Çetinkaya, F.C.Yozgat, G.B.2025-05-132025-05-1320222008-4889https://doi.org/10.22068/ijiepr.33.2.11https://hdl.handle.net/20.500.12416/9727This study introduces a new variant of the customer order scheduling (COS) problem in which each customer orders several products processed in a two-machine flow shop. Customers' orders are satisfied by the job-based processing approach in which the same products ordered by different customers form a product lot (job). Each customer's order for a product is processed as a sublot (batch) of identical products processed together by the same machine without intermingling the sublots of other products. A sequence-independent attached setup on each machine is required before starting the process of a product lot. Each customer order is delivered in a single shipment when processing all products in that customer order is finished. The aim is to construct an optimal schedule of product lots and the sublots' sequence in every job lot by minimizing the sum of completion times of the customer orders. In our study, a mixed-integer linear programming (MILP) model and a multi-phase heuristic algorithm are developed for solving the problem. The computational experiments reveal that the proposed model solves the small-scale problem instances with and without setups optimally within three hours of a run-time limit. However, our proposed algorithm finds optimal or near-optimal solutions for the medium and large-scale problem instances in less than five seconds. © 2022 Iran University of Science and Technology. All rights reserved.eninfo:eu-repo/semantics/closedAccessCustomer Order SchedulingHeuristic AlgorithmJob-Based ProcessingLot StreamingMixed-Integer Linear ProgrammingTotal Completion TimeTwo-Machine Flow ShopArticle10.22068/ijiepr.33.2.112-s2.0-85137708230