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Management of a community storage system: A coal programming model
92
European Journal of OperationalResearch340 (1988) 92-98 North-Holland
Management of a community storage system: A coal programming model Surendra B. SINHA, Somayajula V.C. SASTRY and Rameswar P. M I S R A
Department of Mathematics, lndian Institute of Technology, Kharagpur, 721302 lndia
Abstract: In an agriculture-based country, post-harvest technology plays an important role in the process of development of its economy. The increasing production of foodgrains urges the need for establishment of modern, efficient, community-storage structures. The management of such systems invariable involve multiple objectives. The present paper describes how a linear goal programming model can be developed for such a system. The results are discussed, considering a region under Union Territory of Delhi, India and concluded that the model will give an insight into various activities of the centre and thereby increasing the efficiency and effectiveness of the management through fulfilling the timely needs of the farmer and the industrialist as well. Keywords: Agriculture, storage, management, linear programming, goal programming
1. Introduction In agriculture-based countries like India, postharvest technology plays a crucial role in the wake of economic development of the nation. The hectic losses of foodgrains due to rodents, insects and high-moisture content, deprive the farmer community in getting their due price for their products, and the nation as a whole, although there is a record production of foodgrains by using highyielding methods of crop production, fertilizers, etc. A bumper production of 151.54 million tonnes (1 tonne = 1000 kg = 10 quintals) of foodgrains during 1983-84 against only a 52 million tonnes of 1951-52 has attracted the entire nation to pay their attention towards its preservation and utilization. The increase in the level of foodgrain production has urged the need for developing efficient storage structures and marketing facilities in lifting the economy of the nation. Several studies are made at this juncture, to review the present system of storage and marketing facilities. Khusro (1973) critically reviewed and presented a clear picture of the foodgrain storage situation and also, emphasized the need ReceivedJanuary1986; revisedDecember1986
for developing modern storage system and maintenance of buffer stocks. Bhole and Mahajan (1977) proposed a village panchayat level grain processing and storage facilities by adopting a case study in Maharastra State and presented the cost estimates for a 100 tonne storage facility. Later, in 1979 Government of India formed a National Commission on Agriculture to review the storage and marketing system of foodgrains. The Commission decided to establish a national grid of rural godowns and concluded that the storage losses could be brought down to 2% (which is 1/5th of the present level of losses), if adequate facilities are provided to the farmers. The rural godown will mainly provide storage facility. It may also help the farmer to provide with the credit facility against their stored stock, at concessional rates of interest from the nationalised banks. As these godowns are located in central places, the small and marginal farmers could not utilize this facility. Moreover, most of these godowns are utilized by the Food Corporation of India, big traders and other Co-operatives for the storage of seed, fertilizers etc. Misra et al. (1984, 1985), considered the entire system and proposed a different form of storage facility, called 'Community Storage of Foodgrains', where the farmers can have all the
0377-2217/88/$3.50 © 1988, ElsevierSciencePublishersB.V.(North-Holland)
S.B. Sinha / Management of a community storage system
facilities as in a rural godown and in addition to that, drying, cleaning and marketing facilities provided in a very nearby locality. For the ease of the management of the system they proposed a linear programming (LP) technique to have a look on the arrival, withdrawal, purchase and selling patterns of the grain and on the profit for the financial viability of the centre. Further, referring particularly in the context of an industrially developed region, the industries based on agricultural products like rice mills, flour mills, etc., could not run their mills throughout the year due to a lack of availability of raw materials and also due to a lack of keeping buffer stocks for their future use. As a result, the market for foodgrain is affected and unstabilized. Uma (1971) and Misra (1985) have reviewed and presented a flow chart of the entire marketing system of foodgrains. Keeping in view the above problems, Misra et al. (1984) further propose a similar alternative model for the maintenance of the system. In all these cases above, they considered the single objective of optimization of the profit of the centre only. Since it is a Community Foodgrain Storage, the sole optimization of profit may not be suited. It is desirable to consider several objectives other than maximization of profit, for example minimization of storage and handling losses, maintenance of buffer stocks or other socially useful objectives. These objectives may be of conflicting and noncommensurable nature. At this juncture, the traditional LP technique may not yield a satisfying solution for the management. Goal programming (GP), which can deal efficiently with such multiple, conflicting and noncommensurable objectives, presents a satisficing solution to the management of the centre. It was originated by Charnes and Cooper (1961) in their research of an extention of LP. Later, it has been extensively studied by several other authors and it is worth mentioning the works of Yuji Ijiri (1965), Lee (1972, 1976), Ignizio (1976), Hwang and Masud (1979). Now it is also being applied to various fields of study. For reference one can have a glance at Kornbluth (1975), Ignizio (1976), Lee (1972), Thomas Lin (1980) etc. However, there are hardly any applications to agricultural planning. In this paper it is described how the G P technique can be applied in agricultural planning. Sections 2 and 3 will present the modelling for this study.
