DYMEMULP – Dynamic Model of Process Optimisation in Regional Logistics

The expansion of logistics requirements, limited space and strict requirements of genera - tors of logistics requests (GLR) in terms of service quality complicate the supply of the region, resulting in the necessity to improve logistics models (MoL). Proximity to water, the presence of ports and piers along the coast, new eco vehicles and the development of cooperation between land and water transport are elements for improving the existing MoLs in an economically and environmentally acceptable way. Research on the development of an improved multi-echelon logistics network with variable terminals including the coordination and cooperation of a heterogeneous group of transport agencies for the realisation of goods flows represents an innovation in regional logistics (RL). This article presents an integrated MoL development process using dynamic optimisation with a focus on spatial, temporal, transport


INTRODUCTION
The "regional metabolism" trend represented in terms of [1][2][3][4] (1) larger numbers of inhabitants and GLRs, (2) existence of different supply chains (SC) in a limited area, (3) change in the type and structure of logistical requirements, (4) limitations in the realisation of physical distribution of goods, (5) limited space for system development, (6) increased requirements for the preservation of the environment and historical components, requires the improvement of the existing MoL in order to provide a quality response to new logistical needs. The resulting changes in the SC structure, which are reflected in the specialisation, professionalisation and integration of certain logistics systems (LS) and processes, as well as the greater volume of commodity exchange, affect the implementation of the reengineering process of the existing MoL in the domain of systemic, technological and organisational improvements with an emphasis on optimisation, in order to develop a higher level of logistics. It is required that a new MoL integrates several regional functions [2], i.e. housing, tourism, transit and city logistics, into one functional model, which relies on a new paradigm of logistics. The focus is on [1] the total integration of the system, the efficient and economical operation of the RL system, the development of solutions with minimal spatial interventions and the application of technologies that have a small negative impact on the environment.
Ports today have the characteristics of modern logistics centres (LC) [1]. From a strategic point of view, an important systemic solution is the connection of a large port as a p-Hub with several smaller regional ports and wharves along the entire coast of the region [2], which can exist as a network of city distribution centres (CDC). Piers along the coast represent the basis for the development of a network of cross docking terminals (CDT), with the aim of realising the physical distribution of goods ( Figure 1).
The creation of a new MoL is the result of the need for optimal, efficient, high-quality and ecologically acceptable supply to the region.
The focus on "port-oriented logistics chains" aims to [2]: include the port in RL as an integrum system of the regional importance, enable the transfer of part of the transport to the water side and the goal of reducing the number of trucks on the streets.
The new logistics needs of the region initiate the improvement of the existing MoL with a focus on: (1) the new logistics network in which the p-Hub port is located, (2) the application of eco-vehicles in the process of distribution of goods, (3) the establishment of cooperation and coordination processes and (4) digitisation of all systems and processes. The key optimisation elements go in the direction of [2] coordination on the road-sea route and cooperation on the truck-eco distribution vehicle (cargobike, cargo hopper) route. The development of a CDT network in the form of flow terminals along the coast for receiving solar-electric powered distribution boats carrying delivery containers is an essential technological component of coordination. By connecting CDT and distribution zones on the mainland with eco vehicles that distribute goods to GLR, a naturally paired and improved technological solution can be provided.  [2] This article aims to present the original optimisation procedure DYMEMULP in the reengineering of the regional MoL, which contains a multi-echelon logistics network with variable CDTs, multiple unified sets of vehicles and various forms of coordination and cooperation in the transport process.

PROBLEM DEFINITION AND METHODOLOGY FORMULATION
The reengineering of the regional MoL in this article is focused on the relation [2]: geographic space → logistics profile → clustering → location-allocation problem → system solution → supply optimisation. The development of new MoLs requires comprehensiveness [5]: (1) strategic planning of the logistics network, (2) concentration of logistics flows within the LC, (3) development of CDTs in the function of rapid transfer of goods flows from the water side, (4) representation of the process of cooperation of modes of transport, (5) process coordination in road transport, (6) process management according to the core supply chain management model (7) representation of the new logistics paradigm, (8) integration of several regional functions into one model, (9) digitalisation of processes. The MoL must meet a number of objectives: (1) elimination of delays in the realisation of goods flows, (2) reduction of freight transport in urban and tourist areas, (3) elimination of duplication of capacity with the aim of greater spatial availability, (4) lower costs of operating the system, (5) ensured expected level of supply and quality of logistics service etc.
The MoL development process has 4 phases [2]: (1) determination of the logistics needs of the region, (2) planning of a possible logistics network, which can meet the identified needs, (3) identification of a new MoL based on the DYMEMULP optimisation and (4) comparison of the proposed solution to some other techniques. In the first phase, the border of the region and the number, spatial arrangement of GLRs and their qualitative and quantitative logistical needs are determined. The established logistics profile of the region generates a possible multi-echelon logistics network that can meet the needs. The identified possible network and the transport processes in it need to be optimised. Finally, the new and previous MoLs should be compared based on the criteria.
The problem of determining the optimal location of potential CDCs and CDTs [9,[19][20][21] can be solved by general optimisation, heuristics and metaheuristics. For the purposes of the research presented in this article, the methods of the gravity model are used.

