# for independent solutions, Used literature - Logistics

Let's demonstrate the possibility of actual application of the considered algorithm on a practical example. One of the major distribution companies of St. Petersburg LLC Holding 78, which supplies food to the shops of the city and the Leningrad Region, uses leased rolling stock for transportation. Since daily this company serves up to one and a half thousand customers, which causes serious problems in the formation of routes, the whole city is divided into service areas and transport sectors. Before the dispatchers engaged in the formation of routes, the task is to serve all customers using the minimum number of rolling stock.

The solution of this task has not been automated to date, but there is a certain algorithm, according to which, firstly, a rational rolling stock of the available stock is chosen. Secondly, routes are formed inside the sectors of transport, provided that the number of points integrated into one route should not exceed twelve. If the number of customers in this sector of transportation exceeds twelve, then some of them join the clients of the nearest sectors in such a way that this restriction is met.

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As an example, data on the customer service of this company in the area of ​​the Moscow district of St. Petersburg for one day are taken.

The summary table of freight flows and actually formed routes are presented in Table 10.

Table 10

Summary table of freight flows in the base version

 Date Region Excavation Sector Store number Flight number Amount, kg 32 48 54 55 57 60 61 64 66 Model of rolling stock GAZ 53 GAZ 3302 & quot; Gazelle & quot; GAZ 3302 & quot; Gazelle & quot; GAZ 53 GAZ 3302 & quot; Gazelle & quot; GAZ 3307 GAZ 3307 GAZ 3307 GAZ 3302 & quot; Gazelle & quot; 01/14/04 Moscow District 1 5340 532 5360 368 8192 565 8375 340 2 4277 490 5644 328 3 7254 3746 3800 4 4896 666.8 6455 587.1 5 5728 737 5985 388 6027 652 6501 299 9190 651 9556 459 6 9064 2433 7 5116 124 6166 101 6540 383 9380 182 8 5733 135 8989 138 9184 234 9253 155 9 6843 776 Amount, kg 2433 776 662 2623 790 3746 3800 3186 1253.9 19279.9

Table 10 shows the following data:

1. in the & quot; cap & quot; The tables are marked: date, region, transport sector, store number, flight numbers and vehicle models that served these customers (stores);

2. in the & quot; Sum & quot; column the weight of the order of each store (kg) is indicated;

3. in the & quot; Amount & quot; - the actual load of each car (kg).

In the table cells at the intersection of the corresponding rows and columns, the weight of the goods delivered to the client by the given flight (kg) is shown.

Analysis of this table shows: to service 25 customers, nine units of rolling stock were required, flights 48.54 and 57 were made with extremely low car loading, the order of shop number 7254 was distributed between two rolling stock units, which can be justified only when absence of the car of the required carrying capacity.

The calculation of actual transportation costs is presented in Table 11.

Table 11

 Flight number General costs, rub Cost element 32 48 54 55 7 60 61 64 66 Model of rolling stock GAZ 53 GAZ 3302 & quot; Gazelle & quot; GAZ 3302 & quot; Gazelle & quot; GAZ 53 GAZ 3302 & quot; Gazelle & quot; GAZ 3307 GAZ 3307 GAZ 3307 GAZ 3302 & quot; Gazelle & quot; Rental car, rub 840 780 780 840 780 900 900 900 780 7500 Forwarding, rub 545 545 545 545 545 545 545 545 545 4905 Costs for the flight, rub 1385 1325 1325 1385 1325 1445 1445 1445 1325 12405

The calculation shows that in the basic version, the total cost of transportation, including costs for car rental and freight costs, amounted to 12.405 thousand rubles.

Table 12

The shadow price matrix with ij

 Number Store Flight number Ordered, kg 32 48 54 55 57 (60 + 61) 64 66 Flight Costs 1385 1325 1325 1385 1325 1545 1445 1325 5340 532 5360 368 8192 565 8375 340 4277 490 5644 328 7254 7546 4896 666.8 6455 587.1 5728 737 5985 388 6027 652 6501 299 9190 651 9556 459 9064 2433 5116 124 6166 101 6540 383 9380 182 5733 135 8989 138 9184 234 9253 155 6843 776 Download, PS Carrying capacity, kg 1500 1500 1500 3000 1500 8000 4500 1500

Try to improve this solution. First, we will reduce the number of rolling stock units by providing Kamal-5320 with a load capacity of 8 tons to fulfill the order of the shop number 7254. Secondly, we use the linear programming algorithm to optimize the loading of the rolling stock. Table 12 shows the Shadow Price Matrix. The remaining matrices must be compiled and filled in accordance with the example. Time to complete the task using the & quot; Solution search & quot; can take a long time.

## References

1. Bochkarev AA, Gorbatenko DV Solution of the task of appointing small-batch cargoes in supply chain management // Logistics today. №5. 2004. With. 12-19.

2. Models and methods of the theory of logistics: Textbook. allowance/ed. V.S. Lukinsky. - St. Petersburg: & quot; Peter & quot ;, 2003. - 176 pp.

3. Cisar IF Laboratory work on a personal computer. - M .: Exam, 2004.

4. Effective work with Microsoft Excel 2000/M.Dogge [and others] - St. Petersburg: Peter, 2001.

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