A Fast Dynamic Assignment Algorithm for Solving Resource Allocation Problems

The assignment problem is one of the fundamental problems in the field of combinatorial optimization. The Hungarian algorithm can be developed to solve various assignment problems according to each criterion. The assignment problem that is solved in this paper is a dynamic assignment to find the maximum weight on the resource allocation problems. The dynamic characteristic lies in the weight change that can occur after the optimal solution is obtained. The Hungarian algorithm can be used directly, but the initialization process must be done from the beginning every time a change occurs. The solution becomes ineffective because it takes up a lot of time and memory. This paper proposed a fast dynamic assignment algorithm based on the Hungarian algorithm. The proposed algorithm is able to obtain an optimal solution without performing the initialization process from the beginning. Based on the test results, the proposed algorithm has an average time of 0.146 s and an average memory of 4.62 M. While the Hungarian algorithm has an average time of 2.806 s and an average memory of 4.65 M. The fast dynamic assignment algorithm is influenced linearly by the number of change operations and quadratically by the number of vertices.

Agriculture fleet vehicle routing: A decentralised and dynamic problem

To date, the research on agriculture vehicles in general and Agriculture Mobile Robots (AMRs) in particular has focused on a single vehicle (robot) and its agriculture-specific capabilities. Very little work has explored the coordination of fleets of such vehicles in the daily execution of farming tasks. This is especially the case when considering overall fleet performance, its efficiency and scalability in the context of highly automated agriculture vehicles that perform tasks throughout multiple fields potentially owned by different farmers and/or enterprises. The potential impact of automating AMR fleet coordination on commercial agriculture is immense. Major conglomerates with large and heterogeneous fleets of agriculture vehicles could operate on huge land areas without human operators to effect precision farming. In this paper, we propose the Agriculture Fleet Vehicle Routing Problem (AF-VRP) which, to the best of our knowledge, differs from any other version of the Vehicle Routing Problem studied so far. We focus on the dynamic and decentralised version of this problem applicable in environments involving multiple agriculture machinery and farm owners where concepts of fairness and equity must be considered. Such a problem combines three related problems: the dynamic assignment problem, the dynamic 3-index assignment problem and the capacitated arc routing problem. We review the state-of-the-art and categorise solution approaches as centralised, distributed and decentralised, based on the underlining decision-making context. Finally, we discuss open challenges in applying distributed and decentralised coordination approaches to this problem.

Warranty Matching in a Consumer Electronics Closed-Loop Supply Chain

Problem definition: We examine a dynamic assignment problem faced by a large wireless service provider (WSP) that is a Fortune 100 company. This company manages two warranties: (i) a customer warranty that the WSP offers its customers and (ii) an original equipment manufacturer (OEM) warranty that OEMs offer the WSP. The WSP uses devices refurbished by the OEM as replacement devices, and hence their warranty operation is a closed-loop supply chain. Depending on the assignment the WSP uses, the customer and OEM warranties might become misaligned for customer-device pairs, potentially incurring a cost for the WSP. Academic/practical relevance: We identify, model, and analyze a new dynamic assignment problem that emerges in this setting called the warranty matching problem. We introduce a new class of policies, called farsighted policies, which can perform better than myopic policies. We also propose a new heuristic assignment policy, the sampling policy, which leads to a near-optimal assignment. Our model and results are motivated by a real-world problem, and our theory-guided assignment policies can be used in practice; we validate our results using data from our industrial partner. Methodology: We formulate the problem of dynamically assigning devices to customers as a discrete-time stochastic dynamic programming problem. Because this problem suffers from the curse of dimensionality, we propose and analyze a set of reasonable classes of assignment policies. Results: The performance metric that we use for a given assignment policy is the average time that a replacement device under a customer warranty is uncovered by an OEM warranty. We show that our assignment policies reduce the average uncovered time and the expected number of out-of-OEM-warranty returns by more than 75% in comparison with our industrial partner’s current assignment policy. We also provide distribution-free bounds for the performance of a myopic assignment policy and of random assignment, which is a proxy for the WSP’s current policy. Managerial implications: Our results indicate that, in closed-loop supply chains, being completely farsighted might be better than being completely myopic. Also, policies that are effective in balancing short-term and long-term costs can be simple and effective, as illustrated by our sampling policy. We describe how the performance of myopic and farsighted policies depend on the size and length of inventory buildup.