93
2. The model
The present study is based on the survey undertaken at the industrially developed region of Union Territory of Delhi. The following assumptions are made: 2.1. The system
(a) Wheat is considered as the major crop grown in this region; accordingly, the centre will store wheat and its varieties only. (b) Following Government policy a centre should handle 200 to 1000 tonnes of grain. In the present study, we considered the maximum arrival of 1000 tonnes of wheat only. (c) To coincide with the wheat harvesting season, a marketing year is taken from April to March. (d) On average, the marketable surplus of the farmers of the region is assumed to be 50% of the grain arrived at the centre and the rest of the 50% of the grain may be withdrawn by the farmers in phases. (e) On average, the storage and handling losses of grain is permitted up to 2% of the total arrival. (f) It is assumed that the centre will always maintain huge stocks. (g) It is also assumed that the centre will give preference to retail sale in open market rather than fixed sale to the industry in order to help the small and marginal farmers and also to ensure price stability. 2.2. Other assumptions Arrival (h) There will be large arrival (more than 75%) of grain during the harvesting season, i.e. in the months of April and May. After the rainy season there may be some arrival. Before the harvesting season the arrival is nil. Withdrawal (i) There will be no withdrawal of grain in the first two months of harvesting season and more than 50% after rainy season and in other months more or less uniform withdrawal by the farmers is assumed. Farmers' sale (j) There will be more than 50% sale by the
S.B. Sinha / Management of a community storage system
94
farmers during harvesting season and at the time of high price. In other months uniform sale is assumed.
d+/dt
: Represents a deviational variable i.e.,
positive/negative deviation from t-th goal; it is assumed that d +, d;- >/0 and d + • d;- = 0 for all t.
Centres' sale
(k) The Centre's sale will be of two kinds. One is a fixed amount of grain every month to industries and the other one is the sale by the centre on open market. The price for the fixed amount of grain is determined by the Government i.e., Rs. 2 0 8 / - per quintal at 1983 level and the other sale at the whole sale market prices i.e., for the purpose of computations, we have taken the prices at 1983 level. The retail market sale can vary according to market prices.
3. Formulation of goal constraints and system constraints
For the computational ease only one variety of a single major crop, namely wheat, is considered and hence the suffix j is omitted in framing the model. The functional relationships between the variables have been established based on the assumptions stated in the above section and formed the associated goal and system constraints sequentially as hereunder.
The net storage
(1) In any month the net stock at the centre will be a function of previous months stock, arrival, withdrawal and sale of grain by the centre in that month. (m) Without loss of generality, all the variables of the model are assumed to be non-negative. 2.3. The variables
Arrival of grain in the i-th month of the j-th crop in quintals. No : Net stored grain by the centre in the i-th month of the j-th crop in quintals. YE.j : Withdrawal by farmers in the i-th month of the j-th crop in quintals. YPij : Sale by farmers in the i-th month of the j-th crop in quintals. YMij : Fixed sale to industries by the centre in i-th month of the j-th crop in quintals. YRij : Retail sale in open market by centre in the i-th month of the j-th crop in quintals. Servicing charges for cleaning, etc. (Re. C 1 / - per quintal is assumed for computational study). Rental charges for storage of grain (Re. d 1 / - per quintal per month is assumed for computational study). Wholesale market price of grain in the eij i-th month for the j-th crop per quintal. em j " Fixed price by the Government for industrial sale for the j-th crop per quintal (Rs. 2 0 8 / - per quintal at 1983 price level). xij
:
3.1. Goal constraints
The goal constraint equations are formulated by associating a positive and negative deviational variable to each of the functional relationships. In all summations i varies from 1 to 12 (corresponding to April to March) unless otherwise stated explicitly. (i) Arrival. The goal constraint equations (1) and (2) relate to the bulk arrival of wheat at the centre, while the equations (3) to (9) represent the uniform arrival in all other months except in the pre-harvest period--March. 0.75 E x i -
=O,
(2)
x6 + d3 - d~- = 0,
(3)
xa - x2 + dy - d ;
0.01 Z x , -
x6-xi+dt-d+=O, X12 nt- d 9 -
(1)
Xl - x2 q- d l - d? = O,
d~
i=t+3;
t = 4 . . . . . 8, (4)-(8) (9)
= 0.
(ii) Withdrawal. The goal constraint equations (10), (16), (19) and (21) relate to the bulk withdrawal pattern by the farmers during the post-rainy season and pre-harvest periods, while the other equations represent the uniform withdrawal of wheat in other periods. 0.50 Z YFi - YF6 - YF? - YF, o - YF11 + d~0 - d?0 = 0, YF,+d~-d~=0
(10) fori=l,2;
t=11,12, (11)-(12)
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S.B. Sinha / Management of a community storage system
0.01 E Y F , - Y F 3 + d]-3 - d~-3 = 0, YF 3-YFi+d~--d
(13)
+ =0,
for i = 4, 5, 12; t = 14, 15, 22, Y F 6 + YF 7 - YFlo
--
Y F u + dl-6 - -
(14),(15),(22) d~- 6 =
0,
(16)
- YE~ + YFs + d~-7 - d~-7 = O,
(17)
- Y F ~ + YF10 + d~8 - d~8 = 0,
(18)
Y F 6 - Y F 7 + d~-9 - d~9 = 0,
(19)
YF8 - Y F 9 + d2o = 0,
(20)
YFlo - Y F u + d2~ - d2+~ = 0.
(21)
(iii) Purchase by the centre. The goal constraint equations (23) through (26) relate to the bulk selling pattern of wheat by the farmers to the centre during the i m m e d i a t e post-harvest and at the time of high-price seasons. The other equations represent some a m o u n t of crop sale in the remaining months. 0.50 Y'~YP, - YP, - YP2 - Yelo - Y e u (23)
+ d23 - d2+3 = O,
YP, + YP2 - YPlo - Y P u + d~4 - d2+4= 0,
(24)
YP, - YP2 + d25 - d2+s = 0,
(25)
YP, o - Y P u + d26 - d~-6 = 0,
(26)
net storage requirements of the crop in every month. Also the goal ensures the buffer stock m a i n t e n a n c e objective and helps in determining the optimal storage capacity. x, + N~_ 1 - N, - YF, - Y M , -
Y K + d? - d + = 0
for i = 1 . . . . . 12; t = 59 . . . . . 70.
