01. ahmad fauzi

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Maximizing Farm Income in Agroforestry SectorUsing Linear Programming Model

P. Ahmad Fauzi1, O. Suzyana2, M. Huda Farhana1 & A. R. Rohana1

1 Forest Research Institute Malaysia, 52109 Kepong, Selangor Darul Ehsan 2 International Islamic University Malaysia, P.O. Box 10, 50728 Gombak, Kuala Lumpur

Linear programming was used to determine the optimal net farm incomeof several agroforestry cropping system options in Malaysia. Many practicalproblems in operational research can be expressed in the form of linearprogramming problems. A number of algorithms for other types of optimization

problems could be solved simultaneously by using linear programming. Linearprogramming model (LINDO) was applied in this study in order to find out the best options to optimize the net farm income. The results from this study

will be used to recommend the most feasible and optimal cropping systemsuitable in Malaysia.

INTRODUCTION

Linear programming is a problem-solving approach that helps managers makedecisions in the allocation of their limited resources to meet certain criteria.

The objective is usually to minimize cost or maximize profit, revenues, etc. Thereason it is called linear programming is because the objective and the restrictions(constraints) involved in making the decisions are formulated mathematically,

which enable managers to derive optimal solutions using known mathematicaltechniques. Linear programming has found practical application in almost allfacets of business, from advertising to production planning. Transportation andaggregate production planning problems are the most typical objects of linearprogramming analysis. A number of assumptions of the model are made, namely,in optimization, fixedness, finiteness, determinism, continuity, homogeneity,addictively and proportionality (Hazell & Norton 1986). The addictively and

proportionality together define linearity in the activities, thereby, giving rise tothe name linear programming.Linear programming is a mathematical procedure for determining optimal

allocation of scarce resources (Schrage 1986). Further, linear programming is amethod of determining an optimum program of interdependent activities withinavailable resources and arises whenever two or more activities compete for limitedresources. The term linear assumes that all relationships involved in the particularproblem to be solved by this method are linear. It is not only capable of allocatingresources in order to achieve optimal return but also capable of selecting themost profitable activities in the business operation. In agricultural projects, linear



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Data for study

The most important data for the linear programming matrix is the cost per unit

of each input requirement (Table 1). This was the basis used for selecting the best combination of crops which maximized the net income.

The estimated linear programming model is as shown in Appendix 1. Themodel was based on the objectives of study which were to maximize the net farmincome in agroforestry sector and at the same time optimize the constraintsimposed by available resources. The description of variables used in the linearprogramming is shown in Appendix 2.

Cost (RM) X1* X2* X3* X4* X5*

Total gross income (TGI) 624994.634 380288.32 363294.6 620970.3 122612.7Land clearing 0 800 0 0 0Farm road 0 799.2 0 0 399.6Planting material 2379.2 616 2379.2 2156 839.2Replanting material 1248.65 225 1308.17 1248.65 225Cover crop 300.00 1351.39 300 300 44.14Lining 830.00 220.72 0 830 220.72Seedling# 1307.25 336 0 1307.25 336Holing 451.70 952.18 0 392.18 560Total fix cost 7816.79 5855.49 3987.37 7534.07 3239.18TSP 26.04 0 26.04 0 26.04

