Paper on Modeling Agricultural Products Transportation Planning
Abstract This paper establishes a model based on the conditions and requirements of the problem. This is a multi-variable linear programming model. By solving this model, the complete solved the problem.
The profit objective function is additive, and the supply of agricultural products exceeds demand, that is, all agricultural products can be sold, and the total sales volume remains unchanged. Therefore, the algorithm of minimum transportation cost can be directly applied to find the maximum profit problem of the base.
The modeling process is generally divided into 8 parts: 1. Restatement of the problem; 2. Model assumptions; 3. Symbols and text descriptions; 4. Problem analysis; 5. Model establishment; 6. Model Solving; 7. Analysis of the results of the model; 8. Evaluation and further discussion of the model.
In the modeling, the preservation of agricultural products is not considered, nor are the costs other than transportation costs.
The formulation of an agricultural product transportation plan is a plan to arrange the sales of eight kinds of vegetables to six markets.
In the linear programming model, profit obtained = total sales - total transportation costs. Total sales remain unchanged, so only total shipping costs are considered. Since the objective function of this model is multi-variable linear, the obtained profit = total sales - total transportation costs = 1,505,885 yuan.
The article makes certain results analysis of this model, which has wider applicability.
Finally, this issue was deeply discussed.
Keywords transportation plan model hypothesis analysis model establishment model results analysis model evaluation and discussion
1. Restatement of the problem
Direct question
2. Model assumptions
(1) When formulating a plan to transport agricultural products, the data is accurate to 1 unit , that is, accurate to tons. This assumption guarantees more accurate results in theory.
(2) Damage to vegetables during transportation is not considered.
(3) There is no need to consider other costs during the transportation of vegetables except freight.
3. Symbols and text descriptions
Y represents the profit earned from selling vegetables at the base;
i=1, 2…, 8 where 1 represents cabbage, 2 represents potatoes, 3 represents tomatoes, 4 represents beans, 5 represents cucumbers, 6 represents pumpkins, 7 represents eggplants, and 8 represents zucchini;
j=1, 2,...,6 among which 1 represents market A, 2 represents market B, 3 represents market C, 4 represents market D, 5 represents market E, and 6 represents market F;
Indicates that the i-th (i=1, 2,...,8) vegetables are transported to The total volume of the jth (j=1, 2, ..., 6) market.
4. Problem analysis
The formulation of an agricultural product transportation plan is to arrange the sales of vegetables from No. 8 Middle School to six markets. The goal is to make the most profit. From the data given in the question, it is obvious that the supply of vegetables exceeds demand, so all the vegetables in the base can be sold and made a profit. Therefore, the total income of the base is the income after selling all the vegetables, and has nothing to do with the transportation plan. Therefore, in order to maximize profits, it is necessary to adjust the transportation plan of agricultural products. In addition, it can be seen from the table that the supply of agricultural products exceeds demand, so the transportation plan is limited by the supply of the base and the market demand.
Linear programming model is used.
5. Establishment of the model
Basic model
Decision variables: Suppose the total amount of the i-th agricultural product transported to the j-th market is .
Objective function: Let the profit be Y yuan.
From the question
MaxY=400x11 400x12 400x13 400x14 400x15 400x16-80x11-130x12-150x13-120x14-100x15-110x16 320x21 320x22 320x23 320x24 320x25 320x26-65x21-105x22-120x23-100x24-80x25-85x26 510x31 510x32 510x33 510x34 510x35 510x36-100x31-165x32-170x33-140x34-120x35-130x36 300x41 300x42 300x43 300x44 300x45 300x46-70x41-110x 42-125x43-105x44-85x45-90x46 230x51 230x52 230x53 230x54 230x55 230x56-95x51-160x52-165x53-135x54-115x55 -125x56 650x61 650x62 650x63 650x64 650x65 650x66-60x61-100x62-120x63-100x64-80x65-85x66 500x71 500x72 500x73 500x74 500x75 500x76-90x71-150x72-160x73-130x74-110x75-120x76 260x81 260x82 260x83 260x84 260x85 260x86-90x81-160x82-165x83 -130x84-115x85-120x86.
Constraints:
The total amount of raw materials transported for various agricultural products must not exceed the supply, and since supply exceeds demand, all supplied agricultural products can be sold, that is,
x11 x12 x13 x14 x15 x16=826
x21 x22 x23 x24 x25 x26=594
x31 x32 x33 x34 x35 x36=600
x41 x42 x43 x44 x45 x46=356
x51 x52 x53 x54 x55 x56=423
x61 x62 x63 x64 x65 x66=890
x71 x72 x73 x74 x75 x76=600
x81 x82 x83 x84 x85 x86=500
Market demand The quantity of various agricultural products transported to each market shall not exceed the demand for the corresponding agricultural products in the corresponding market, that is,
x11lt;=160;x12lt;=130;x13lt;=200;x14lt;=150;x15lt;=140;x16lt;=180;
x21lt;=60; ;=160;x24lt;=100;x25lt;=20;x26lt;=130;
x31lt;=100;x32lt;=140; ;x36lt;=90;
x41lt;=70;x42lt;=90;x43lt;=140;x44lt;=100; x51lt;=50;x52lt;=100;x53lt;=130;x54lt;=90;x55lt;=90;x56lt;=70;
x61lt;=200; 130;x64lt;=100;x65lt;=240;x66lt;=150;
x71lt;=120;x72lt;=150; ;=90;
x81lt;=60;x82lt;=90;x83lt;=150;x84lt;=140;x85lt;=100;x86lt;=80.
None of the non-negative constraints can be negative, that is, gt; = 0.
6. Solution to the model
6.1 Algorithm idea
This problem is solved using linear programming. The algorithm is relatively simple and clear. The total sales revenue of agricultural products minus the total transportation cost is equal to the profit obtained, and the optimal solution is obtained through linear programming.
Solution to the 6.2 model
According to Appendix 4, the transportation plan is:
The total amount transported to each market (unit; tons)
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