceding f ive years.

' M adras Ferti l izers Ltd. (1986). akshman Rao H.K.


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4. St an da rd deviation s.d. of the d ata for which th e average has beenobtained must me calculated.T he minimum and M aximum inventory levels to be maintained a t the

wa reho use for th e product during the month is given by :

Lower limit: X - s.d m ultiplied by 1.141Upp er l imit: X+ 8.d multiplied by 1.1415.7 CONCLUSION

In order to mak e th e fertilizer m arketing system effective and toreduce t h e cost of ma rketing operations there is scope to adopt qu antitativ etechniqu es in th e ar ea of planning implementation and control. Mark etingprog ram s an d strateg ies can be evaluated and their relative impacts can bem ea sur ed utilizing optimization tools an d techniques. Software computerpackages a re available in all the a reas discussed. In this chapter detaileddiscussions of th e various quan titative and optimization techniques th a t canbe adopted for fertilizer ma rketing system have been ma de with illustrativeexamples .

In th is chap ter a Transportation model based on L.P. technique ha sbeen discussed. A logistics plan based on least transportation cost for sevenfertilizer factories located in South India h as been developed. Th e ad va nta geof ado pting thi s plan for minimizing the logistics cost ha s been b rought out.

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