Other chemical fertilizer 9510 9148.38 0 9510 9148.38NPK 15:15:15 460.33 0 460.33 0 460.33NPK 12:12:17:2 553.35 0 553.35 0 553.35Organic fertilizer 527.56 0 527.56 0 527.56General weedicide 6385.86 5278.38 5887.86 6362.86 1101.37General insecticide 4463.78 1576.58 4312.43 4200 1840.36Plastic beg 21.35 0 21.35 0 21.35Total variable cost 21948.28 16003.34 11788.93 20072.86 13678.76L planting 0 555 0 0 614.52L fertilizer application 549.60 158.92 549.60 544.86 163.65L weedicide application 446.46 219.87 413.26 434.2813 198.84L insecicide application 288.86 126.13 288.86 283.784 131.20L pruning 417.33 37.692 404.86 417.3313 25.23L wrapping of fruit 3.04 0 3.04 0 5.07L plant maintenance 10.15 0 0 0 10.15L harvesting 4470.15 2702.52 4290.15 4438.02 2554.65Total cost of labour per MD 6185.58 3245.13 5949.77 6118.28 3088.79Total labour cost 92783.67 48676.8919 89246.48 91774.19 46331.8Land tax 9600 1500 1500 9600 1500Contingency (10%) 13214.87 7203.57192 10652.28 12898.11 6474.974TOTAL COST 121532.21 81200.59 93982.99 118355.6 63959.85

x1*- oil palm + sentang + banana; x2*- rubber + sentang; x3*- banana + oil palm; x4*- oil palm + sentang; x5*-

banana + rubber

Table 1 Data from agroforestry sectors



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RESULTS AND DISCUSSION

The net income showed that a 0.2 ha plantation crop of oil palm + sentang gave a

high return of about RM12724.95 (Appendices 3 and 4). The combine crops of oilpalm + sentang were more profitable than other combine crops. The combinationof oil palm + sentang gave a total gross income of RM15739.95 and for plantingmaterials, the combination gave a value of only RM54.65.

For the second run of linear programming, the combination of agroforestry data for the five plantations needed a little refinement. This showed that linearprogramming was able to allocate the variable costs to others matter such as thecost of labour and maintenance.

The total variable cost of oil palm + sentang can be minimized to RM508.79in order to maximize the net income to RM12724.95. The result showed that the

combination needed a value of RM243.33 to run this project using land tax. Resultsof the total cost of labour per man day can be reduced to give RM155.08. Totallabour cost included the costs for planting, application of fertilizer, weedicide andinsecticide, wrapping of fruits, plant maintenance and also cost for harvesting.Total fixed cost for the combination of oil palm + sentang was RM190.97 and thetotal variable cost was RM508.79.

CONCLUSION

Linear programming application is a very useful tool for solving optimizationproblems. This study emphasized on maximizing the net income of each cropcombination, i.e. oil palm + sentang + banana, rubber + sentang, banana + oilpalm, oil palm +sentang and banana + rubber. Linear programming showedthat the intention could optimize the input requirement cost especially land andlabour. Based on the results obtained, we conclude that combination of oil palm+ sentang increased net income by RM12724.95 annually and gave more profit than other combine crops.

Besides that, this study also indicated how linear programming playedimportant roles in the agroforestry system to achieve the goals of optimizationimposed by available resources.

ACKNOWLEDGEMENTS

We are extremely grateful to the Ministry of Science, Technology and Innovation(MOSTI) for the financial support (Project Number: 05-04-01-0099 EA001). TheDirector-General of FRIM, Dr. Joseph Jawa Kendawang and Mr. Dawend Jiwanfrom Forest Department Sarawak are thanked for their continuous guidance andencouragement throughout the project. Our thanks are also due to Dr. Woon WengChuen and Dr. Norini Haron for their leadership and collaboration.



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REFERENCES

A HMAD F AUZI, P. 1994. Investment Decision Model in Regional Land Evaluation in Recent

Developments in Land Evaluation . Malaysian Society of Soil Science, Kuala Lumpur. A HMAD F AUZI, P., MOHD SHAHWAHID, O. & A MIR A BDUL N ASIR , S. 2002. Optimizing log supply

from timber concession complex, Dungun, Terengganu to their subsidiaries downstream processing mills using linear programming model. Pp. 197–209 in Jamaluddin,K., Ahmad, S., Mohd Noor, R., Hafizah, K. & Muzammil, M. (Eds.) The Proceedings of the Science, Techonology & Social Science National Seminar . 27−28 May 2002, Kuantan.

H AZELL, P. B. R & NORTON, R. D. 1986. Mathematical Programming for Economic Analysis in Agriculture . Macmillan Publishers Company, New York.

