EXTENDING A PLANT PRODUCTION MODEL WITH A VIEW TO PLANNING MONTHLY CASH-FLOW BALANCE, HIRED MACHINERY AND LABOUR COSTS

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1 EXTENDING A PLANT PRODUCTION MODEL WITH A VIEW TO PLANNING MONTHLY CASH-FLOW BALANCE, HIRED MACHINERY AND LABOUR COSTS P. DRIMBA, I. ERTSEY, M. HERDON Debrecen University Centre for Agricultural Science, Debrecen, Hungary drimba@date.hu, ertsey@date.hu, herdon@date.hu ABSTRACT When preparing an agricultural plan, apart from planning the expected income and the production structure required to achieve it, the producer must be aware of the monthly expenses necessary to carry out the process of production. In the critical months it is often necessary to make use of rented machinery (hired labour). The model we have used for planning is an extended linear programming one, in which the data for technological planning giving the production expenses required in the different months and the monthly cash-flow balance are also defined. Farmers can assess the number of hours of potential machinery (and labour) hire and can include them in the constraints of the model. When hired machinery hours (resources) are used the extra expenses over the farmer s own machinery costs, which the technological plan calculates, are taken into account. The model is demonstrated by using the income figures for the five crops winter wheat, maize, sugar beet, alfalfa and corn for silage planned in the Production Co-operative in Hajdúszovát for the year INTRODUCTION When preparing a plan for agricultural production it is not only the structure of production and its end results are important factors that have to be defined. The planner must be aware of the costs incurred to achieve the expected results and also the balance of expenses and returns in the course of production, e.g. on a monthly basis. This is an indication of the necessary amount of capital required to carry out the production process. Often it is the case that the temporary use of hired resources results in more efficient farming. Our model makes it possible for a plant production enterprise to prepare yearly plans that ensure optimal incomes. Based on technological planning data our plan defines the structure of production and demonstrates monthly cash flows and the amount of resources to hire. MATERIAL AND METHODS The assessment is presented by using the income figures for the five crops winter wheat, maize, sugar beet, alfalfa and corn for silage planned in the Production Co-operative in Hajdúszovát for the year The planned specific break-even amounts are the figures indicated in Table

2 TABLE 1. Planned gross margins for the crops produced (Hajdúszovát Production Cooperative, 1998) Wheat Maize Sugar Alfalfa Corn for Item beet silage Gross margins ( 000 HUF/ha) As a start for the planning we applied the deterministic income maximisation model proposed by HAZELL et. al (1974). x 0 A x b E = p y v x max where x the size of activities (n by 1 vector) A x b linear constraints for the resources to be used and other constraints p planned produce prices (n by 1 vector) v specific variable expenses (n by 1 vector) y = M x, n by 1 vector for all produced output M n by n diagonal matrix, where m jj is the specific yield of activity j. The objective function includes income maximisation (Sign refers to the transpose of the vector). In addition to the constraints in the first two lines of the model we included the following three new series of conditions: (1) H x I g sg H represents an m by n matrix whose elements contain the u machinery hours of a plant n at any r peak time (m r by u). I is an m by m identity matrix, g and sg represent the number of hired machinery hours and own machinery hours, respectively and both of them are m by 1 vectors. This condition is required for defining the number of hired machinery hours. (2) I g bg With this constraint the limit for hired machinery hours is given provided we know the value of the hire limit (bg). (3) S x Tg + Q v = 0 When the technological plan-based balance for the monthly expenses and incomes for different k months of production of any n number of crops are included in the k by n matrix S, and the extra costs in excess of own machine hours calculated with in the technological plan are included in the k by m matrix T, then the k by 1 vector v will provide the monthly cash flow balances. Q is a k by k matrix whose main diagonal contains 1 at every point whereas directly below these values we can find 1. Considering the gross margin amounts (c is a 1 by n vector) the objective function prescribes the maximisation of enterprise level gross margin amount (summative vector u containing number k the figure 1). max E = c x u T g 148

