A novel approach to optimization of jobs in groups

Abstract

This study deals with scheduling groups of jobs, their arrival and delivery, and individual processing of each of them. All jobs in a group should be delivered at the same time after processing. The objective of the problem is to minimize the average delivery time of the group containing that job (waiting period). The authors present a novel way of modeling the optimization problem – a hybrid approach to modeling. This approach includes the design and implementation of the optimization model in the MILP (Mixed-Integer Linear Programming) environment, an iterative algorithm for solving the model under the dynamic emergence of new orders as well as transformation and linearization of the model in CLP/MILP environments. In addition, the paper proposes new functionalities based on the CLP (Constraint Logic Programming) environment and illustrative models for service providers (a restaurant).