## 1. Introduction

_{2}emission as environmental issue, and maximizing the total social influence as social issue; Sherafati et al. (2019) maximize profit primarily while capturing social development by prioritizing the less developed regions and dealing with ecological aspect by using environmentally friendly transport facilities [16]. Accordingly, optimization problems that are related to sustainable supply chain design are solved as multi-objective problems [15,16,17,18]. The authors of the paper [14] have analyzed more than 100 papers, including documents studying supply chains, and came up with the conclusion that modern literature emphasizes the environmental aspects of the supply chain design, but does not pay much attention to social criteria. It should be noted that the commonly used efficiency criterion that allows for considering three directions of sustainable development is the total costs, which include all of the losses and expenses related to environmental and social issues [19,20,21].

## 2. Methodology

#### 2.1. Problem Statement

- The formation of alternative LC variants, determining the structure of the technological scheme. Alternatives are determined on the basis of the availability of cargo terminals, customs points, as well as partner forwarders operating in the appropriate geographic area.
- The efficiency evaluation for a set of alternative structures. The assessment is carried out on the basis of average market value indicators, while taking the random nature of technological parameters into account. The result of the evaluation for each LC variant is a random value of the efficiency criterion.
- The selection of the optimal LC structure and subsequent measures related to the determination of the LC participants and the development of specific technological processes. The choice of the optimal LC structure is carried out on the basis of a comparative assessment of characteristics of random variables that describe the effectiveness criterion for each alternative structure. For the presented formulation of the problem (1), the choice is made according to the minimum expected value of the total costs.

#### 2.2. Basic Alternative Variants of the Logistics Chains’ Structure

#### 2.3. Evaluating the Effectiveness of the Logistic Chain Structures

- costs of finding a client;
- costs associated with the preparation of documentation for the delivery of a shipment from a consignor to a consignee;
- costs of finding a carrier, partner forwarder (if appropriate), 3PL-provider (if appropriate);
- costs of the organization and implementation of loading and unloading processes;
- costs of the carrier (carriers) services;
- expenses for payment of the 3PL-provider (providers) services;
- customs payments; and,
- tax deductions.

- costs of forming a transport package;
- losses due to freezing of funds that constitutes the shipment value; and,
- payment for the services of forwarders.

- direct costs of delivery operations;
- costs of idle time under loading and unloading;
- costs of idle time in the customs point; and,
- tax deductions.

- costs of transshipment (unloading and loading);
- costs of the formation and disbandment of transport packages;
- costs of interim storage operations;
- tax deductions.

## 3. Results

## 4. Discussion

- set the incoming requests’ interval as a constant parameter (for the flow of requests, the expected value of the requests interval is taken);
- define ranges on the set of possible values of the delivery distance;
- for the accepted value of the requests’ arrival interval and the upper bound of the delivery distance range, determine the roots of equation (23) for all pairs of the LC structures; and,
- the obtained solutions determine the bounds of the areas of the most efficient use of the alternative LC structures, the corresponding dependencies of the total costs form the lower polygonal chain on the graph.

- the use of the simplest version of the LC is optimal for the delivery by road transport of small consignments (up to three tons);
- the use in road transport of the LC variant with the participation of two freight forwarders is not characterized by the lowest possible total costs regardless of the values of the consignment weight and the delivery distance; therefore, the 2F-variant of the LC should only be used in cases when it is not possible to arrange delivery without the participation of the contractor forwarder; and,
- the bounds of the areas of the most effective LC structures (for the consignment volume as a parameter) inversely depend on the delivery distance.

- having the areas substantiated for the given demand parameters, decision-makers (freight forwarders or other logistics operators) can choose the proper LC structure without calculating the costs for all possible alternative structures;
- the proposed methodology contributes to decreasing of the clients servicing time and reduces possible mistakes made by operators while making a decision concerning the LC structure, and in total – supports the sustainable operation of transport on a regional scale; and,
- the areas of the most efficient use of the LC structures can be implemented in specialized tools of information systems supporting decisions of logistics operators.

## 5. Conclusions

## Funding

## Conflicts of Interest

## Appendix A

- ${t}_{search}$ is time spent by a dispatcher while searching for a customer (h);
- ${N}_{d}^{FF}$ is the number of employed dispatchers.

- justification of the LC structure for servicing the received request for the consignment delivery;
- search for a carrier (carriers) and conclusion of relevant agreements;
- search for contractors for loading operations (if this type of work is not performed by other participants) and conclusion of contracts with them;
- registration of transport and customs documentation;
- search for a cargo terminal and conclusion of relevant contracts; and,
- search for a foreign partner forwarder and conclusion of relevant agreements.

