Assignment problem

About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.

A robust optimization approach to the integrated berth allocation and quay crane assignment problem

Abstract: This paper investigates the integrated berth allocation and quay crane assignment problem in container terminals. A deterministic model is formulated by considering the setup time of quay cranes. However, data uncertainties widely exist, and it may cause the deterministic solution to be infeasible. To handle the uncertainties, a robust optimization model is established. Furthermore, to control the level of conservativeness, another robust optimization model with the price constraints is proposed. A genetic algorithm and an insertion heuristic algorithm are suggested to obtain near optimal solutions. Computational experiments indicate that the presented models and algorithms are effective to solve the problems.

A cost assignment policy for home care patients

Abstract: The patient assignment problem in Home care (HC) consists of allocating each newly admitted patient to his/her reference operator, chosen among a set of possible operators. The continuity of care, where pursued, imposes that the assignment is not changed for a long period. The main goal of the assignment is to balance the workload among the operators. In the literature, the problem is usually solved with numerical approaches based on mathematical programming that do not consider the stochastic aspects of the problem. We derive a structural policy to assign a newly admitted patient while balancing the workload among the operators, by minimizing the expected value of a cost function that penalizes the overtime of operators. The workloads already loaded to the operators are assumed to be random variables as they are in the practice, while the demand related to the new patient is considered both deterministic and stochastic. Results show that the variability of the new patient’s demand is negligible with respect to the variability of the already assigned workloads and that similar assignments are obtained both in the presence or in the absence of this demand variability. A numerical comparison with the current practice of assigning the new patient to the operator with the highest expected available capacity shows that better balancings and cost savings can be reached by implementing the proposed policy.

Assigning cells to switches in cellular mobile networks using taboo search

Abstract: The design of wireless telecommunications networks is a complex process, which requires solving simultaneously many difficult combinatorial optimization problems. We propose a taboo-search approach dedicated to one of the aforementioned design optimization problems, namely the cell assignment problem. Our approach defines a series of moves applicable to an initial solution in order to improve the cost and establish the feasibility of the solution. For this purpose, we identify a gain structure with update procedures to efficiently choose the best solution in the current neighborhood. The results are generally good in comparison with those obtained through other heuristic methods.

Finding maximum flows in undirected graphs seems easier than bipartite matching

Abstract: Consider an n-vertex, m-edge, undirected graph with maximum flow value v. We give a method to find augmenting paths in such a graph in amortized sub-linear (O(npv)) time per path. This lets us improve the time bound of the classic augmenting path algorithm to O(m+ nv3=2) on simple graphs. The addition of a blocking flow subroutine gives a simple, deterministic O(nm2=3v1=6)-time algorithm. We also use our technique to improve known randomized algorithms, giving O(m+nv5=4)-time and O(m+n11=9v)-time algorithms for capacitated undirected graphs. For simple graphs, in which v n, the last bound is O(n2:2), improving on the best previous bound of O(n2:5), which is also the best known time bound for bipartite matching.

Assessing optimal assignment under uncertainty: An interval-based algorithm

Abstract: We consider the problem of multi-robot task-allocation when robots have to deal with uncertain utility estimates. Typically an allocation is performed to maximize expected utility; we consider a means for measuring the robustness of a given optimal allocation when robots have some measure of the uncertainty (e.g. a probability distribution, or moments of such distributions). We introduce the interval Hungarian algorithm, a new algorithm that extends the classic Kuhn—Munkres Hungarian algorithm to compute the maximum interval of deviation, for each entry in the assignment matrix, which will retain the same optimal assignment. The algorithm has a worst-case time complexity of O(n4); we also introduce a parallel variant with O(n3) running time, which is able to exploit the concurrent computing capabilities of distributed multi-robot systems. This provides an efficient measurement of the tolerance of the allocation to the uncertainties and dynamics, for both a specific interval and a set of interrelated intervals. We conduct experiments both in simulation and with physical robots to validate the approach and to gain insight into the effect of location uncertainty on allocations for multi-robot multi-target navigation tasks.