SCHRAGE, L. 1986. Linear, Integer and Quadratic Programming with LINDO . Third edition. TheScientific Press, University Avenue, Palo Alto.



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MODEL:- MAX = -15*L1 -15*L2 -15*L3 -15*L4 -15*L5 -15 + 503462.42 *X1 + 299087.73 *X2 +269311.61 *X3 + 502614.73 *X4 + 58652.84 *X5 ;

[LABOUR1] L1 >= 0;[LABOUR2] L2 >= 0;[LABOUR3] L3 >= 0;[LABOUR4] L4 >= 0;[LABOUR5] L5 >= 0;[LAND1] LD1 -X1 >= 0;[LAND2] LD2 -X2 >= 0;[LAND3] LD3 -X3 >= 0;[LAND4] LD4 -X4 >= 0;[LAND5] LD5 -X5>= 0;[SYNLAND] X1 + X2 + X3 + X4 +X5 <= 10;[TOTAL_GROSS_INCOME] 624994.634*X1 + 380288.32*X2 + 363294.6*X3 +620970.3*X4 +122612.7*X5 >= 0;

[LAND_CLEARING] 800*X2 + 47300*X6 + 82800*X7 + 356160*X8 + 50500*X9 + 33950*X10 +18000*X11 + 20700*X12 + 12320*X13 + 7000*X14 + 100000*X15 + 96600*X16 + 170000*X17 >= 0;[FARM_ROAD] 799.2*X2 + 399.6*X5 + 1400000*X6 + 138000*X7 + 592000*X8 + 15700*X10 +60000*X11 +140000*X12 +70000*X13 + 72000*X14 >= 0;[PLANTING_MATERIAL] 2379.2*X1 + 616*X2 + 2379.2*X3 + 2156*X4 + 839.2*X5 + 119524.68*X6+ 24242.8*X7 + 277260.02*X8 + 187069.08*X9 + 53115.04*X10 >= 0;[REPLANTING_MATERIAL] 1248.65*X1 + 225*X2 + 1308.17*X3 + 1248.65*X4 + 225*X5 >= 0;[COVER_CORP] 300*X1 + 1351.39*X2 + 300*X3 + 300*X4 + 44.14*X5 >= 0;[LINING] 830.00*X1 + 220.72*X2 + 830*X4 + 220.72*X5 >= 0;[SEEDLING] 1307.25*X1 + 336*X2 + 1307.25*X4 + 336*X5 >= 0;[HOLING] 451.70*X1 + 952.18*X2 + 392.18*X4 + 560*X5 >= 0;[TOTAL_FIXED_COST] 7816.79*X1 + 5855.49*X2 + 3987.37*X3 + 7534.07*X4 + 3239.18*X5 >= 0;[TSP] 26.04*X1 + 26.04*X3 + 26.04*X5 >= 0;[OTHER_CHMCL_FERTLZR] 9510*X1 + 9148.38*X2 + 9510*X4 + 9148.38*X5 >= 0;