## Appendix B

- $\begin{array}{cc}\hfill {a}_{I}^{FF}=& {s}_{h}^{FF}\xb7{N}_{d}^{FF}+\frac{{\mathsf{\delta}}_{VAT}}{100+{\mathsf{\delta}}_{VAT}}\xb7\left[{N}_{d}^{FF}\xb7{s}_{h}^{FF}\xb7\left(1+{R}_{FF}\right)-{s}_{h\left(paid\right)}^{FF}\right]+\hfill \\ & +\frac{{\mathsf{\delta}}_{PT}}{100+{\mathsf{\delta}}_{VAT}}\xb7\left[0.02\xb7{\mathsf{\delta}}_{VAT}\xb7{s}_{h\left(paid\right)}^{FF}-{N}_{d}^{FF}\xb7{s}_{h}^{FF}\xb7\left(0.01\xb7{\mathsf{\delta}}_{VAT}-{R}_{FF}\right)\right].\hfill \end{array}$

- ${a}_{Q}^{C}={s}_{h}^{C}\xb7\left({\tilde{t}}_{t}^{L}+{\tilde{t}}_{t}^{U}\right)\xb7\left(1-\frac{{\mathsf{\delta}}_{PT}}{100}\right)$;
- ${a}_{L}^{C}=(1-\frac{{\mathsf{\delta}}_{PT}}{100})\xb7(\frac{{s}_{h}^{C}}{\tilde{V}}+{s}_{km}^{C})+(\frac{2\xb7{\mathsf{\delta}}_{PT}}{100}-1)\xb7\frac{{\mathsf{\delta}}_{VAT}}{100+{\mathsf{\delta}}_{VAT}}\xb7{s}_{km}^{C}$;
- ${a}_{QL}^{C}=(1-\frac{{\mathsf{\delta}}_{PT}}{100})\xb7\frac{{\mathsf{\delta}}_{VAT}}{100+{\mathsf{\delta}}_{VAT}}\xb7{T}_{tkm}^{C}+\frac{{\mathsf{\delta}}_{PT}}{100}\xb7{T}_{tkm}^{C}$.

- ${a}_{Q2}^{FO}=\frac{{c}_{t}\xb7\mathsf{\alpha}}{365\xb724\xb7100}\xb7\left({\tilde{t}}_{t}^{L}+{\tilde{t}}_{t}^{U}\right)\xb7\left(1+{N}_{FT}\right)$;
- ${a}_{QL}^{FO}=\frac{{c}_{t}\xb7\mathsf{\alpha}}{365\xb724\xb7100\xb7\tilde{V}}+{T}_{tkm}^{C}$;
- ${a}_{Q}^{FO}=\frac{{c}_{t}\xb7\mathsf{\alpha}\xb7{\tilde{t}}_{cust}\xb7{N}_{CP}}{365\xb724\xb7100}+{N}_{LU}\xb7{T}_{t}^{LU}+{N}_{FT}\xb7{T}_{ser}^{FT}+0.01\xb7{c}_{t}\xb7\left({\mathsf{\delta}}_{cust}+{\mathsf{\delta}}_{imp}\right)\xb7{N}_{CP}+\frac{1}{{q}_{cont}}\xb7\left({\tilde{t}}_{cont}\xb7{s}_{h}^{FO}+{c}_{pack}+{k}_{turn}\xb7{c}_{cont}\right);$
- ${a}_{I}^{FO}={N}_{d}^{FF}\xb7{s}_{h}^{FF}\xb7\left(1+{R}_{FF}\right)$.

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**Figure 7.**Dependence of the boundary value of the areas of the most efficient use of 1T- and 2T- structures on the delivery distance.

Delivery Distance | 1F-Structure | 2F-Structure | 1T-Structure | 2T-Structure |
---|---|---|---|---|

up to 300 km | up to 3 tons | - | 3…122 tons | more than 122 tons |

301…500 km | up to 3 tons | - | 3…31 tons | more than 31 tons |

501…700 km | up to 3 tons | - | 3…23 tons | more than 23 tons |

701…900 km | up to 2 tons | - | 2…20 tons | more than 20 tons |

901…1100 km | up to 2 tons | - | 2…19 tons | more than 19 tons |

1101…1300 km | up to 2 tons | - | 2…18 tons | more than 18 tons |

more than 1300 km | up to 2 tons | - | 2…17 tons | more than 17 tons |

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