The hybrid vehicle routing problem is an extension of the green vehicle routing problem where vehicles can use different fuels. In this research, a bi-objective hybrid vehicles routing problem is presented and solved bu considering alternative paths, various lengths and reliabilities. The first objective function minimizes overall system costs and fuel consumption and greenhouse gas emissions, whereas the second objective function maximizes the reliability of the entire system with alternative paths and several reliabilites. The proposed model is formulated as mixed-integer nonlinear programming and a bi-objective simulated annealing (MOSA) algorithm along with the e-constraint method is used as solution strategy. The implementation of the proposed method is presented using some numerical instances.

This paper addresses the stochastic permutation flow shop problem (SPFSP) in which the stochastic parameters are the processing times. This allows the modeling of setups and machine breakdowns. Likewise, it is proposed a multi-objective greedy randomized adaptive search procedure (GRASP) coupled with Monte-Carlo Simulation to obtain expected makespan and expected tardiness. To manage the bi-objective function, a sequential combined method is considered in the construction phase of the meta-heuristic. Moreover, the local Search combines 2-optimal interchanges with a Pareto Archived Evolution Strategy (PAES) to obtain the Pareto front. Also, some Taillard benchmark instances of deterministic permutation flow shop problem were adapted in order to include the variation in processing times. Accordingly, two coefficients of variation (CVs) were tested: one depending on expected processing times values defined as twice the expected processing time of a job, and a fixed value of 0.25. Thus, the computational results on benchmark instances show that the variable CV provided lower values of the expected makespan and tardiness, while the con-stant CV presented higher expected measures. The computational results present insights for further analysis on the behavior of stochastic scheduling problems for a better approach in real-life scenarios at industrial and service systems.

In this paper, we study no-wait flow shop problem where setup times depend on sequence of operations. The proposed problem considers sequence-independent removal times, release date with an additional assumption that there are some preliminary setup times. There are two objectives of weighted mean tardiness and makespan associated with the proposed model of this paper. We formulate the resulted problem as a mixed integer programming, where a two-phase fuzzy programming is implemented to solve the model. To examine the performance of the proposed model, we generate several sample data, randomly and compare the results with other methods. The preliminary results indicate that the proposed two-phase model of this paper performed relatively better than Zimmerman & apos; s single-phase fuzzy method.

This paper addresses a bi-criteria scheduling problem with deteriorating jobs on a single machine. We develop a model for a single machine bi-criteria scheduling problem (SMBSP) with the aim of minimizing total tardiness and work in process (WIP) costs. WIP cost increases as a job passes through a series of stages in the production process. Due to the uncertainty involved in real-world scheduling problems, it is sometimes unrealistic or even impossible to acquire exact input data. Hence, we consider the SMBSP under the hypothesis of fuzzy L-R processing time's knowledge and fuzzy L-R due date. The effectiveness of the proposed model and the denoted methodology is demonstrated through a test problem.