(59)-(70)
(vii) Profit function. If we observe the centre's income and expenditure pattern, the profit function of the centre can be derived as follows. Inc o m e to the centre is through the service, rent and sale and the expenditure is through service, maintenance of the grains and on farmer's payment. H e n c e the profit function can be seen as mathematically: ZVMi(em
+ d) + E(YR,-
YP,)(e, + d ) .
A target value of Rs. 100 0 0 0 / - p.a. is assigned to the profit function and forms the goal constraint as hereunder. Y'~YM,(e m + d ) + E ( Y 1 % - Y ~ ) ( e ,
+ d)
(71)
+ d ~ - dv~ = 100000.
3.2. The system constraints 0.01 E Y P i - YP3 + d27 - d~7 YP3-YP~ +dt-
=
0,
(27)
d+ = 0
for i = 4 . . . . ,9, 12, t = 28 . . . . . 34.
(28)-(34)
(iv) Centre's fixed sale. Similarly, the selling pattern of wheat by the centre to the agro-industries is represented by the equations (35) through (46), while the other goal constraint equations (47) through (58) relate to the selling pattern of wheat in open market. The quantity of sale m a y vary depending u p o n prices. 0.01 E Y M , -
Y M , + d35 - dr5 = 0,
Y M , - Y M i + d / - d + = 0, fori=2
The assumptions on the system as stated in Section 2.1 above are m o u l d e d mathematically to f o r m the system constraints of the model. Alternatively these are also called absolute rigid goals of the m a n a g e m e n t . ~ x i = 10000,
(72)
- 0 . 5 0 E x , + E Y F , >~ 0,
(73)
- 0 . 5 0 ~_,x i + E Y P ~ ~< 0,
(74)
(35)
ZX
i --
Z Y F , - Z Y P s = 0,
(75)
(36)-(46)
EX
i --
~ Y F i - Y'~YM~- ~ Y R , >/0,
(76)
- 0.02 E x , + EYe, - E Y M , -
. . . . . 12; t = 3 6 . . . . . 46
EYR
(77)
(v) Centre's retail sale. 0.01 E Y K
- Y K + d7 - d,+ = 0
= 0,
(47)-(58)
ZYMi-
ZYR/~
(78)
O,
for i = 1 . . . . . 12; t = 4 7 . . . . . 58. (vi) Net storage at the centre. T h e goal constraint equations (59) through (70) determine the
and the non-negativity restrictions Xi, YFi, YPi, Y M i, YR, >1 0
for all i,
(79)
S.B. Sinha / Management of a community storage system
96 and
d+t, d t > l O ,
dt+ . d ~ - = 0
for a l l t .
(80)
Table 1 The arrival, withdrawal and purchase pattern of grain in each month at the storage centre Month
Arrival of grain
Withdrawalof grain by farmers
Centre's purchase
April May June July August September October November December January February march
3750.00 3750.00 0.00 0.00 0.00 416.67 416.67 416.67 416.67 416.67 416.67 0.00
0.00 0.00 416.67 416.67 416.67 625.00 625.00 416.67 416.67 625.00 625.00 416.67
625.00 625.00 312.50 312.50 312.50 312.50 312.50 312.50 312.50 625.00 625.00 312.50
3.3. The achievement function In goal p r o g r a m m i n g the model's achievem e n t / o b j e c t i v e function will be always of the minimization type and it consists of the deviational variables in accordance with a preemptive priority ranking i.e., in the order Pk >>> Pk+l, for all k = 1, 2 . . . . etc. A positive deviational variable for the underachievement of the goal, a negative deviational variable for the overachievement of the goal and b o t h positive and negative deviational variables for the exact achievement of the goal will be present in the achievement function b y assigning the priority structure as hereunder. However, the system constraints will have highest priority during the process of optimization. P~ : To ensure the needs of the farmers. : To see the farmers to get their rightful share of returns on their produce. : To ensure the customers from price-threat or market stabilization. : To see the industries based on foodgrains to maintain their production run continuously. : The Centre maintains some stocks. : To meet the N a t i o n ' s sudden and unforeseen needs. P2 : Maximization of profit to the centre.
