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The purpose of this study is to develop a novel general mathematical model to find the optimal product mix of commercial graphite products, which has a complex production process with alternative sub-processes in the graphite mining production process.

The network optimization was adopted to model the complex graphite mining production process through the optimal allocation of raw graphite, byproducts, and saleable products with comparable sub-processes, which has different processing capacities and costs. The model was tested on a selected graphite manufacturing company, and the optimal graphite product mix was determined through the selection of the optimal production process. In addition, sensitivity and scenario analyses were carried out to accommodate uncertainties and to facilitate further managerial decisions.

The selected graphite mining company mines approximately 400 metric tons of raw graphite per month to produce ten types of graphite products. According to the optimum solution obtained, the company should produce only six graphite products to maximize its total profit. In addition, the study demonstrated how to reveal optimum managerial decisions based on optimum solutions.

This study has made a significant contribution to the graphite manufacturing industry by modeling the complex graphite mining production process with a network optimization technique that has yet to be addressed at this level of detail. The sensitivity and scenario analyses support for further managerial decisions.

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.