This research studies the capacitated green vehicle routing problem (CGVRP), which is an extension of the green vehicle routing problem (GVRP), characterized by the purpose of harmonizing environmental and economic costs by implementing effective routes to meet any environmental concerns while fulfilling customer demand. We formulate the mathematical model of the CGVRP and propose a simulated annealing (SA) heuristic for its solution in which the CGVRP is set up as a mixed integer linear program (MILP). The objective of the CGVRP is to minimize the total distance traveled by an alternative fuel vehicle (AFV). This research conducts a numerical experiment and sensitivity analysis. The results of the numerical experiment show that the SA algorithm is capable of obtaining good CGVRP solutions within a reasonable amount of time, and the sensitivity analysis demonstrates that the total distance is dependent on the number of customers and the vehicle driving range.

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In the manufacturing industry, several identical parts can be processed in batches, and setup time is needed between two consecutive batches. Since the processing times of batches are not always fixed during a scheduling period due to learning and deterioration effects, this research deals with batch scheduling problems with simultaneous learning and deterioration effects. The objective is to minimize total actual flow time, defined as a time interval between the arrival of all parts at the shop and their common due date. The decision variables are the number of batches, integer batch sizes, and the sequence of the resulting batches. This research proposes a heuristic algorithm based on the Lagrange Relaxation. The effectiveness of the proposed algorithm is determined by comparing the resulting solutions of the algorithm to the respective optimal solution obtained from the enumeration method. Numerical experience results show that the average of difference among the solutions is 0.05%.

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