MATHEMATICAL FORMULATION OF THE DYMEMULP MODEL
One region constitutes a set of clusters ={e}, divided into zones j, j∈J. Within the zones there are GLRs z, z∈Z, which generate flows of goods.
Each zone is represented by essential attributes: A) number of objects No z , with a defined probability of belonging by zone: C) average daily quantity of delivered goods q , No z · jt λ · jt q , by zones: Each GLR from the set Z={z} has attributes D={d z }: GIS position (x, y), quantity of goods q(d z ), requested in the period t(d z ) within the zone j(d z ), which should be delivered in the interval [t 1 (d z ), to t m (d z )]. Delivery frequency W(d z ), quantity of one delivery Vis(d z ) and required delivery time Zvi(d z ) are also attributes. The values of q(d z ) and W(d z ) are defined by the quantitative O-D matrix.
All GLRs from the set Z={z}, according to logistic requirements (type of goods etc.), are divided into five groups: G = {1, ... , 5}: A "day before" delivery strategy was defined for GLRs.
Each cluster e has a defined graph A=B·V of the transport network consisting of: (1) class of nodes B={1, ..., n} and (2) class of links V=B·B.
The regional p-Hub (P h ) is located within the port ( Figure 2) and has a given location due to the location of the port itself. Fixed satellites P h , in the form of CDCs, I={i}, are in operation throughout the year. Their potential location is determined based on preferential supply zones. Every satellite i∈I has a defined capacity and set of vehicles k. In period t 2 , when the demand for goods increases h(q j +q * Every P h , CDC and CDT owns a set of vehicles k, k∈K. Vehicle type set K=5: − k=1, truck, load capacity g 1 =5 t and load factor η 1 =0.9, − k=2, cargohopper, load capacity g 2 =5 t and load factor η 2 =0.9 − k=3, cargo bike, load capacity g 3 =0.5 t and load factor η 3 =0.9, − k=4, eco boat, load capacity g 4 =20 t and load factor η 4 =0.9, − k=5, tow truck, load capacity g 5 =26 t and load factor η 5 =0.9. It is accepted that there are two periods: tourist season (n 1 =120 days) and the offseason (n 2 =245 days). The transport process is presented as a vector of transport activity. Total transport activity represents the sum of individual transport processes between echelons: where q et represents quantity of goods and d et is a distance between echelons e in period t.
Capacities S p ={g r } within P h and CDC meet storage needs in the period T, ∑ is the total demand GLR, and 1 j W = ∑ the total frequency of deliveries. Sum capacity P h and CDC must be ≥ q jt from the demand of the zones j.
The consolidated supply process is realised by vehicles of the types k 4 and k 5 , transporting the aggregate quantity goods q∈Q from P h to one or more satellites from the set I or L.
Distribution of goods is realised from satellites i, i∈I оr l, l∈L, vehicle types k 1 , k 2 , k 3 and k 4 ; so that the total amount of goods q∈Q points to the GLR for the defined zone j, j∈J.
Vehicles k have defined movement routes r kt , in period t. Each route is defined based on: total demand − k 5 , k 5 ∈K moves along a defined route r Pik 5 t transporting a quantity of goods q jt from P h to the satellite and by water. Boat k 4 delivers goods q jt in period t 2 from P h to satellite i or l or directly to zone j, returning after unloading to satellite from satellite l to zone j distributing goods q jt , and returns after The location of the satellite l determines the affiliation of the routes 2 ljk t r with zones of preference l in period t 2 ; − k 3 , k 3 ∈K, moves along a defined route 3 ljk t r , from satellite l to zone j, distributing goods q jt , and returns after Transport means k 2 and k 3 are coordinated with means k 1 (truckeco vehicle). The use of a particular vehicle type k is defined through the following indicators: δ jkt -indicator of the use of vehicles of type k for the supply of zone j in period t, δ jkt ={0,1}; δ lkt -indicator of the use of vehicles of type k for supplying satellites l in period t, δ lkt ={0,1}.
Defined distances between LCs require unit costs to be defined as k ξ with respect to using type k vehicles for transporting goods at a distance of 1 km: CDC Z ijkt C − − the cost of one tour of a type k vehicle from CDC to zone j and within it, CDT Z ljkt C − − the cost of one tour of a type k vehicle from CDT to zone j and within it =( ) The mathematical formulation of the DYMEMULP model is: with the following restrictions: Function 6 minimises the costs of supplying the zones of the region by choosing the most convenient CDTs and CDT locations, the opening of which is associated with fixed costs, as well as by using the most convenient transport chains. Constraint 7 ensures that the quantity of goods required in each of the observed periods is delivered to the zones of the region. Constraint sets 8

