Two Echelon Location Routing Problem with Simultaneous Pickup and Delivery: Mixed Integer Programming Formulations and Comparative Analysis

An exact algorithm for Two-Echelon Location-Routing problem with simultaneous pickup and delivery

This paper addresses a new variant of the location routing problem (LRP), namely the heterogeneous fleet LRP with simultaneous pickup and delivery and overloads (HFLRPSPDO) which has not been previously tackled in literatures. In this problem, the heterogeneous fleet is comprised of vehicles with different capacities, and the vehicle overloads up to a specified upper bound is allowed. This paper proposes a polynomial-size mixed integer linear programming formulation for the problem in which a penalty function, allowing capacity violations of vehicles, is integrated into objective function. Furthermore, two heuristic algorithms, respectively based on tabu search and simulated annealing, are proposed to solve HFLRPSPDO. Computational results on simulated instances show the effectiveness of the proposed problem formulation and the efficiency of the proposed heuristic algorithms.

In this paper, we consider a variant of the location-routing problem (LRP), namely the the multiobjective regional low-carbon LRP (MORLCLRP). The MORLCLRP seeks to minimize service duration, client waiting time, and total costs, which includes carbon emission costs and total depot, vehicle, and travelling costs with respect to fuel consumption, and considers three practical constraints: simultaneous pickup and delivery, heterogeneous fleet, and hard time windows. We formulated a multiobjective mixed integer programming formulations for the problem under study. Due to the complexity of the proposed problem, a general framework, named the multiobjective hyper-heuristic approach (MOHH), was applied for obtaining Pareto-optimal solutions. Aiming at improving the performance of the proposed approach, four selection strategies and three acceptance criteria were developed as the high-level heuristic (HLH), and three multiobjective evolutionary algorithms (MOEAs) were designed as the low-level heuristics (LLHs). The performance of the proposed approach was tested for a set of different instances and comparative analyses were also conducted against eight domain-tailored MOEAs. The results showed that the proposed algorithm produced a high-quality Pareto set for most instances. Additionally, extensive analyses were also carried out to empirically assess the effects of domain-specific parameters (i.e., fleet composition, client and depot distribution, and zones area) on key performance indicators (i.e., hypervolume, inverted generated distance, and ratio of nondominated individuals). Several management insights are provided by analyzing the Pareto solutions.

In the simultaneous pickup and delivery problem, every customer has both delivery demand and pick-up demand, and both demands need to be served simultaneously．Under this condition, a location-routing problem with simultaneous pickup and delivery model was established to minimize the sum of location cost, routing cost and transportation cost. For solving this model, a Hybrid Immune Algorithm was developed. The initial solution was generated by greedy clustering algorithm; The antibody was evaluated and sorted by the original immune algorithm; And the immune operation of the original algorithm was improved by the neighborhood search operation. Finally, the feasibility of the model and the effectiveness of the algorithm were verified by using the Hybrid Immune Algorithm, the original Immune Algorithm, the simulated annealing algorithm and the ant colony algorithm.

This study proposes a three-index flow-based mixed integer formulation to solve a two-echelon location routing problem with simultaneous pickup and delivery. In this formulation, pickup and delivery demands can be addressed using the same vehicle in each echelon of the network to reduce costs and increase logistics efficiency. We solve such NP-hard problem by developing a multistart hybrid heuristic with path relinking (MHH-PR) which is composed of local search and a variable neighbourhood descent algorithm. In the algorithm, three constructive heuristics are applied to generate diversified initial solutions, and path relinking is introduced for intensification and postoptimisation. Results indicate that MHH-PR can reduce the gap between the near optimal and global optimal solutions by 1%-2%. The proposed algorithm significantly improves computational efficiency by reducing the computational time of more than 10 min for existing cases involving 20 nodes to less than 10 s.

Objectives: Underreporting of adverse drug reactions (ADRs) is a global problem due to its potential to result in morbidity, mortality, and increased healthcare costs that can be avoided. Therefore, this study aimed to evaluate the knowledge, attitude, and practice of ADR reporting among healthcare workers (HCW) in primary and secondary healthcare facilities (SHCs) in Lagos State, Nigeria. Materials and Methods: A comparative descriptive survey was carried out among 300 HCWs from selected primary and SHCs in Lagos State, Nigeria, to assess their knowledge, attitudes, and practices affecting ADR reporting in Lagos State, Nigeria. Data were summarized using descriptive statistics, whereas the Chi-square test was used to evaluate categorical variables at p < 0.05. Results: Good knowledge of ADR reporting was found in 90.7% of health workers in primary facilities versus 75.3% in secondary facilities. An understanding of the most crucial purpose of pharmacovigilance was present in 62% of health workers in primary facilities and 69.3% in secondary facilities. A positive attitude toward ADR reporting occurred in 91.3% of health workers in primary facilities and 98.7% in secondary facilities. Profession, level of education, ethnicity, and marital status were found to be associated with knowledge, attitude, and practice of ADR reporting. Conclusion: The study demonstrates that respondents in primary and SHCs in Lagos, Nigeria, had good knowledge and attitude toward ADR reporting. However, the practice has been poor despite the level of awareness among HCWs who participated in the study. Sociodemographic factors also influence knowledge and practice. These findings highlight the need for targeted training and continuous sensitization programs to strengthen pharmacovigilance practices across all healthcare levels.