first two m o n t h s after the harvesting and the threshing season, but there is some withdrawal even in the rainy season for their personal cons u m p t i o n / u s e . After the monsoon, again the withdrawal will increase and also in J a n u a r y and F e b r u a r y and in other months it is evenly distributed. There will be a large sale of wheat in the first two months, i.e. immediately after harvesting season, to meet their financial needs and since the prices are high in the months of J a n u a r y and F e b r u a r y to ensure profits the sale quantity is more. In the remaining months the a m o u n t of sale is evenly distributed. F r o m Table 2 it is observed that every m o n t h
4. Results and discussion The model developed was run on a Burroughs6700 series and the result obtained is shown in Table 1. All the figures in the tables are in quintals. Table 1 depicts the arrival and withdrawal pattern of wheat at the centre. It is observed that the m a x i m u m arrival of wheat is in the first two months, i.e., immediately after the harvesting season. Because the next three m o n t h s are rainy season, no farmer would like to bring his p r o d u c e to the centre and again this gives time to the centre to process the bulky arrival of first two months. F r o m September to F e b r u a r y the arrival of wheat is evenly distributed and in the last m o n t h no m o r e grain is expected at the centre. There will be no withdrawal of wheat in the
Table 2 The selling pattern by the centre and the net storage requirement of the centre at the storage centre Month
Fixed sale
Retail sale
April May June July August September October November December January February March
200.00 24.00 200.00 24.00 200.00 24.00 200.00 24.00 2 0 0 . 0 0 24.00 199.99 24.00 200.00 24.00 200.00 24.00 200.00 24.00 200.00 2135.99 200.00 24.00 200.00 24.00
Total storage Net storage requirement requirement 3750.00 7276.00 6411.33 5770.66 5129.99 5546.66 5114.33 4682.00 4458.00 4234.00 1689.67 1257.33
3526.00 7051.99 6411.33 5770.66 5129.99 4697.66 4265.33 4041.33 3817.33 1273.00 840.66 200.00
S.B. Sinha / Management of a community storage system
there will be a fixed sale of wheat to industries by the centre and uniformly some amount of wheat to the open market. It is observed that in January there will be large selling by the centre, i.e. at the time of high price, to ensure the price stabilization and to earn some profits for its commercial viability. It is observed that the m a x i m u m net storage requirement by the centre is given by 7052 quintals, that is, about 70.5% of total grain to be handled at the centre and the percentage of occupancy of storage capacity is more than 60% of the net storage upto December. The remaining months give the centre time to clean the storage and to prepare for the forthcoming arrivals. From Table 3 it is observed that the values of the deviational variables are present in the final optimal solution of the problem. All other deviational variables are zero. F r o m these values the actual values of the goals are obtained by adding/subtracting correspondingly the negative/ positive deviation from the aspired level of that particular goal. Accordingly, the actual values of the goals are also presented. As far as the goals of the Management are concerned it has achieved all at the first priority level. At the second priority level, it has achieved all the targets of the centre and ensured the farmers to get their due price for their products, industrialists to run their industries throughout the year and it has ensured larger amounts of storage of wheat for Nation's sudden and unforeseen needs of the society. But it also resulted in an underachievement of profit of the centre. The actual profit of the centre has been kept at Rs. 43 1 8 3 / i.e., Rs. 4.32 per quintal. Although the profit per quintal is marginal, as it is a community storage centre, more profit earning is not the main aim Table 3 Values of deviational variables and the actual value of the goals S1. no.
Deviational variable
Value
Actual value of the goal
1 2 3 4 5 6 7
d3 dis d(8 d25 d3-5 d6s d71
316.67 366.67 208.33 252.50 176.00 2111.99 56817.00
416.67 416.67 625.00 312.50 200.00 2135.99 43183.00
97
and it has to meet the other important objectives of the nation.
5. Conclusions For the Union Territory of Delhi it is concluded that there is a definite need for a series of such multi-objective storage facilities, having a capacity of 705.2 tonnes for the 1000 tonnes total arrival of wheat to the centre. The system presented here promised the fulfilment of the needs of the farmer, consumer and the industrialist in running their industry throughout the year. The model thus developed can be used by the management of any such similar storage system of any other crop(s) and , / i t s varieties of any other region after making an in-depth study over the production and processing of material and also the marketing system of that region. The model also yields optimum storage capacity of the centre. In a similar pattern the decision manager of the system can incorporate some more goals, or he can review the priority structure or review the input data in the model. F r o m the solution of the model, the management of the storage centre can have an insight in the achievement of various levels of the objectives/goals, which helps for the efficient running of the centre. Finally, this paper concludes with the efficiency and potentiality of the goal programming technique in agricultural planning.
References Bhole, N.G., and Mahajan, R.B. (1977), "Village panchayat level grain processing and storage facilities for Maharastra', Technical report, Indian Institute of Technology, Kharagput, India. Charnes, A., and Cooper, W.W. (1961), Management Models and Industrial Application of Linear Programming, Wiley, New York. Hwang, C.L., and Masud, A.S.M. (1979), Multiple objective Decision Making-- Methods and Applications, Lecture notes in Economics and Mathematical Systems 164, Springer, Berlin. Ignizio, J.P. (1976), Goal Programming and Extensions, Lexington Books, Lexington, MA. Ignizio, J.P. (1978), "A review of goal programming: a tool for multiobjective analysis", Journal of the Operational Research Society, 29 (11), 1109-1119. Khusro, A.M. (1973), Buffer Stocks and Storage of Foodgrains in India, Tata/McGraw-Hill, New Delhi.
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Kornbluth, J.S.H. (9175), "A survey of goal programming", OMEGA 1, 193-205. Lee, S.M. (1972), Goal Programming for Decision Analysis, Auerbach, Philadelphia, PA. Lee, S.M. (1976), Linear Optimization for Management, Petrocelli, New York. Misra, R.P., Bhole, N.(3., Sastry, S.V.C., and Sinha, S.B. (1984), "A new policy for storage and marketing of foodgrains--A case for system dynamics application", Proc. of National Seminar on System Dynamics, IIT, Kharagpur, India. Misra, R.P., Sastry, S.V.C., Sinha, S.B. and Bhole, N.G. (9185), "Optimization of foodgrain storage structures", Proc. of H
Int. Conf. on Computer Aided Analysis and Design in Civil Engineering, University of Roorkee, India. Misra, R.P. (1985), "Community storage of foodgrains--An OR approach", unpubfished thesis submitted to I.I.T., Kharagpur. Thomas Lin, W. (1980), "A survey of goal programming applications", OMEGA 8 (1) 115-117. Uma, J. Lele (1971), Foodgrain Marketing in I n d i a - Private Performance and Public Policy, Cornell University Press, London. Yuri, ljiri (1965), Management Goal and Accounting for Control, Rand-Mc Nally, Chicago, IL.
