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Keywords = subset-row inequality

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27 pages, 2640 KB  
Article
An Exact Approach for Multitasking Scheduling with Two Competitive Agents on Identical Parallel Machines
by Xin Xin, Suxia Zhou and Jinsheng Gao
Appl. Sci. 2025, 15(22), 12111; https://doi.org/10.3390/app152212111 - 14 Nov 2025
Viewed by 412
Abstract
The cloud manufacturing (CMfg) platform serves as a centralized hub for allocating and scheduling tasks to distributed resources. It features a concrete two-agent model that addresses real-world industrial needs: the first agent handles long-term flexible tasks, while the second agent manages urgent short-term [...] Read more.
The cloud manufacturing (CMfg) platform serves as a centralized hub for allocating and scheduling tasks to distributed resources. It features a concrete two-agent model that addresses real-world industrial needs: the first agent handles long-term flexible tasks, while the second agent manages urgent short-term tasks, both sharing a common due date. The second agent employs multitasking scheduling, which allows for the flexible suspension and switching of tasks. This paper addresses a novel scheduling problem aimed at minimizing the total weighted completion time of the first agent’s jobs while guaranteeing the second agent’s due date. For single-machine cases, a polynomial algorithm provides an efficient baseline; for parallel machines, an exact branch-and-price approach is developed, where the polynomial method informs the pricing problem and structural properties accelerate convergence. Computational results demonstrate significant improvements: the branch-and-price solves large-sized instances (up to 40 jobs) within 7200 s, outperforming CPLEX, which fails to find solutions for instances with more than 15 jobs. This approach is scalable for industrial cloud manufacturing applications, such as automotive parts production, and is capable of handling both design validation and quality inspection tasks. Full article
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24 pages, 512 KB  
Article
Branch-and-Price-and-Cut for the Heterogeneous Fleet and Multi-Depot Static Bike Rebalancing Problem with Split Load
by Ye Ding, Jiantong Zhang and Jiaqing Sun
Sustainability 2022, 14(17), 10861; https://doi.org/10.3390/su141710861 - 31 Aug 2022
Cited by 3 | Viewed by 2417
Abstract
Heterogeneous Fleet and Multi-Depot Static Bike Rebalancing Problem with Split Load (HFMDSBRP-SD) is an extension of the Static Bike Rebalancing Problem, considering heterogeneous fleet multiple depots, allowing split load. It consists of finding a set of least-cost repositioning vehicle routes and determining each [...] Read more.
Heterogeneous Fleet and Multi-Depot Static Bike Rebalancing Problem with Split Load (HFMDSBRP-SD) is an extension of the Static Bike Rebalancing Problem, considering heterogeneous fleet multiple depots, allowing split load. It consists of finding a set of least-cost repositioning vehicle routes and determining each station’s pickup or delivery quantity to satisfy the demand of each station. We develop a branch-and-price-and-cut (BPC) where a tabu search column generator and a heuristic label-setting algorithm are introduced to accelerate the column generation procedure, the subset-row (SR) inequalities, the strong minimum number of vehicles (SMV) inequalities, and the enhanced elementary inequalities are extended fitting this problem and applied to speed up the global convergence rate. Computational results demonstrate the effectiveness of the BPC algorithm. Among 360 instances with a maximum size of 30, there are 298 instances capable of achieving optimality within two hour time limitation. Full article
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