MIP Models and Hybrid Algorithms for Simultaneous Job Splitting and Scheduling on Unrelated Parallel Machines

Abstract

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.

Introducing the MCHF/OVRP/SDMP: Multicapacitated/Heterogeneous Fleet/Open Vehicle Routing Problems with Split Deliveries and Multiproducts

“…The proposed local search algorithms, implemented in C#, are performed during the fitness function calculation process. In order to eliminate the infeasible chromosome structure, we were mainly inspired by our previous algorithms related to scheduling problem in the literature [ 14 , 15 ]. The novel characteristic of the studied problem is the capacity constraint.…”

“…In addition, each chromosome also carries the number of suborders for each customer. It would be necessary to note that this chromosome structure is used in our previous study [ 14 ]. Figure 1 illustrates a sample chromosome.…”

“…To enhance the performance of the genetic algorithm, we use a local search algorithm in the literature [ 14 ], which is detailed in the next subsection.…”

“…For instance, the integrating dominance properties method that was originally developed by Chang and Chen [ 17 ] was afterward applied successfully to machine scheduling problem [ 15 ]. In the other paper of researchers, which includes job splitting property in scheduling problem [ 14 ], an advance approach is adopted. And in this paper, finally the algorithm adopted more complex aforementioned logistics problem which contains capacity constraints.…”