European Journal of OperationalResearch340 (1988) 92-98 North-Holland
Management of a community storage system: A coal programming model Surendra B. SINHA, Somayajula V.C. SASTRY and Rameswar P. M I S R A
Department of Mathematics, lndian Institute of Technology, Kharagpur, 721302 lndia
Abstract: In an agriculture-based country, post-harvest technology plays an important role in the process of development of its economy. The increasing production of foodgrains urges the need for establishment of modern, efficient, community-storage structures. The management of such systems invariable involve multiple objectives. The present paper describes how a linear goal programming model can be developed for such a system. The results are discussed, considering a region under Union Territory of Delhi, India and concluded that the model will give an insight into various activities of the centre and thereby increasing the efficiency and effectiveness of the management through fulfilling the timely needs of the farmer and the industrialist as well. Keywords: Agriculture, storage, management, linear programming, goal programming
1. Introduction In agriculture-based countries like India, postharvest technology plays a crucial role in the wake of economic development of the nation. The hectic losses of foodgrains due to rodents, insects and high-moisture content, deprive the farmer community in getting their due price for their products, and the nation as a whole, although there is a record production of foodgrains by using highyielding methods of crop production, fertilizers, etc. A bumper production of 151.54 million tonnes (1 tonne = 1000 kg = 10 quintals) of foodgrains during 1983-84 against only a 52 million tonnes of 1951-52 has attracted the entire nation to pay their attention towards its preservation and utilization. The increase in the level of foodgrain production has urged the need for developing efficient storage structures and marketing facilities in lifting the economy of the nation. Several studies are made at this juncture, to review the present system of storage and marketing facilities. Khusro (1973) critically reviewed and presented a clear picture of the foodgrain storage situation and also, emphasized the need ReceivedJanuary1986; revisedDecember1986
for developing modern storage system and maintenance of buffer stocks. Bhole and Mahajan (1977) proposed a village panchayat level grain processing and storage facilities by adopting a case study in Maharastra State and presented the cost estimates for a 100 tonne storage facility. Later, in 1979 Government of India formed a National Commission on Agriculture to review the storage and marketing system of foodgrains. The Commission decided to establish a national grid of rural godowns and concluded that the storage losses could be brought down to 2% (which is 1/5th of the present level of losses), if adequate facilities are provided to the farmers. The rural godown will mainly provide storage facility. It may also help the farmer to provide with the credit facility against their stored stock, at concessional rates of interest from the nationalised banks. As these godowns are located in central places, the small and marginal farmers could not utilize this facility. Moreover, most of these godowns are utilized by the Food Corporation of India, big traders and other Co-operatives for the storage of seed, fertilizers etc. Misra et al. (1984, 1985), considered the entire system and proposed a different form of storage facility, called 'Community Storage of Foodgrains', where the farmers can have all the
0377-2217/88/$3.50 © 1988, ElsevierSciencePublishersB.V.(North-Holland)
S.B. Sinha / Management of a community storage system
facilities as in a rural godown and in addition to that, drying, cleaning and marketing facilities provided in a very nearby locality. For the ease of the management of the system they proposed a linear programming (LP) technique to have a look on the arrival, withdrawal, purchase and selling patterns of the grain and on the profit for the financial viability of the centre. Further, referring particularly in the context of an industrially developed region, the industries based on agricultural products like rice mills, flour mills, etc., could not run their mills throughout the year due to a lack of availability of raw materials and also due to a lack of keeping buffer stocks for their future use. As a result, the market for foodgrain is affected and unstabilized. Uma (1971) and Misra (1985) have reviewed and presented a flow chart of the entire marketing system of foodgrains. Keeping in view the above problems, Misra et al. (1984) further propose a similar alternative model for the maintenance of the system. In all these cases above, they considered the single objective of optimization of the profit of the centre only. Since it is a Community Foodgrain Storage, the sole optimization of profit may not be suited. It is desirable to consider several objectives other than maximization of profit, for example minimization of storage and handling losses, maintenance of buffer stocks or other socially useful objectives. These objectives may be of conflicting and noncommensurable nature. At this juncture, the traditional LP technique may not yield a satisfying solution for the management. Goal programming (GP), which can deal efficiently with such multiple, conflicting and noncommensurable objectives, presents a satisficing solution to the management of the centre. It was originated by Charnes and Cooper (1961) in their research of an extention of LP. Later, it has been extensively studied by several other authors and it is worth mentioning the works of Yuji Ijiri (1965), Lee (1972, 1976), Ignizio (1976), Hwang and Masud (1979). Now it is also being applied to various fields of study. For reference one can have a glance at Kornbluth (1975), Ignizio (1976), Lee (1972), Thomas Lin (1980) etc. However, there are hardly any applications to agricultural planning. In this paper it is described how the G P technique can be applied in agricultural planning. Sections 2 and 3 will present the modelling for this study.
