The fourth-party logistics routing problem (4PLRP) is an important issue in the operation of fourth-party logistics (4PL). In this paper, the study of fourth-party logistics (4PL) path optimization considers that more third-party logistics (3PL) undertake transportation tasks. Under the condition that the 3PL transportation time, transportation cost, node transit time, and transit cost are uncertain, 4PL provides customers with a set of transportation solutions to transport transportation tasks from the initial node to the destination node according to the customer’s risk aversion preference. The transportation scheme not only meets the customer’s time and cost requirements but also meets the carrying capacity and reputation constraints of 3PL. Between the two nodes, one or more 3PLs will undertake the transportation task. The customer’s risk preference will be measured by the ratio utility theory (RUT). An ant colony system-improved grey wolf optimization (ACS-IGWO) is designed to solve the model, and the grey wolf optimization (GWO) is improved by the convergence factor and the proportional weight. Problem analysis is conducted through simulation experiments.

The third party logistics (3PL) suppliers selection is a key issue in sustainable operation of fourth party logistics (4PL). A two-stage auction mechanism is designed for the selection of 3PL suppliers. Different from previous studies, the paper considers risk preference of 4PL integrators during the auction and uses the prospect theory to establish the auction scoring function of 4PL integrators. First, a first score sealed auction (FSSA) mechanism is used to solve the selection problem. However, the results show that FSSA is not an ideal method. Hence, the English auction (EA) mechanism is combined with the FSSA mechanism to form a two-stage auction. The FSSA is taken as the first stage auction, and the EA is taken as the second stage auction, and the two-stage auction mechanism is constructed. The two-stage auction can improve the utility of the 4PL integrator and the auction efficiency. In addition, for the degree of disclosure of attribute weights in the scoring function, two states, complete information and incomplete information is designed. In case analysis, the validity of the designed two-stage auction mechanism is verified. The 4PL integrator can obtain higher utility under the risk-neutral auction than the risk-averse auction. The complete information auction does not make the 4PL integrator obtain higher utility than the incomplete information auction.

Considering the uncertainty of transportation time and cost due to seasonality and human factors, A multi-objective chance constrained programming model with minimum transportation time and cost was established. According to the characteristics of the problem, the beetle search algorithm with one beetle is changed into multiple beetles and Dijkstra algorithm is embedded, a hybrid beetle swarm optimization algorithm (HBSO) is designed to solve the problem, and the case analysis and algorithm analysis are made for three different examples. By adjusting the model parameters, the minimum objective function value under the combination of parameters is obtained. Under the three examples, the influence of the customer on the time and cost is different, and the impact on the whole logistics and transportation scheme is obtained. The Taguchi test was used to determine the optimal parameter combination of the HBSO under different node scales. The GA and PSO are embedded with Dijkstra algorithm, and are compared with HBSO to verify the optimization ability of the HBSO.

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