A Model for the Designing of Multimodal Transport Processes and the Concept of Its Integration with the EPLOS System

: The paper proposes a new single criterion mathematical model for the designing of multimodal transport processes by taking into account the cargo’s susceptibility and the concept of its inclusion into the EPLOS system , which is done as part of the EUREKA initiative . This system will integrate the data from logistics sources and transport and logistics infrastructure from many sources. In the first phase of its implementation, it will cover the Czech Republic, Polan d, and the Baltic States. Using the EPLOS system integrating data from various sources needed to solve this problem is a proposal to overcome the main barrier to the effective planning of multimodal transport processes – a lack of reliable information.


INTRODUCTION
The planning of technological processes in transport, especially when taking into account many of its branches, is a multi-faceted and complex process. It requires comprehensive knowledge of the features of individual transport technologies, as well as the physical configuration options of the supply chain and shipping offers. Thus, the correct implementation of this process is conditioned by the access to a lot of detailed information regarding transport offers, transport infrastructure, and transshipment terminals. An important part of this information is included in the EPLOS system, created as part of the EUREKA initiative. Hence, its use in the planning of multimodal transport processes can significantly simplify this process and, to some extent, automate it. The EPLOS system will integrate the data on logistics companies, as well as transport and logistics infrastructure, from many sources. In the first phase of its implementation, it will cover the Czech Republic, Poland, and the Baltic States.
It is noteworthy that in literature, the modeling of multimodal load-shifting technologies is recognized primarily from the perspective of planning routes for moving material goods and their transshipments between different 1 The simplification of this approach to the issue of the selection of unimodal transport technologies, including the choice of the means of types of transport (see, e.g. [30] or [31]). In the model proposed in this article, by extending this issue considerably, the focus was also on the selection of freight transport forms and work resources. Additionally, which distinguishes the model presented below, it includes a formalized approach to the mapping of cargo transport susceptibility.
The model described, e.g., in [3], is quite complicated because it includes a significant number of features of perishable loads. The new model offers maximum simplification in this respect, which can be taken into account only in the case of loads sensitive to moisture, solar radiation, and temperature conditions. Some specific conditions necessary for perishable products are omitted here, as well as the issues regarding sensitivity to static and dynamic effects. However, only the costs were taken into account as the evaluation criterion. This model was further simplified by taking into consideration work resources instead of separately analyzing technical measures and employees. At the same time, in the presented model, the issue of the temporal availability of individual work resources was included, which means that it may have significant practical importance. Thus, the article proposes an original single criterion model for designing multimodal transport processes, taking into account the vulnerability of loads, selection of work resources, along with the temporal availability of work resources. Moreover, particular attention was paid to the scope of the required data for this model and references were made to the possibility of obtaining this data from the EPLOS system.

A MODEL FOR DESIGNING MULTIMODAL TRANSPORT PROCESSES
In accordance with the previous comments, the following subsections present a single criterion mathematical model for the selection of multimodal technologies for transporting perishable loads sensitive only to moisture, solar radiation, transport and the form of transport loads has been described in the monograph [6]. and/or temperature conditions, taking into account the temporal availability of work resources. The adopted assumptions and elements of the model were characterized, as well as a formal record of decision variables, constraints, and the assessment criterion, which are transport baskets.

Assumptions and General Form of the Model
The basic assumption is the freedom to choose a transport technology for specific transport tasks, including the ability to choose the work resources with service under each technology. Transport technologies have been defined, taking into account transport forms, performed activities, displacement routes, and work resources with their service. On the other hand, the technological process within the technology was recorded as a series of ordered activities, of which for each is known: the form of the transport of loads, displacement routes and work resources with their service, which may be involved in its implementation.
Transport tasks included in the model relate to the movement of selected products, which may have a number of features determining their transport susceptibility. At the same time, only load features were seen as the most important due to their transport susceptibility and hence were taken into account. For each activity of the technological process, the possibility of choosing different forms of cargo transportation was assumed. The impact of the transport form of loads on their transport susceptibility was also taken into account.
It was also assumed that for each transport form, the number of load units that will fit in is known (equal to 1 in the case of loose cargo). Additionally, for each means of transport, the number of pieces of cargo that will fit in its cargo space when transported is known. This means that the issue of forming load units and planning the distribution of load units in the vehicle's cargo space -such as the problem of allocating employees to devices -has been excluded from this decision problem as a separate optimization issue.
Moreover, it was assumed that the used multimodal transport technologies must guarantee the safety of transported loads, taking into account their transport conditions. On the other hand, the assessment of the selection of multimodal transport technologies is carried out by taking into account the minimization of the costs of moving cargo.
Additionally, it was assumed that the problem of selecting a transport technology for tasks to be carried out within a specified time horizon was considered. As a consequence, individual technical resources, together with human resources, can be allocated in this period to perform only one activity identified in the technological process, and their time availability for individual activities is known due to their current load and location.
Considering the above, the model for selecting multimodal technologies for the transport of perishable products, MDT, was formally written as follows: where: BF -loads, PF -form of transport, UF -work resources and their service, TF -displacement routes, TM -multimodal transport technologies, ZM -transport tasks, O -organization reflecting the manner of the implementation of transport tasks, including decisions regarding the selection of the transport technology and work resources with employees.