93
2. The model
The present study is based on the survey undertaken at the industrially developed region of Union Territory of Delhi. The following assumptions are made: 2.1. The system
(a) Wheat is considered as the major crop grown in this region; accordingly, the centre will store wheat and its varieties only. (b) Following Government policy a centre should handle 200 to 1000 tonnes of grain. In the present study, we considered the maximum arrival of 1000 tonnes of wheat only. (c) To coincide with the wheat harvesting season, a marketing year is taken from April to March. (d) On average, the marketable surplus of the farmers of the region is assumed to be 50% of the grain arrived at the centre and the rest of the 50% of the grain may be withdrawn by the farmers in phases. (e) On average, the storage and handling losses of grain is permitted up to 2% of the total arrival. (f) It is assumed that the centre will always maintain huge stocks. (g) It is also assumed that the centre will give preference to retail sale in open market rather than fixed sale to the industry in order to help the small and marginal farmers and also to ensure price stability. 2.2. Other assumptions Arrival (h) There will be large arrival (more than 75%) of grain during the harvesting season, i.e. in the months of April and May. After the rainy season there may be some arrival. Before the harvesting season the arrival is nil. Withdrawal (i) There will be no withdrawal of grain in the first two months of harvesting season and more than 50% after rainy season and in other months more or less uniform withdrawal by the farmers is assumed. Farmers' sale (j) There will be more than 50% sale by the
S.B. Sinha / Management of a community storage system
94
farmers during harvesting season and at the time of high price. In other months uniform sale is assumed.
d+/dt
: Represents a deviational variable i.e.,
positive/negative deviation from t-th goal; it is assumed that d +, d;- >/0 and d + • d;- = 0 for all t.
Centres' sale
(k) The Centre's sale will be of two kinds. One is a fixed amount of grain every month to industries and the other one is the sale by the centre on open market. The price for the fixed amount of grain is determined by the Government i.e., Rs. 2 0 8 / - per quintal at 1983 level and the other sale at the whole sale market prices i.e., for the purpose of computations, we have taken the prices at 1983 level. The retail market sale can vary according to market prices.
3. Formulation of goal constraints and system constraints
For the computational ease only one variety of a single major crop, namely wheat, is considered and hence the suffix j is omitted in framing the model. The functional relationships between the variables have been established based on the assumptions stated in the above section and formed the associated goal and system constraints sequentially as hereunder.
The net storage
(1) In any month the net stock at the centre will be a function of previous months stock, arrival, withdrawal and sale of grain by the centre in that month. (m) Without loss of generality, all the variables of the model are assumed to be non-negative. 2.3. The variables
Arrival of grain in the i-th month of the j-th crop in quintals. No : Net stored grain by the centre in the i-th month of the j-th crop in quintals. YE.j : Withdrawal by farmers in the i-th month of the j-th crop in quintals. YPij : Sale by farmers in the i-th month of the j-th crop in quintals. YMij : Fixed sale to industries by the centre in i-th month of the j-th crop in quintals. YRij : Retail sale in open market by centre in the i-th month of the j-th crop in quintals. Servicing charges for cleaning, etc. (Re. C 1 / - per quintal is assumed for computational study). Rental charges for storage of grain (Re. d 1 / - per quintal per month is assumed for computational study). Wholesale market price of grain in the eij i-th month for the j-th crop per quintal. em j " Fixed price by the Government for industrial sale for the j-th crop per quintal (Rs. 2 0 8 / - per quintal at 1983 price level). xij
:
3.1. Goal constraints
The goal constraint equations are formulated by associating a positive and negative deviational variable to each of the functional relationships. In all summations i varies from 1 to 12 (corresponding to April to March) unless otherwise stated explicitly. (i) Arrival. The goal constraint equations (1) and (2) relate to the bulk arrival of wheat at the centre, while the equations (3) to (9) represent the uniform arrival in all other months except in the pre-harvest period--March. 0.75 E x i -
=O,
(2)
x6 + d3 - d~- = 0,
(3)
xa - x2 + dy - d ;
0.01 Z x , -
x6-xi+dt-d+=O, X12 nt- d 9 -
(1)
Xl - x2 q- d l - d? = O,
d~
i=t+3;
t = 4 . . . . . 8, (4)-(8) (9)
= 0.
(ii) Withdrawal. The goal constraint equations (10), (16), (19) and (21) relate to the bulk withdrawal pattern by the farmers during the post-rainy season and pre-harvest periods, while the other equations represent the uniform withdrawal of wheat in other periods. 0.50 Z YFi - YF6 - YF? - YF, o - YF11 + d~0 - d?0 = 0, YF,+d~-d~=0
(10) fori=l,2;
t=11,12, (11)-(12)
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S.B. Sinha / Management of a community storage system
0.01 E Y F , - Y F 3 + d]-3 - d~-3 = 0, YF 3-YFi+d~--d
(13)
+ =0,
for i = 4, 5, 12; t = 14, 15, 22, Y F 6 + YF 7 - YFlo
--
Y F u + dl-6 - -
(14),(15),(22) d~- 6 =
0,
(16)
- YE~ + YFs + d~-7 - d~-7 = O,
(17)
- Y F ~ + YF10 + d~8 - d~8 = 0,
(18)
Y F 6 - Y F 7 + d~-9 - d~9 = 0,
(19)
YF8 - Y F 9 + d2o = 0,
(20)
YFlo - Y F u + d2~ - d2+~ = 0.
(21)
(iii) Purchase by the centre. The goal constraint equations (23) through (26) relate to the bulk selling pattern of wheat by the farmers to the centre during the i m m e d i a t e post-harvest and at the time of high-price seasons. The other equations represent some a m o u n t of crop sale in the remaining months. 0.50 Y'~YP, - YP, - YP2 - Yelo - Y e u (23)
+ d23 - d2+3 = O,
YP, + YP2 - YPlo - Y P u + d~4 - d2+4= 0,
(24)
YP, - YP2 + d25 - d2+s = 0,
(25)
YP, o - Y P u + d26 - d~-6 = 0,
(26)
net storage requirements of the crop in every month. Also the goal ensures the buffer stock m a i n t e n a n c e objective and helps in determining the optimal storage capacity. x, + N~_ 1 - N, - YF, - Y M , -
Y K + d? - d + = 0
for i = 1 . . . . . 12; t = 59 . . . . . 70.
