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This study aims to minimize the transportation-related cost in distribution while utilizing a heterogeneous fixed fleet to deliver distinct demand at different geographical locations with a proper workload balancing approach. An increased cost in distribution is a major problem for many companies due to the absence of efficient planning methods to overcome operational challenges in distinct distribution networks. The problem addressed in this study is to minimize the transportation-related cost in distribution while using a heterogeneous fixed fleet to deliver distinct demand at different geographical locations with a proper workload balancing approach which has not gained the adequate attention in the literature.

This study formulated the transportation problem as a vehicle routing problem with a heterogeneous fixed fleet and workload balancing, which is a combinatorial optimization problem of the NP-hard category. The model was solved using both the simulated annealing and a genetic algorithm (GA) adopting distinct local search operators. A greedy approach has been used in generating an initial solution for both algorithms. The paired t-test has been used in selecting the best algorithm. Through a number of scenarios, the baseline conditions of the problem were further tested investigating the alternative fleet compositions of the heterogeneous fleet. Results were analyzed using analysis of variance (ANOVA) and Hsu’s MCB methods to identify the best scenario.

The solutions generated by both algorithms were subjected to the t-test, and the results revealed that the GA outperformed in solution quality in planning a heterogeneous fleet for distribution with load balancing. Through a number of scenarios, the baseline conditions of the problem were further tested investigating the alternative fleet utilization with different compositions of the heterogeneous fleet. Results were analyzed using ANOVA and Hsu’s MCB method and found that removing the lowest capacities trucks enhances the average vehicle utilization with reduced travel distance.

The developed model has considered both planning of heterogeneous fleet and the requirement of work load balancing which are very common industry needs, however, have not been addressed adequately either individually or collectively in the literature. The adopted solution methodologies to solve the NP-hard distribution problem consist of metaheuristics, statistical analysis and scenario analysis are another significant contribution. The planning of distribution operations not only addresses operational-level decision, through a scenario analysis, but also strategic-level decision has also been considered.

The planning of distribution operations not only addresses operational-level decisions, but also strategic-level decisions conducting a scenario analysis.

Achieving swift and even flow of cargo through the border, the ultimate objective of cross-border logistics (CBL) requires the close coordination and collaboration of a multitude of stakeholders, as well as optimally configured systems. To achieve and sustain competitiveness in a dynamic international trade environment, CBL processes must undergo periodic analysis, improvement and optimization. This study aims to develop a modelling framework to capture CBL processes for analysis and improvement.

Relying on the extant literature, a meta-model is developed incorporating significant perspectives required to model CBL processes. Popular process modelling notations are evaluated against the meta-model and their ease of comprehension is also evaluated. The selected notation through evalution is augmented with addendums for a comprehensive depiction of CBL processes.

The capacity of role activity diagrams (RADs) to depict all perspectives, including interactions in a single diagram, makes them particularly suitable for modelling CBL processes. RADs have been complemented with physical flow diagrams and methods to capture temporal dimension, enabling a comprehensive view of CBL processes laying the foundation for insightful analysis.

The meta-model developed in this paper paves the way to develop an analysis framework which requires further research.

The lack of well-accepted modelling notations for studying CBL processes prompts researchers to search and adapt different formalisms. This study has filled this gap by proposing a comprehensive modelling framework able to capture CBL processes at different granularities in rich detail. Not only does the developed meta-model aid in selecting the notation, it is also useful in analysing the constituent elements of CBL processes.