Model Elements
The loads BF were mapped based on a set of their types and a set of their characteristics FB: -the gross mass of one piece of load or unit package of b th type (for non-unit loads of any small value), kg, ) ( min b t -the lowest permissible temperature for the transport of b th type load, K, ) ( max b t -the highest permissible temperature for the transport of b th type load, K, Similarly, the transport characters PF were mapped, taking into account a set of numbers of their types {1, ..., , ..., } p P = P and a set of their characteristics FP: ) ( p ow -the ability to protect the load against water by the p th form of transport, ) ( p os -the ability to protect the load against solar radiation and light by the p th form of transport. ) ( p w t -the ability to change the temperature in the immediate vicinity of the load by the p th form of transport, ) ( Moreover, the work resources and their service UF were mapped, taking into account a set of numbers of their types } ,..., ,..., and a set of their characteristics U F . However, in this case, the set U was decomposed into a set of numbers of types: • of means of transport with the service 1 U , • of loading devices with the service 2 U .
Thus, a set of characteristics of the means of transport with the service 1 U F and a set of characteristics of loading devices with the service 2 U F was obtained: ) (u NU -number of the u th type of the means of transport available with the service, pcs, ) ( min u t r -the minimum air temperature during transport in the cargo space of the means of transport of the u th type, K, ) ( max u t r -the maximum air temperature during transport in the cargo space of the means of transport of the u th type, K, ) (u t rz ∆ -the maximum air temperature fluctuations during transport in the cargo space of the means of transport of the u th type, K, ) (u v sr -the average speed of transport of the means of transport of the u th type, km/h, ) (u ow u -the possibility of protecting against the direct effects of water on the load by the means of transport of the u th type, ) (u os u -the ability to provide load protection against light and solar radiation for the means of transport of the u th type, ) (u k ts -the unit cost of operation depending on the mileage for the means of transport of the u th type, PLN/km, ) (u k tt -the unit cost of operation depending on transport time for the means of transport of the u th type, PLN/h, ) (u k tw -unit labor cost dependent on the time of work of all service employees for the means of transport of the u th type, PLN/h, ) (u UU -a set of numbers of the types of loading devices with the service that can be operated by the means of transport of the u th type, ) ( 1 u U P -a set of numbers of the load transport forms served by the means of transport of the u th type, ) , , ( b p u N p -the capacity of the means of transport of the uth type in the number of units of the p th transport form for the b th type of load, pcs.    -a set of numbers of the types of work resources together with the service that can be used to carry out the z th transport task.
Considering the above, a set of numbers of types of multimodal transport technologies, which can be used to implement the z th transport task, was defined as follows:

Decision Variables
The model includes the following four types of decision variables: that assumes a value of 1 when the z th transport task is to be performed according to the d-type technology and 0 in the opposite case, In accordance with the above, the next of the considered decision variables relate to the selection of a transport technology for tasks, the selection of work resources with service for the implementation of individual activities under the given technologies, and the moment of commencing the implementation of subsequent activities.

Constraints
The constraints included in the model result from the characteristics considered to be significant, i.e. load characteristics, characteristics of loading forms, and means of transport, as well as from the characteristics of multimodal transport technologies themselves. It was assumed that the implementation of tasks should be ensured by selecting technologies for them (1), while for the activities included in the selected technologies, it is necessary to choose work resources with service (2) and (3). It is also necessary to take into account the constraints resulting from the available number of these work resources (4). Additionally, the requirements regarding the transport temperature (5)-(7), as well as the protection of the load against the adverse effects of water (8) and solar radiation and light (9), were taken into account. The following constraint includes the possibility of cooperation of the means of transport with the loading devices (10) and (11), as well as the possibility of handling the selected forms of transport by the chosen means of transport (12) and (13), the possibility of using them to perform specific tasks (14), the selection for individual technological activities (15) and their movement on individual routes (16), or admissibility of a selection of individual technologies for the considered transport tasks (17). The conditions resulting from the permissible loading of loading devices (18) are also important. The last of the constraints result from the temporary availability of work resources for the implementation of tasks and the earliest start and end moments of completion of individual tasks (19)- (22), and from the unambiguous allocation of subsequent work resources of individual types (23).