(59)-(70)
(vii) Profit function. If we observe the centre's income and expenditure pattern, the profit function of the centre can be derived as follows. Inc o m e to the centre is through the service, rent and sale and the expenditure is through service, maintenance of the grains and on farmer's payment. H e n c e the profit function can be seen as mathematically: ZVMi(em
+ d) + E(YR,-
YP,)(e, + d ) .
A target value of Rs. 100 0 0 0 / - p.a. is assigned to the profit function and forms the goal constraint as hereunder. Y'~YM,(e m + d ) + E ( Y 1 % - Y ~ ) ( e ,
+ d)
(71)
+ d ~ - dv~ = 100000.
3.2. The system constraints 0.01 E Y P i - YP3 + d27 - d~7 YP3-YP~ +dt-
=
0,
(27)
d+ = 0
for i = 4 . . . . ,9, 12, t = 28 . . . . . 34.
(28)-(34)
(iv) Centre's fixed sale. Similarly, the selling pattern of wheat by the centre to the agro-industries is represented by the equations (35) through (46), while the other goal constraint equations (47) through (58) relate to the selling pattern of wheat in open market. The quantity of sale m a y vary depending u p o n prices. 0.01 E Y M , -
Y M , + d35 - dr5 = 0,
Y M , - Y M i + d / - d + = 0, fori=2
The assumptions on the system as stated in Section 2.1 above are m o u l d e d mathematically to f o r m the system constraints of the model. Alternatively these are also called absolute rigid goals of the m a n a g e m e n t . ~ x i = 10000,
(72)
- 0 . 5 0 E x , + E Y F , >~ 0,
(73)
- 0 . 5 0 ~_,x i + E Y P ~ ~< 0,
(74)
(35)
ZX
i --
Z Y F , - Z Y P s = 0,
(75)
(36)-(46)
EX
i --
~ Y F i - Y'~YM~- ~ Y R , >/0,
(76)
- 0.02 E x , + EYe, - E Y M , -
. . . . . 12; t = 3 6 . . . . . 46
EYR
(77)
(v) Centre's retail sale. 0.01 E Y K
- Y K + d7 - d,+ = 0
= 0,
(47)-(58)
ZYMi-
ZYR/~
(78)
O,
for i = 1 . . . . . 12; t = 4 7 . . . . . 58. (vi) Net storage at the centre. T h e goal constraint equations (59) through (70) determine the
and the non-negativity restrictions Xi, YFi, YPi, Y M i, YR, >1 0
for all i,
(79)
S.B. Sinha / Management of a community storage system
96 and
d+t, d t > l O ,
dt+ . d ~ - = 0
for a l l t .
(80)
Table 1 The arrival, withdrawal and purchase pattern of grain in each month at the storage centre Month
Arrival of grain
Withdrawalof grain by farmers
Centre's purchase
April May June July August September October November December January February march
3750.00 3750.00 0.00 0.00 0.00 416.67 416.67 416.67 416.67 416.67 416.67 0.00
0.00 0.00 416.67 416.67 416.67 625.00 625.00 416.67 416.67 625.00 625.00 416.67
625.00 625.00 312.50 312.50 312.50 312.50 312.50 312.50 312.50 625.00 625.00 312.50
3.3. The achievement function In goal p r o g r a m m i n g the model's achievem e n t / o b j e c t i v e function will be always of the minimization type and it consists of the deviational variables in accordance with a preemptive priority ranking i.e., in the order Pk >>> Pk+l, for all k = 1, 2 . . . . etc. A positive deviational variable for the underachievement of the goal, a negative deviational variable for the overachievement of the goal and b o t h positive and negative deviational variables for the exact achievement of the goal will be present in the achievement function b y assigning the priority structure as hereunder. However, the system constraints will have highest priority during the process of optimization. P~ : To ensure the needs of the farmers. : To see the farmers to get their rightful share of returns on their produce. : To ensure the customers from price-threat or market stabilization. : To see the industries based on foodgrains to maintain their production run continuously. : The Centre maintains some stocks. : To meet the N a t i o n ' s sudden and unforeseen needs. P2 : Maximization of profit to the centre.