General test example
For a general example, two sets of randomly generated problem instances were determined ( Table 1): instances of medium dimensions (Ω=50) and instances of large dimensions (Λ=50).  The average degree of utilisation of the vehicle's carrying capacity η k =0.9 The concept of generating instances included: (1) different number of randomly generated zones j, (2) randomly generated quantities of goods for distribution q jt , whereby the growth of future demand was varied * , to +400% compared to current demand, (3) randomly generated number and spatial arrangement of satellites i, i∈I and l, l∈L, (4) randomly generated distances between network nodes d ikt , d lkt , d ijkt , d ljkt , d ilkt , i (5) different opening costs satellites F i CDC and F l CDT . The defined set of test instances ( Table 2) was solved by applying the DYMEMULP model, using the CPLEX 12.2 program on a computer with an Intel i3-540 processor at 3.07 GHz, 4 GB of RAM memory. The analysis was realised with a limited problem solving time of 3600 seconds. Input data processing was implemented in the C++ programming language.
The program varies 12 types of data in an acceptable time and can provide optimal solutions to instances of type Ω and type Λ for regions up to level: I=30CDC, L=75CDT, J=160 supply zones, K=5 sets of vehicles, T=1 time interval with two periods observed.

Case study
The proposed DYMEMULP optimisation was tested on the Montenegrin coast region. Empirical data were collected and systematically processed. The traffic network of the region was created using the GPS system in the WGS84 coordinate system. For easier processing, i.e. to calculate the distance of points in a plane and not on an ellipsoid, all data from WGS84 were transferred to the UTM34 coordinate system, namely to ESRI Shape -UTM34 standard GIS format, which is supported by every GIS program. The projection of all data was done in Google Earth and transferred to the QGIS program (version 2.2).
It was established that there were 1456 GLRs in the winter period and 2365 GLRs during the tourist season in the region. K-means clustering determined 21 clusters and 37 supply zones. For each zone j, j∈J the centre of the network was determined, using the program Python ver. 2.7.8. The defined centre of the zone ( Table 3) was the basis for defining the routes within those zones. All defined routes are constant and do not change during time periods t 1 and t 2 . Defined routes in DYMEMULP are treated as a cost incurred by the vehicle during the distribution of goods.
In order to define the cost of construction, the author made conceptual solutions of CDCs and CDTs in Au-toCAD. The construction costs are: (1) CDC1 -Bar €698,460.80, (2) CDC2 -Verige €713,449.48, (3) CDC3  The potential network structure (Figure 3) consists of: Ph in Bar, three CDCs -Bar, Verige and Zelenika, 15 CDTs that are interactively connected with the Ph and CDCs and supply 37 zones. Transport processes are realised by five unified sets of vehicles k, k∈K: (1) tow truck with a capacity of 26 t, (2) a boat with a capacity of 20 t, (3) a diesel truck with a capacity of 5 t, (4) a cargohopper with a capacity of 5 t, and (5) a cargobike with a capacity of 0.5 t. It was determined that there are 6 types of transport chains: (1) tow truck -truck, (2) boat -cargohopper, (3) boat -cargobike, (4) tow truck -boat -cargohopper, (5) tow truck -boat -cargobike, (6) tugboat -boat. By changing the transport chain, the unit cost changes ξ k for vehicle k, k∈K.
The optimisation results are as follows:  Based on the results of the optimisation process, it is concluded that an optimal multi-echelon regional network has been established, consisting of: 1 p-Hub, 2 CDCs (Bar and Zelenika), as well as 13 CDTs, which function in the period t 2 .