[NPK_15_15_15] 460.33*X1 + 460.33*X3 + 460.33*X5 >= 0;[NPK_12_12_17_2] 553.35*X1 + 553.35*X3 + 553.35*X5 >= 0;[ORG_FERTLZR] 527.56*X1 + 527.56*X3 + 527.56*X5 >= 0;[GNRL_WEEDICIDE] 6385.86*X1 + 5278.38*X2 + 5887.86*X3 + 6362.86*X4 + 1101.37*X5 >= 0;[GNRL_INSECTICIDE] 4463.78*X1 + 1576.58*X2 + 4312.43*X3 + 4200*X4 + 1840.36*X5 >= 0;[PLASTIC_BAG] 21.35*X1 + 21.35*X3 + 21.35*X5 >= 0;[TOTAL_VAR_COST] 21948.28*X1 + 16003.34*X2 + 11788.93*X3 + 20072.86*X4 + 13678.8*X5>= 0;[L_PLANTING] 555*X2 + 614.52*X5 >= 0;[L_FERTLZR_APPL] -L1 + 549.60*X1 + 158.92*X2 + 549.60*X3 + 544.86*X4 + 163.65*X5 - TL >= 0;[L_WEEDICIDE_APPL] -L2 + 446.46*X1 + 219.87*X2 + 413.26*X3 + 434.2813*X4 + 198.84*X5- TL >= 0;[L_INSECTICIDE_APPL] -L3 + 288.86*X1 + 126.13*X2 + 288.86*X3 + 283.784*X4 + 131.20*X5+ - TL >= 0;[L_PRUNNING] -L4 + 417.33*x1 + 37.692*x2 + 404.86*x3 + 417.3313*x4 + 25.23*x5 - TL >= 0;[L_WRAPPG_OF_FRUITS] 3.04*x1 + 3.04*x3 + 5.07*x5 - TL >= 0;[L_PLANT_MAINTENANCE] 10.15*x1 + 10.15*x5 + 71100.00*x6 - TL >= 0;[L_HARVESTING] 4470.15*x1 + 2702.52*x2 + 4290.15*x3 + 4438.02*x4 + 2554.65*x5 - TL >= 0;[TOTAL_COST_OF_LBR_PER_MD] 6185.58*x1 + 3245.13*x2 + 5949.77*x3 + 6118.28*x4 +3088.79*x5 >= 0;[TOTAL_LBR_COST] 92783.66*x1 + 48676.89*x2 + 89246.48*x3 + 91774.19*x4 + 46331.8*x5 >= 0;[LAND_TAX] 9600*x1 + 1500*x2 + 1500*x3 + 9600*x4 + 1500*x5 >= 0;[CONTINGENCY] 13214.87*x1 + 7203.57*x2 + 10652.28*x3 + 12898.11*x4 + 6474.974*x5 >= 0;[TOTAL_COST] 121532.21*x1 + 81200.59*x2 + 93983*x3 + 118355.6*x4 + 63959.8*x5 <= 3000;[TOTAL_LABOUR] TL <= 20;[PO1] LD4 >= 5;

Appendix 1 Estimated linear programming model



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Variable name Description

LABOUR[1] L1 Labour for combination 1 (oil palm + sentang + banana)LABOUR[2] Labour for combination 2 (rubber + sentang)LABOUR[3] Labour for combination 3 (banana + oil palm)LABOUR[4] Labour for combination 4 (banana + oil palm)LABOUR[5] Labour for combination 5 (banana + rubber)LAND1 Land use for combination 1 (oil palm + sentang + banana)LAND2 Land use for combination 2 (rubber + sentang)LAND3 Land use for combination 3 (banana + oil palm)LAND4 Land use for combination 4 (banana + oil palm)LAND5 Land use for combination 5 (banana + rubber)(TGI) Total gross income[LAND_CLEARING] Land clearing[FARM_ROAD] Farm road[PLANTING_MATERIAL] Planting material[REPLANTING_MATERIAL] Replanting material[COVER_CORP] Cover crop[LINING] Lining[SEEDLING] Seedling[HOLING] Holing[TOTAL_FIXED_COST] Total fix cost [TSP] TSP[OTHER_CHMCL_FERTLZR] Other chemical fertilizer[NPK_15_15_15] NPK 15:15:15[NPK_12_12_17_2] NPK 12:12:17:2[ORG_FERTLZR] Organic fertilizer

[GNRL_WEEDICIDE] General weedicide[GNRL_INSECTICIDE] General insecticide[PLASTIC_BAG] Plastic beg[TOTAL_VAR_COST] Total variable cost [L_PLANTING] Labour in planting[L_FERTLZR_APPL] Labour in fertilizer application[L_WEEDICIDE_APPL] Labour weedicide application[L_INSECTICIDE_APPL] Labour insecicide application[L_PRUNNING] Labour in pruning[L_WRAPPG_OF_FRUITS] Labour in wrapping of fruit [L_PLANT_MAINTENANCE] Labour in plant maintenance[L_HARVESTING] Labour inharvesting[TOTAL_COST_OF_LBR_PER_MD] Total cost of labour per MD