first two m o n t h s after the harvesting and the threshing season, but there is some withdrawal even in the rainy season for their personal cons u m p t i o n / u s e . After the monsoon, again the withdrawal will increase and also in J a n u a r y and F e b r u a r y and in other months it is evenly distributed. There will be a large sale of wheat in the first two months, i.e. immediately after harvesting season, to meet their financial needs and since the prices are high in the months of J a n u a r y and F e b r u a r y to ensure profits the sale quantity is more. In the remaining months the a m o u n t of sale is evenly distributed. F r o m Table 2 it is observed that every m o n t h
4. Results and discussion The model developed was run on a Burroughs6700 series and the result obtained is shown in Table 1. All the figures in the tables are in quintals. Table 1 depicts the arrival and withdrawal pattern of wheat at the centre. It is observed that the m a x i m u m arrival of wheat is in the first two months, i.e., immediately after the harvesting season. Because the next three m o n t h s are rainy season, no farmer would like to bring his p r o d u c e to the centre and again this gives time to the centre to process the bulky arrival of first two months. F r o m September to F e b r u a r y the arrival of wheat is evenly distributed and in the last m o n t h no m o r e grain is expected at the centre. There will be no withdrawal of wheat in the
Table 2 The selling pattern by the centre and the net storage requirement of the centre at the storage centre Month
Fixed sale
Retail sale
April May June July August September October November December January February March
200.00 24.00 200.00 24.00 200.00 24.00 200.00 24.00 2 0 0 . 0 0 24.00 199.99 24.00 200.00 24.00 200.00 24.00 200.00 24.00 200.00 2135.99 200.00 24.00 200.00 24.00
Total storage Net storage requirement requirement 3750.00 7276.00 6411.33 5770.66 5129.99 5546.66 5114.33 4682.00 4458.00 4234.00 1689.67 1257.33
3526.00 7051.99 6411.33 5770.66 5129.99 4697.66 4265.33 4041.33 3817.33 1273.00 840.66 200.00
S.B. Sinha / Management of a community storage system
there will be a fixed sale of wheat to industries by the centre and uniformly some amount of wheat to the open market. It is observed that in January there will be large selling by the centre, i.e. at the time of high price, to ensure the price stabilization and to earn some profits for its commercial viability. It is observed that the m a x i m u m net storage requirement by the centre is given by 7052 quintals, that is, about 70.5% of total grain to be handled at the centre and the percentage of occupancy of storage capacity is more than 60% of the net storage upto December. The remaining months give the centre time to clean the storage and to prepare for the forthcoming arrivals. From Table 3 it is observed that the values of the deviational variables are present in the final optimal solution of the problem. All other deviational variables are zero. F r o m these values the actual values of the goals are obtained by adding/subtracting correspondingly the negative/ positive deviation from the aspired level of that particular goal. Accordingly, the actual values of the goals are also presented. As far as the goals of the Management are concerned it has achieved all at the first priority level. At the second priority level, it has achieved all the targets of the centre and ensured the farmers to get their due price for their products, industrialists to run their industries throughout the year and it has ensured larger amounts of storage of wheat for Nation's sudden and unforeseen needs of the society. But it also resulted in an underachievement of profit of the centre. The actual profit of the centre has been kept at Rs. 43 1 8 3 / i.e., Rs. 4.32 per quintal. Although the profit per quintal is marginal, as it is a community storage centre, more profit earning is not the main aim Table 3 Values of deviational variables and the actual value of the goals S1. no.
Deviational variable
Value
Actual value of the goal
1 2 3 4 5 6 7
d3 dis d(8 d25 d3-5 d6s d71
316.67 366.67 208.33 252.50 176.00 2111.99 56817.00
416.67 416.67 625.00 312.50 200.00 2135.99 43183.00
97
and it has to meet the other important objectives of the nation.
5. Conclusions For the Union Territory of Delhi it is concluded that there is a definite need for a series of such multi-objective storage facilities, having a capacity of 705.2 tonnes for the 1000 tonnes total arrival of wheat to the centre. The system presented here promised the fulfilment of the needs of the farmer, consumer and the industrialist in running their industry throughout the year. The model thus developed can be used by the management of any such similar storage system of any other crop(s) and , / i t s varieties of any other region after making an in-depth study over the production and processing of material and also the marketing system of that region. The model also yields optimum storage capacity of the centre. In a similar pattern the decision manager of the system can incorporate some more goals, or he can review the priority structure or review the input data in the model. F r o m the solution of the model, the management of the storage centre can have an insight in the achievement of various levels of the objectives/goals, which helps for the efficient running of the centre. Finally, this paper concludes with the efficiency and potentiality of the goal programming technique in agricultural planning.
References Bhole, N.G., and Mahajan, R.B. (1977), "Village panchayat level grain processing and storage facilities for Maharastra', Technical report, Indian Institute of Technology, Kharagput, India. Charnes, A., and Cooper, W.W. (1961), Management Models and Industrial Application of Linear Programming, Wiley, New York. Hwang, C.L., and Masud, A.S.M. (1979), Multiple objective Decision Making-- Methods and Applications, Lecture notes in Economics and Mathematical Systems 164, Springer, Berlin. Ignizio, J.P. (1976), Goal Programming and Extensions, Lexington Books, Lexington, MA. Ignizio, J.P. (1978), "A review of goal programming: a tool for multiobjective analysis", Journal of the Operational Research Society, 29 (11), 1109-1119. Khusro, A.M. (1973), Buffer Stocks and Storage of Foodgrains in India, Tata/McGraw-Hill, New Delhi.
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Kornbluth, J.S.H. (9175), "A survey of goal programming", OMEGA 1, 193-205. Lee, S.M. (1972), Goal Programming for Decision Analysis, Auerbach, Philadelphia, PA. Lee, S.M. (1976), Linear Optimization for Management, Petrocelli, New York. Misra, R.P., Bhole, N.(3., Sastry, S.V.C., and Sinha, S.B. (1984), "A new policy for storage and marketing of foodgrains--A case for system dynamics application", Proc. of National Seminar on System Dynamics, IIT, Kharagpur, India. Misra, R.P., Sastry, S.V.C., Sinha, S.B. and Bhole, N.G. (9185), "Optimization of foodgrain storage structures", Proc. of H
Int. Conf. on Computer Aided Analysis and Design in Civil Engineering, University of Roorkee, India. Misra, R.P. (1985), "Community storage of foodgrains--An OR approach", unpubfished thesis submitted to I.I.T., Kharagpur. Thomas Lin, W. (1980), "A survey of goal programming applications", OMEGA 8 (1) 115-117. Uma, J. Lele (1971), Foodgrain Marketing in I n d i a - Private Performance and Public Policy, Cornell University Press, London. Yuri, ljiri (1965), Management Goal and Accounting for Control, Rand-Mc Nally, Chicago, IL.