Algorithm for operational planning of transportation by machine shipments in long-distance traffic

. Efficient operational planning of transportation is crucial in long-distance traffic, where the coordination of shipments plays a pivotal role in optimizing logistics operations. This article presents an algorithm designed to streamline the planning process for machine shipments in long-distance transportation. The algorithm leverages advanced optimization techniques and machine learning to address the complexities associated with route selection, scheduling, and resource allocation.


Introduction
The current economic situation calls for special attention to intercity transportation.Regular assessment of competitiveness indicates that transport companies and manufacturers need to focus on reducing costs and improving the efficiency of freight transportation.For transportation service consumers, the timely and reliable delivery of goods is becoming increasingly important.In freight transportation, the just-in-time (JIT) delivery factor is gaining dominance, and it turns out that not all carriers are able to meet the specified delivery parameters.This, in turn, leads to competition for quality transportation services and gaining competitive advantages.Achieving the specified delivery parameters is possible only through proper transportation planning that takes into account all aspects of the transportation process [1,2,3].

Methodology and research methods
The methodology and research methods were chosen based on previously published works in the field of freight transportation by trucks [4,5,6,7,8,9], which include: 1.The concept of the development of the theory of freight transportation by trucks.2. Classification of road transport systems for freight transportation (RTSFT).3. Dependencies of the impact of technical and operational indicators (TOI) on the performance of road transport vehicles (RTV) in RTSFT.
4. Descriptive mathematical models of the functioning of RTSFT, taking into account the discreteness of the transportation process.Depending on the configuration of routes, the capacity of freight flows, and the number of required RTVs, freight transportation can be considered as different types of systems, indicating the presence of a systemic approach within the research.The systemic approach, as a direction of the methodology of scientific knowledge, is based on considering the object of research as a system: a holistic complex of interconnected elements [10].
The transportation plan must be feasible.The principle of commitment to plan execution should be incorporated into the research, otherwise the interests of customers and carriers may suffer.
The research should follow the principle of "from simple to complex."In road freight transportation, this means working on the issue at the level of operational planning.Based on the principle of commitment to plan execution, the execution of transportation can be implemented in a shift-day mode, when they are actually carried out.
The methodology and research methods include the principles of the theory of freight transportation by trucks, economic-mathematical methods in transport, statistics, scientific works, and production experience in optimizing freight transportation processes.Research methods include observation, comparison, measurement; analysis, synthesis, modeling, and programming.In the work, electronic computing equipment (computer) and software products were used as research tools.
One of the conditions contributing to achieving high performance in production of road transport activities, as stated in [11], is properly organized operational planning of freight transportation.Operational planning of freight transportation includes: 1. Development of a shift-day plan for freight transportation.
2. Development of transportation routes and preparation of planned tasks for freight transportation for each driver.3. Planning and organization of vehicle dispatching.4. Monitoring and operational analysis of shift-day plan execution.

Results
The algorithm (Figure 1) proposed in this work allows for calculating the required number of transportation vehicles when planning freight transportation using truckload shipments in intercity communication.The algorithm takes into account inventory management system and calculates the demand for transportation vehicles based on checking the coincidence/mismatch of delivery days for a specific cycle and the end of delivery from the previous cycle.
For the algorithm's validation, the following initial data were taken as an example.The company conducts intercity freight transportation in four directions: 1. Omsk -Astrakhan;

Database of attracted vehicles
Calculation of the optimal order size Does the consignee agree with the optimal order size?

Calculation of application parameters
The volume of the order at the request of the consignee Construction of schedules for replenishment and expenditure of stocks for all applications Have all cycles within the application been reviewed?Amount of vehicles for all applications ≤ own transport?
Vehicles from among own vehicles are selected to fulfill the i-th application