This paper addresses the Multi-Vehicle Routing Problem with Time Windows and Simultaneous Pickup and Delivery (MVRPTWSPD), aiming to optimize logistics distribution routes and minimize total costs. A vehicle routing optimization model is developed based on the operational requirements of the KS Logistics Center, focusing on minimizing vehicle dispatch, loading and unloading, operating, and time window penalty costs. The model incorporates constraints such as vehicle capacity, time windows, and travel distance, and is solved using a genetic algorithm to ensure optimal route planning. Through MATLAB simulations, 34 customer points are analyzed, demonstrating that the simultaneous pickup and delivery model reduces total costs by 30.13%, increases vehicle loading rates by 20.04%, and decreases travel distance compared to delivery-only or pickup-only models. The results demonstrate the significant advantages of the simultaneous pickup and delivery mode in reducing logistics costs and improving vehicle utilization, offering valuable insights for enhancing the operational efficiency of the KS Logistics Center.

The aim of this work is to develop an intelligent optimization software based on enhanced VNS meta-heuristic to tackle Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD). An optimization system developed based on enhanced Variable Neighborhood Search with Perturbation Mechanism and Adaptive Selection Mechanism as the simple but effective optimization approach presented in this work. The solution method composed by combining Perturbation based Variable Neighborhood Search (PVNS) with Adaptive Selection Mechanism (ASM) to control perturbation scheme. Instead of stochastic approach, selection of perturbation scheme used in the algorithm employed an empirical selection based on each perturbation scheme success along the search. The ASM help algorithm to get more diversification degree and jumping from local optimum condition using most successful perturbation scheme empirically in the search process. A comparative analysis with a well-known exact approach is presented to test the solution method in a generated VRPSPD benchmark instance in limited computation time. Then a test to VRPSPD scenario provided by a liquefied petroleum gas distribution company is performed. The test result confirms that solution method present superior performance against exact approach solution in giving best solution for larger sized instance and successfully obtain substantial improvements when compared to the basic VNS and original route planning technique used by a distributor company.

A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery

The delay management problem arises in public transportation networks, often characterized by the necessity of connections between different vehicles. The attractiveness of public transportation networks is strongly related to the reliability of connections, which can be missed when delays or other unpredictable events occur. Given a single initial delay at one node of the network, the delay management problem is to determine which vehicles have to wait for the delayed ones, with the aim of minimizing the dissatisfaction of the passengers. In this paper, we present strengthened mixed integer linear programming formulations and new families of valid inequalities. The implementation of branch-and-cut methods and tests on a benchmark of instances taken from real networks show the potential of the proposed formulations and cuts.

Strong cutting planes for the capacitated multi-pickup and delivery problem with time windows

This paper provides a green vehicle routing problem with simultaneous pickup and delivery with time windows. The objective of this study is to minimize total costs including fuel cost and carbon emission cost while satisfying customer pickup and delivery demands simultaneously with time windows and capacity constraints. In this paper, fuel consumption is computed considering vehicle load and distance. Firstly, a mathematical model is developed to describe the VRPSPDTW problem. This study proposes a genetic algorithm to optimize cost. The computational experiments are conducted under three crossover (one point, two point and cyclic crossover) and two mutation (swap and inverse) operator. The computation between swap and inverse mutation under three crossover are compared and the results show that swap mutation perform better than inverse mutation under every crossover operator.

A hyper heuristic for the green vehicle routing problem with simultaneous pickup and delivery

The impact of loading restrictions on the two-echelon location routing problem

Electric vehicles (EVs) are a promising option to reduce air pollution and shipping costs, especially in urban areas. To provide scientific guidance for the growing number of logistics companies using EVs, we investigated an electric-vehicle-routing problem with simultaneous pickup and delivery that also considers non-linear charging and load-dependent discharging (EVRPSPD-NL-LD). The objective was to minimize the total number of EVs and the total working time, including travel time, charging time, waiting time, and service time. We formulated the problem as a mixed integer linear program (MILP), and small-size problems could be solved to optimality in an acceptable amount of time using the commercial solver IBM ILOG CPLEX Optimization Studio (CPLEX). In view of the fact that the problem is NP-hard, an adaptive large neighborhood search (ALNS) metaheuristic method was proposed to solve large-size problems. Meanwhile, new operators and a time priority approach were developed to provide options for different scenarios. The results of our computational investigation and sensitivity analysis showed that the proposed methods are effective and efficient for modified benchmark instances.