[TOTAL_LBR_COST] Total labour cost [LAND_TAX] Land tax[CONTINGENCY] Contingency (10%)[TOTAL_COST] Total coat for all combination[TOTAL_LABOUR] Total of labour used[PO1] Policy used

Appendix 2 Description of variables



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Appendix 3 Otimization linear programming matrix for agroforestry

Appendix 4 Optimization LINDO output

Global optimal solution foundObjective value: 12724.95Total solver iterations: 1

Variable Value Reduced Cost

L1 0.000000 15.00000L2 0.000000 15.00000L3 0.000000 15.00000L4 0.000000 15.00000L5 0.000000 15.00000X1 0.000000 12642.26X2 0.000000 45742.70X3 0.000000 129801.2

X4 0.2534734E-01 0.000000X5 0.000000 212962.0LD1 0.000000 0.000000LD2 0.000000 0.000000LD3 0.000000 0.000000LD4 5.000000 0.000000LD5 0.000000 0.000000X6 0.000000 0.000000X7 0.000000 0.000000X8 0.000000 0.000000X9 0.000000 0.000000X10 0.000000 0.000000



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X11 0.000000 0.000000X12 0.000000 0.000000X13 0.000000 0.000000

X14 0.000000 0.000000X15 0.000000 0.000000X16 0.000000 0.000000X17 0.000000 0.000000Row Slack@ surplus Dual PriceLABOUR1 0.000000 0.000000LABOUR2 0.000000 0.000000LABOUR3 0.000000 0.000000LABOUR4 0.000000 0.000000LABOUR5 0.000000 0.000000LAND1 0.000000 0.000000LAND2 0.000000 0.000000LAND3 0.000000 0.000000

LAND4 4.9764653 0.000000LAND5 0.000000 0.000000SYNLAND 9.974653 0.000000TOTAL_GROSS_INCOME 15739.95 0.000000LAND_CLEARING 0.000000 0.000000FARM_ROAD 0.000000 0.000000PLANTING_MATERIAL 54.64887 0.000000REPLANTING_MATERIAL 31.64996 0.000000COVER_CORP 7.604203 0.000000LINING 21.03829 0.000000SEEDLING 33.13531 0.000000HOLING 9.940721 0.000000TOTAL_FIXED_COST 190.9687 0.000000TSP 0.000000 0.000000OTHER_CHMCL_FERTLZR 241.0532 0.000000NPK_15_15_15 0.000000 0.000000NPK_12_12_17_2 0.000000 0.000000ORG_FERTLZR 0.000000 0.000000GNRL_WEEDICIDE 161.2816 0.000000GNRL_INSECTICIDE 106.4588 0.000000PLASTIC_BAG 0.000000 0.000000TOTAL_VAR_COST 508.7937 0.000000L_PLANTING 0.000000 0.000000L_FERTLZR_APPL 13.81075 0.000000L_WEEDICIDE_APPL 11.00788 0.000000

L_INSECTICIDE_APPL 7.193170 0.000000L_PRUNNING 10.57824 0.000000L_WRAPPG_OF_FRUITS 0.000000 0.000000L_PLANT_MAINTENANCE 0.000000 0.000000L_HARVESTING 112.4920 0.000000TOTAL_COST_OF_LBR_PER_MD 155.0821 0.000000TOTAL_LBR_COST 2326.232 0.000000LAND_TAX 243.3345 0.000000CONTINGENCY 326.9328 0.000000TOTAL_COST 0.000000 4.246649TOTAL_LABOUR 20.00000 0.000000PO1 0.000000 0.000000

01. ahmad fauzi

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