3 Planning the use of custom work can be done in the same way as in the case of planning hired machinery hours, whose demonstration here is neglected for reasons of space available. RESULTS The more detailed constraint lines of the model applied: x j, g m 0 (j = 1,,5 m = 1,,7) Σ j a ij x j b i (i = 1,2,3) Σ j h mj x j - g m sg m (m = 1,,7) g m bg m (m = 1,,7) j s kj x j -Σ m t km g m + v k-1 v k = 0 (k = III,IV,,X), v 2 = 0 where Serial numbers in m are u = tr, Tr, ko, tgk machines and r = III, VII, IX, X on the basis of the combinations of peak months m(u,r): trvii=1, trix=2, TRIX=3, TRX=4, kovii=5, koix=6, tgkiii=7 The second series of constraints refer to the total area and the limitations concerning the areas of wheat and sugar beet according to table 2. The third and fourth series of constraints refer to limitations concerning the total number of machinery hours of the 7 machines used, and also the limitations on the hours of machines that can be hired (the limitations for machinery hours of own and hired machinery are included in table 2). The last series of conditions give the total cash flow values (v k ) for 8 months (months III- X) as the sum of the current month s income-expense balance and the total cash flow ending with the previous month. The specific gross margin amounts c j j c j x j - Σ m (Σ k t km )g m in the objective function are taken from table 1. TABLE 2. Limitations as regards machinery hours and area at Hajdúszovát Production Cooperative Total area = 100 Area (ha) Wheat limitation 40 Sugar beet limitation 15 Small tractor, month VII (tr VII) 50 40* Small tractor, month IX (tr IX) 50 40* Machinery hours (h) Big tractor, month IX (TR IX) 80 30* (own, hired*) Big tractor, month X. (TR X) 80 50* Combine harvester, month VII. (ko VII) 40 30* Combine harvester, month IX. (ko IX) 40 50* Truck, month III. (tgk III) 40 40* The model was solved by making use of a Microsoft Excel Solver programme. The solution is given in table 3. According to this solution, when growing maize on 85 ha and sugar beet on 15 ha the farm can have a maximum gross margin amount of HUF 3,788,000. Apart from October, the 149

4 monthly cash flow balance is negative in every case. Monthly variations in the cash flow can be defined as the differences in v k -v k-1 in the monthly cash flow balances. Up until October the monthly variation in the cash flow is always negative, i.e. every month as is seen in the table a variable amount of money, HUF 229,000-2,834,000, has to be invested in the production process. The amount of cash to be invested during the production process is HUF 9,339,000. The farmer must have at least this amount of capital, which can come from either his/her own financial resources or taking out loans in response to the fluctuating money requirements. The negative balance of HUF 9,339,000 accumulating by September will turn into a positive result of HUF 3,788,000 as a consequence of the positive change of HUF 13,128,000 in the cash flow in October. Planning cash flow and hired machinery can also be incorporated in other non-linear, risk programming, etc. models (DRIMBA, 1999). REFERENCES DRIMBA P. (1999): A kockázat figyelembevétele a mezőgazdasági döntési modellekben. Ph.D disszertáció. DATE. (Risk Considerations in Agricultural Decision Supporting Models Ph.D dissertation. Debrecen Agricultural University, Hungary.) HAZELL P.B.R.-SCANDIZZO P.L. (1974): Competitive Demand Structures under Risk in Agricultural Linear Programming Models. Amer. J. Agr. Econ

5 TABLE 3. The model and its solution ITEM winter wheat maize sugar beet alfalfa corn for silage tr VII tr IX TR IX TR X ko VII ko IX tgk III V3 v4 v5 v6 v7 v8 v9 v10 REL. Cap acity Utilisa tion Area = ,0 Wheat limit <= 40 0,0 Sugar beet <= 15 15,0 limit tr VII 2,8 0,4 0,2 1,75 0, <= 50 37,0 tr IX 0,12 0, <= 50 41,1 TR IX 0, , <= 80 80,0 TR X H 0,5 0,17 0, <= 80 16,6 ko VII <= 40 0,0 ko IX 0 0, , <= 40 40,0 tgk III 0,25 0,25 1 0,5 0, <= 40 36,3 tr VII <= 40 0,0 tr IX <= 40 0,0 TR IX <= 30 20,0 TR X <= 50 0,0 ko VII <= 30 0,0 ko IX <= 50 11,0 tgk III <= 40 0,0 III -8,858-4,1-29,472-14,937-6, , = 0 0,0 IV -5,002-24,516-29, , = 0 0,0 V -4,028-17,587-19,392 8,508-18, = 0 0,0 VI -7,262-6,2-16,262 11,53-3, = 0 0,0 VII -15,85-4,028-4,262 11,53-3,5-0, = 0 0,0 VIII 112,6 0-15,262 11,53 95, = 0 0,0 IX ,3-20, , ,3-0, , = 0 0,0 X -25,7 121, ,2-4, , = 0 0,0 S T Q specific data 25,9 35,5 53,5 8,3 32-0,3-0,3-0,6-0,6-2 -1,8-0, Max 3788,2 v' result 0,0 85,0 15,0 0,0 0,0 0,0 0,0 20,0 0,0 0,0 11,0 0, = Mothly balances x' g' area sown hired machinery hours cash flow fluctuation/month

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