Appointment of a vehicle for all applications
We assign a vehicle from the following conditions: We take from the number of borrowed vehicles Search for a third-party company to replenish the fund of attracted vehicles  The calculation period used in the example is one quarter.The initial data are presented in Table 1.
Let's assume that:  i -request (i = 1,2,3...I);  j -cycle within the request (j = 1,2,3...J); The methodology is as follows: 1. Input of initial data from two databases (DB): the request database and the carrier database.The request database includes information about shippers and consignees.The carrier database includes information about own and possible contracted (i.e., information about vehicles of the transport company with which a cooperation agreement is concluded), namely: Qi -volume of transportation, tons per request; N -number of requests for the calculation period, units; Q it -volume of transportation, tons per calculation period; t i -time for request fulfillment, days; t ih -time for request fulfillment, hours; t a -time of vehicle usage per day, hours; t o -driver rest time per route, minutes; t j -estimated cycle time, hours per calculation period; V t -average technical speed, km/h; A t -number of own and А attracted vehicles, T p -loading time and unloading time, hours per route; L -route length, including zero mileage, km; α b -line release coefficient; q -vehicle carrying capacity; γ -coefficient of carrying capacity utilization.
The initial data are presented in Table 2.
Based on the initial data, data for further calculations are generated using known eqautions: t tr -turnover time, hours per turnover; M -number of possible turnovers, units per calculation period; M req -required number of turnovers, units per calculation period; Wpossible vehicle productivity, tons per calculation period; W req -required vehicle productivity, tons per calculation period; l -vehicle mileage, km per calculation period; Аnumber of vehicles in operation, units; А vh -vehicle-hours of vehicle usage for the reporting period, vehicle-hours/reporting period; L t -total mileage for the reporting period, km/reporting period; Q it -volume of transportation, tons per reporting period.
The calculation results are presented in Table 3. 2. It is necessary to determine the order volume: based on the request or calculated (according to the order management system).In this study, the "minimum-maximum" order management method [12,13] was taken as an example.For this purpose, the following information is entered for each i-th request: Vt -average technical speed, km/h; A -cost of fulfilling one order, rubles; Q -annual material demand, tons; f -cost of maintaining one unit of goods in stock, rubles; D -number of working days in a year, days; T d -delivery time, days; T del -delivery delay time, days.
Initial data for inventory management system are presented in Table 4. Based on the data from the specified system, the following parameters are calculated: q opt .-optimal order quantity, tons; Q d -expected daily consumption, tons; Т l -order lead time, days; Q exp -expected consumption during lead time, tons; Q max -maximum consumption during lead time, tons; SS -Safety stock, tons; RP -Reorder point, tons; MDO -Maximum desirable order quantity, tons; Т pp -Time until reaching reorder point, days; Т ss -start day of shipment, date; Т es -end day of shipment, date.
The results of the inventory management system parameter calculation are presented in Table 5. 3.After determining whether the consignee accepts the calculated optimal order level or the volume specified in the consignee's request, we proceed to calculate the parameters for the request and obtain results for each j-th cycle within the i-th request (starting with the first step, assuming i=1 and j=1).After considering all j-th cycles within the i-th request, we move on to the next request.Similar iterations are performed until all requests (i -request (i = 1, 2, 3... I)) have been reviewed.
4. According to the proposed algorithm, the next step is to create a graph of stock replenishment and consumption for all requests.
5. We start assigning transport vehicles by checking the condition of matching/mismatching delivery days of a specific cycle with the end of delivery from the previous cycle.First, we consider all cycles within one request, and only then do we move on to the next request (i=i+1) Graphs of stock replenishment, consumption, and transport vehicle activity are presented in Figures 3-6.    6.After reviewing all requests, the total number of required vehicles is calculated.The assignment of vehicles for all requests is done based on the following conditions:  If the total number of required vehicles does not exceed the total number of owned vehicles (A owned), then the required vehicles are assigned from the pool of owned vehicles (A owned).Proceed to building the work schedule for all requests. If the total number of required vehicles exceeds the total number of owned vehicles (A owned), then the assignment of vehicles follows these conditions:  Assign the maximum possible number of vehicles from the pool of owned vehicles (A owned). Assign the remaining difference between the required number of vehicles (A plan) and A owned from the pool of hired vehicles (A hired).It is important to note that at this step a check is needed:  If the difference between the required number of vehicles (A plan) and A owned exceeds A hired, then the specified assignment of vehicles is not possible, and we move on to finding an external company to replenish the pool of hired vehicles. If the difference between the required number of vehicles (A plan) and A owned does not exceed A hired, then the specified assignment of vehicles is possible, and we proceed to building the work schedule for all requests.7. The work schedule for all requests is built, and the algorithm proceeds to the end.The schedule is presented in Figure 7.

Discussion
In modern conditions of economic activity, isolated planning (i.e., separately for each request) does not yield satisfactory results when planning the required number of vehicles and scheduling the work of transport vehicles, as it does not take into account that the assigned vehicle within the framework of isolated planning may already be occupied with other requests.
It is necessary to consider the inventory management system for all requests, the coincidence/discrepancy of delivery days for each specific cycle, and as a result, the possibility of fulfilling the transportation plan with a specific transport vehicle.
Planning from a systemic approach allows taking these aspects into account and brings the developed plan closer to the condition of feasibility.

Conclusions
The proposed algorithm allows obtaining a schedule of work for each request, coordinating them among themselves, and arriving at a general schedule of the system's operation.The algorithm takes into account the inventory management system, calculates the demand for transport vehicles considering the verification of coincidence/discrepancy of delivery days for a specific cycle and the completion of delivery for the previous cycle.It also allows calculating the required number of transport vehicles when planning shipments of goods in intercity communication with batch shipments.Some further research directions could include adapting the proposed algorithm for other types of communication and developing a software complex for automating calculations based on the algorithm.

Fig. 3 .
Fig. 3. Stock replenishment and consumption graph for the first request.

Fig. 4 .
Fig. 4. Stock replenishment and consumption graph for the second request.

Fig. 5 .
Fig. 5. Stock replenishment and consumption graph for the third request.

Fig. 6 .
Fig. 6.Stock replenishment and consumption graph for the fourth request.

Fig. 7 .
Fig. 7. Work Schedule of Vehicles for All Requests.

Table 1 .
Source data of routes.

Table 2 .
Source data of routes.

Table 4 .
The initial data for the inventory management system.

Table 5 .
Results of inventory management system parameters calculation.