Assessment Criterion
In the model, as the criteria for assessing solutions, the criterion of the total transport costs was included, including the cost of the work of the means of transport and loading equipment, as well as the labor costs of employees servicing them. Formally, this criterion was written as follows:

THE CONCEPT OF THE INTEGRATION OF THE MODEL FOR THE SELECTION OF MULTIMODAL TRANSPORT TECHNOLOGIES WITH THE EPLOS SYSTEM
In its basic form, the EPLOS system, created as part of the EUREKA initiative, is a database system which integrates, from various sources, information taken into account when making strategic and operational decisions in the area of logistics related to the movement of material goods between economic entities. In the first phase of its implementation, it will cover the Czech Republic, Poland, and the Baltic States. The primary assumed functionality of this tool is to provide information to the TMS class systems and other systems used by individual enterprises (for more detailed characteristics of the EPLOS system, see [30] and [31]). Nevertheless, there is a great potential of the EPLOS tool in terms of their extension with the individual methods of solving decision problems -especially those that are not included in the TMS class systems. One such issue is the selection of multimodal transport technologies for fixed transport tasks.
Assuming that the problem of the selection of multimodal transport technologies is formulated following the model presented in Chapter 2, to solve it, it is justified to use the EPLOS database in the scope of: • information about the available means of transport (their type, number and supported forms of transport), • information about the available loading devices (their type, number, capacity, and supported transport forms), • data on the transport routes for external transport (mileage, length, authorized means of transport, costs of using the infrastructure), • generating variant solutions for the technological process in transport (searching for transport offers and transshipment options together with the assessment of the availability of the loading equipment and means of transport -the assumed target functionality of the EPLOS system).
The use of the proposed model by using the EPLOS system will, therefore, involve the need to enter additional data regarding: In the case of extending the functionality of the EPLOS system by planning multimodal transport technologies, it is also possible to include in it a number of catalogs useful in this field, such as the catalog of loads and their characteristics, or the catalog of transport forms. Moreover, it is possible to implement a number of algorithms that estimate the data required to solve the analyzed problem (e.g., characteristics of reloading relations, predicted stoppages of the means of transport, and anticipated times of work of other employees serving them). This approach will minimize the need to manually enter the data that reflects the decision problem in the selection of multimodal load handling technologies.
The described concept of the integration of the model for the selection of multimodal transport technologies with the EPLOS system, taking into account its variant, is schematically presented in Fig. 1.  Figure 1 The concept of using the EPLOS system and its development in the selection of multimodal transport technologies

CONCLUSIONS
The issue of the selection of multimodal transport technologies analyzed in the article can be considered for a specific company that has a specific transport potential, while the implementation of the agreed transport tasks can be carried out with the involvement of both its own logistics potential, as well as the logistics potential of transport and forwarding companies as well as providing reloading services. Assuming that the transport tasks taken into account may relate to the movement of loads with different characteristics and forms of transport in various relations, the problem of the selection of multimodal transport technologies becomes very complex, and its solutions require a number of data that are subject to constant changes in the market economy conditions. This makes it justified to use the EPLOS system and even its extension with additional functionalities (estimation of some model parameters, catalogs).
At the same time, it should be noted that in real conditions, the selection of the best solution in the field of transport technology is often determined by non-cost criteria, such as transport time and load safety. Importantly, these factors are often taken into account simultaneously. This means that it is justified at the next stage to develop the proposed approach by a multi-criteria assessment method of transport technology variants, including, e.g., the point method or the MAJA method [32][33][34].

Data exchange interfaces
Airport database  transport tasks  loads and their transport forms,  characteristics of the means of transport in terms of guaranteed transport conditions, labor costs, capacity and service capabilities by loading devices,  labor costs of loading equipment,  characteristics of transshipment relations,  the expected stopping times of means of transport on the routes of external transport and the time of work of other employees carrying out the movements and their additional labor costs.