An exact extended formulation for the unrelated parallel machine total weighted completion time problem

The plethora of research on NP-hard parallel machine scheduling problems is focused on heuristics due to the theoretically and practically challenging nature of these problems. Only a handful of exact approaches are available in the literature, and most of these suffer from scalability issues. Moreover, the majority of the papers on the subject are restricted to the identical parallel machine scheduling environment. In this context, the main contribution of this work is to recognize and prove that a particular preemptive relaxation for the problem of minimizing the total weighted completion time (TWCT) on a set of unrelated parallel machines naturally admits a non-preemptive optimal solution and gives rise to an exact mixed integer linear programming formulation of the problem. Furthermore, we exploit the structural properties of TWCT and attain a very fast and scalable exact Benders decomposition-based algorithm for solving this formulation. Computationally, our approach holds great promise and may even be embedded into iterative algorithms for more complex shop scheduling problems as instances with up to 1000 jobs and 8 machines are solved to optimality within a few seconds

A statistical comparison of metaheuristics for unrelated parallel machine scheduling problems with setup times

Manufacturing scheduling aims to optimize one or more performance measures by allocating a set of resources to a set of jobs or tasks over a given period of time. It is an area that considers a very important decision-making process for manufacturing and production systems. In this paper, the unrelated parallel machine scheduling problem with machine-dependent and job-sequence-dependent setup times is addressed. This problem involves the scheduling of tasks on unrelated machines with setup times in order to minimize the makespan. The genetic algorithm is used to solve small and large instances of this problem when processing and setup times are balanced (Balanced problems), when processing times are dominant (Dominant P problems), and when setup times are dominant (Dominant S problems). For small instances, most of the values achieved the optimal makespan value, and, when compared to the metaheuristic ant colony optimization (ACOII) algorithm referred to in the literature, it was found that there were no significant differences between the two methods. However, in terms of large instances, there were significant differences between the optimal makespan obtained by the two methods, revealing overall better performance by the genetic algorithm for Dominant S and Dominant P problems.FCT—Fundação para a Ciência e Tecnologia through the R&D Units Project Scope UIDB/00319/2020 and EXPL/EME-SIS/1224/2021 and PhD grant UI/BD/150936/2021

An integrated approach of artificial neural networks and system dynamics for estimating product completion time in a semiautomatic production

The determination of completion time to produce a new product is one of the most important indicators for manufacturers in delivering goods to customers. Failure to fulfil delivery on-time or known as tardiness contributes to a high cost of air shipment and production line down at other entities within the supply chain. The uncertainty of completion time has created a big problem for manufacturers of audio speakers which involved semiautomatic production lines. Therefore, the main objective of this research is to develop an integrated model that enhances the artificial neural networks (ANN) and system dynamics (SD) methods in estimating completion time focusing on the cycle time. Three ANN models based on multilayer perceptron (MLP) were developed with different network architectures to estimate cycle time. Furthermore, a proposed momentum rate equation was formulated for each model to improve learning process, where the 3-2-1 network emerged as the best network with the smallest mean square error. Subsequently, the estimated cycle time of the 3-2-1 network was simulated through the development of an SD model to evaluate the performance of completion time in terms of product quantity, manpower fatigue and production workload scores. The success of the proposed integrated ANNSD model also relied on a proposed coefficient correlation of causal loop diagram (CLD) to identify the most influential factor of completion time. As a result, the proposed integrated ANNSD model provided a beneficial guide to the company in determining the most influential factor on completion time so that the time to complete a new audio product can be estimated accurately. Consequently, product delivery was smooth for on-time shipment while successfully fulfilling customers’ demand

Data Driven Efficiency for E-Warehousing: Descriptive and Prescriptive Analytics

Based on data provided by a warehouse logistics management company, we analyze the warehousing operation and its major processes of order picking and order consolidation. Without access to the actual layouts and process flow diagrams, we analyze the data to describe the processes in detail, and prescribe changes to improve the operation. We investigate the characteristics of the order preparation process and the order consolidation operation. We find that products from different orders are mixed for effective picking. Similar products from different orders are picked together in containers called totes. Full totes are stored in a buffer area, and then routed to a conveyor system where products are sorted. The contents of the totes are then consolidated into orders. This order consolidation process depends on the sequence in which totes are processed and has a huge impact on the order completion time. OCP is a new problem for both the warehouse management system and the parallel machine scheduling literature. We provide mathematical formulations for the problem and devise two solution methods. The first is a simulated annealing metaheuristic, while the second is an exact branch-and-price method. We test the solutions on both random and industry data. Simulated Annealing is found to achieve near optimal solutions within 0.01 % of optimality. For the branch-and-price approach, we use a set partitioning formulation and a column generation method where the subproblems are single machine scheduling problems that are solved using dynamic programming. We also devise a new branching rule and new dynamic programming algorithm to solve the subproblem after branching. To assess the efficiency of the proposed branch-and-price methodology, we compare against the branch-and-price approach of Chen and Powell (1999) for the parallel machine scheduling problem. We take advantage of the fact that OCP is a generalization of the parallel machine scheduling problem. The proposed, more general, branch-and-price approach achieves the same solution quality, but takes more time