A Batch Scheduling Model for a Three-stage Hybrid Flowshop Producing Products with Hierarchical Assembly Structures

Abstract

This paper addresses a batch scheduling problem for a three-stage hybrid flowshop consisting of a machining stage processing common and unique components on unrelated parallel machines, an assembly stage combining the components into assembled products with complex assembly structures, and a differentiation stage processing the assembled products on dedicated machines to produce different product types. The common components are the same for all products and are processed in batches, while the unique components are dedicated to respective given product types and are processed individually (one-by-one component). The goal is to schedule all the products with different assembly structures to minimize total actual flow time (TAFT) defined as total time interval of components to be processed from their arrival times to their common due date. A non-linear programming model is proposed, where small size problems can be solved optimally using the LINGO software, and large size problems is to be solved using a heuristic algorithm. The proposed algorithm consists of two sub-algorithms. The first one is constructed using a shortest processing time (SPT) based heuristic to get a job sequence as an initial solution and the second one is to improve the initial solution using the variable neighbourhood descent (VND) method with neighbourhood insert and swap move operators. In solving the problem with the algorithm, two scenarios arise, e.g., the same and the different sequences for all stages. A set of hypothetical data is generated for different hierarchical assembly structures to test the model and the algorithm, and the results show that the different sequences for all stages obtain solutions with better performances than the same ones.

Multi-objective Batch Scheduling in Collaborative Multi-product Flow Shop System by using Non-dominated Sorting Genetic Algorithm

“…Maulidya, Suprayogi, Wangsaputra, and Halim [10] proposed batch scheduling model that is implemented for hybrid flow shop system. Its objective was to minimize total actual flow time.…”

“…Equation (9) shows that the mutation occurs when the generated uniform random number is less than the mutation threshold. The mutation occurs by switching the packets position of the two selected packets in a flow shop as it is shown in (10). Both packets are selected among packets in a flow shop as it is shown in (11) and (12).…”

“…There is not any single model that is the best to solve all problems in batching process. Most studies in batching process focused on the batch scheduling [10,11] while others focused on determining the batch size [2] and the number of batches [2].…”

“…Like the flow shop scheduling problem, batch scheduling problem is also a combinatorial optimization problem. There are many methods or algorithms to solve the batch scheduling problem, such as genetic algorithm (GA) [8,13], mixed integer linear programming (MILP) [15], shortest processing time (SPT) [10], variable neighborhood descent (VND) [10], backward dynamic programming [5], memetic algorithm [16], back-off decomposition algorithm [17], longest due date (LDD) [9], adjacent pairwise interchange (API) [9], permutation method (PM) [9], and so on. There are several parameters that were used as objective in a batch scheduling studies.…”

“…The most common parameter is make-span [14,15]. Other parameters are total actual flow time (TAFT) [9,10], total tardiness [18], total earliness [18], revenue [17], overstocking [16], delay [16], inefficiency cost [16], total completion time [5,12], total energy cost [19], number of late jobs [6], run time [20], and so on.…”