Comparing mathematical formulations for customer order scheduling with dedicated machines

The Customer Order Scheduling (COS) problem arises when performance measures are defined at the order level, and each order consists of multiple jobs. This article studies the COS problem with dedicated machines, aiming to minimize the total completion time of orders. Four mathematical formulations are examined and compared: three Mixed-Integer Linear Programming (MILP) models based on positional, precedence and time-indexed variables, and a Constraint Programming (CP) formulation, which is introduced for the first time in the literature. Computational experiments on benchmark instances show that the models provide good balances between solution quality and implementation complexity.