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We developed mixed integer programming (MIP) models and hybrid genetic-local search algorithms for the scheduling problem of unrelated parallel machines with job sequence and machine-dependent setup times and with job splitting property. The first contribution of this paper is to introduce novel algorithms which make splitting and scheduling simultaneously with variable number of subjobs. We proposed simple chromosome structure which is constituted by random key numbers in hybrid genetic-local search algorithm (GAspLA). Random key numbers are used frequently in genetic algorithms, but it creates additional difficulty when hybrid factors in local search are implemented. We developed algorithms that satisfy the adaptation of results of local search into the genetic algorithms with minimum relocation operation of genes' random key numbers. This is the second contribution of the paper. The third contribution of this paper is three developed new MIP models which are making splitting and scheduling simultaneously. The fourth contribution of this paper is implementation of the GAspLAMIP. This implementation let us verify the optimality of GAspLA for the studied combinations. The proposed methods are tested on a set of problems taken from the literature and the results validate the effectiveness of the proposed algorithms.

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In this paper, we analyze a real-world OVRP problem for a production company. Considering real-world constrains, we classify our problem as multicapacitated/heterogeneous fleet/open vehicle routing problem with split deliveries and multiproduct (MCHF/OVRP/SDMP) which is a novel classification of an OVRP. We have developed a mixed integer programming (MIP) model for the problem and generated test problems in different size (10–90 customers) considering real-world parameters. Although MIP is able to find optimal solutions of small size (10 customers) problems, when the number of customers increases, the problem gets harder to solve, and thus MIP could not find optimal solutions for problems that contain more than 10 customers. Moreover, MIP fails to find any feasible solution of large-scale problems (50–90 customers) within time limits (7200 seconds). Therefore, we have developed a genetic algorithm (GA) based solution approach for large-scale problems. The experimental results show that the GA based approach reaches successful solutions with 9.66% gap in 392.8 s on average instead of 7200 s for the problems that contain 10–50 customers. For large-scale problems (50–90 customers), GA reaches feasible solutions of problems within time limits. In conclusion, for the real-world applications, GA is preferable rather than MIP to reach feasible solutions in short time periods.