Figure 4 -Establishment of logistics network after DYMEMULP optimisation
The effects of applying the optimisation process are shown in Table 4.

DISCUSSION
Economies of regions depend more and more on LSs and their degree of operability. Greater intensity of freight transport in regions initiates the application of new technological solutions, organisational forms, forms of cooperation and management methods in order to reduce their negative impact on space, systems, processes and the environment. The main goals of logistics today are [1−5] process optimisation, system integration, space rationalisation and digitisation. The application of simple solutions in the function of complex optimisation is the task of strategic logistics planning. By initiating new strategic approaches, it should enable the integration and rationalisation of the usage of various micro, meta and macro networks and LSs in a region with the aim of its optimal supply. Reengineering MoLs goes into the direction of seeking a minimum balance between needs, wishes and possibilities in a region, applying postulates, economics, logistics, management and ecology. Because SCs have the character of a bridge in connecting micro, meta and macro LSs [2], the new logistics paradigm emphasises the optimisation of all its links. The application of optimisation in the development process of regional MoLs represents an approach to defining the cargo balance, selection of logistics networks and services and the design of an improved logistics service. It supports making strategic decisions in the function of realising operational processes.
In the expansion of logistics activities in the regions, and the increasing spatial limitation within them, the creation of a cooperative distribution model is one of the possible sustainable solutions. Distribution solutions based on the cooperation of road and water transport systems, as well as those solutions that enable coordination in road traffic, can influence the creation of a series of positive effects: reduction of total logistics costs, increase in flexibility, reliability and quality in supply, reduction of traffic congestion, reduction of environmental pollution, creation of a higher quality tourist service, increase in the level of safety etc.
The results obtained by testing the DYMEMULP optimisation procedure indicate: 1) Justification of its application in solving real problems in regional logistics; 2) The possibility of monitoring 4 components: time, transport, economic and environmental; 3) The possibility of iterative action, changing the input data in the instance if the optimal solution is not found; 4) The possibility of parallel optimisation of a large number of SCs with the quantification of effects for each SC separately; 5) Openness of the model for adding restrictions, related to the capacity of the LC, management of stock of goods in the LC, definition of optimal routes in order to monitor the operation of the entire system; 6) That a program that varies 12 types of data in acceptable time can offer optimal solutions of instances of type Ω and type Λ for regions of size up to level I=30 CDC, L=75 CDT, J=160 supply zones, K=5 sets of vehicles in time interval with two periods observed; 7) Efficiency in solving a concrete example for the Montenegrin littoral region where a case of cooperation and coordination was observed by valorising the port and CDTs. It was shown that the new MoL solution for the Montenegrin coastal region has an average of +30% time savings in transport, +28.49% economic profit, and 16.5% less transport work compared to the current solution; 8) A high level of environmental acceptability of the new MoL for the Montenegrin littoral region due to the application of technologies with a low negative impact on the environment. The average achieved positive environmental effects amount to +74.99%, which is a significant level of acceptability.

CONCLUSION
The goal of the research presented in this article was to develop an MoL based on a system analysis using the original DYMEMULP optimisation procedure as a quality basis for the development of strategic solutions for an optimal multi-echelon logistics network and the process of dynamic routing of a heterogeneous group of vehicles, which will be able to contribute to: a higher level of operability of RL, reducing the total costs of logistics, reducing the time of order realisation in conditions of uncertainty, achieving greater spatial and ecological effects, reducing traffic jams by using the sea as a road and preserving the natural and historical heritage by using eco vehicles.
The obtained results provide a direct answer to the question of which system structure is justified to establish, which transport chains are acceptable, and which model of cooperation and coordination is acceptable, which essentially represents a gradual approach to total logistics integration. The work contributes to the field of logistics theory in the area of strategic planning due to finding new forms of cooperation and transport coordination. It contributes to optimisation theory as it shows the development of a new original, universal and flexible optimisation model open to innovation, where after minor adjustments it can be applied to solve capacitive routing problems in general optimisation or heuristics and metaheuristics.
The practical implications of addressing the logistical issues in this article are in providing guidance for policy makers and decision makers in regional entities when defining new integrated MoLs. An additional practical implication is the developed model that provides a simple but effective tool for decision makers in solving all kinds of practical multi-criteria problems in RL. Its practicality is also reflected in the fact that it enables investigating the additional application of existing, and especially new, rapidly emerging transport technology solutions, and using the possibility of evaluating and selecting new solutions.