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This is the source code and dataset that we used in the paper: "A Stackelberg Game for Managing AI Sensing Tasks in Mobile Crowdsensing"

We consider a class of games played on networks in which the utility 4 functions consist of both deterministic and random terms. In order to find the Nash 5 equilibrium of the game we formulate the problem as a variational inequality in a 6 probabilisticLebesguespacewhichissolvednumericallytoprovideapproximations 7 for the mean value of the random equilibrium. We also numerically compare the 8 solution thus obtained, with the solution computed by solving the deterministic 9 variational inequality derived by taking the expectation of the pseudo-gradient of 10 the game with respect to the random parameters.

The paper deals with a sequencing and routing problem originated by a real-world application context. The problem consists in defining the best sequence of locations to visit within a warehouse for the storage and/or retrieval of a given set of items during a specified time horizon, where the storage/retrieval location of an item is given. Picking and put-away of items are simultaneously addressed, by also considering some specific requirements given by the layout design and operating policies which are typical in the kind of warehouses under study. Specifically, the considered sequencing policy prescribes that storage locations must be replenished or emptied one at a time by following a specified order of precedence. Moreover, two fleet of vehicles are used to perform retrieving and storing operations, whose routing is restricted to disjoint areas of the warehouse. We model the problem as a constrained multicommodity flow problem on a space-time network, and we propose two Mixed-Integer Linear Programming formulations, whose primary goal is to minimize the time traveled by the vehicles during the time horizon. Since large-size realistic instances are hardly solvable within the time limit commonly imposed in the considered application context, a matheuristic approach based on a time horizon decomposition is proposed. Finally, we provide an extensive experimental analysis aiming at identifying suitable parameter settings for the proposed approach, and testing the matheuristic on particularly hard realistic scenarios. The computational experiments show the efficacy and the efficiency of the proposed approach.

We consider a storage allocation problem which combines storage location assignment with sequencing decisions about the assigned storage locations, and which originates from a real-world application context. We propose a very efficient successive constrained shortest path method, which outperforms a matheuristic approach recently proposed in the literature in terms of both the computational time required and regarding the quality of the solutions found.

We use the theory of stochastic variational inequalities to develop a network equilibrium model of the whole supply chain of electricity markets: power generation, supply, transmission, and consumption. In particular, we take into account the case where the market demand functions are not exactly known but are affected by some kind of uncertainty. A discretization and truncation procedure is used to numerically solve the stochastic variational inequality model. Monotonicity properties of the operator are investigated and the affine case is analysed in detail. Finally, numerical experiments show the impact of different probability densities of the random variables on the approximated solutions and the scalability of the proposed numerical method for real-world sized problems.

Braess' paradox is a classical result in the theory of congestion games. It motivates theoretically why adding a resource (e.g., an arc) to a network may sometimes worsen, rather than improve, the overall network performance. Differently from previous literature, which studies Braess' paradox in a non-cooperative game-theoretic setting, in this work, a framework is proposed to investigate its occurrence by exploiting cooperative games with transferable utility (TU games) on networks. In this way, instead of focusing on the marginal contribution to the network utility provided by the insertion of an arc when a single initial scenario is considered, the arc average marginal utility with respect to various initial scenarios, that is, its Shapley value in a suitably-defined TU game, is evaluated. It is shown that, for choices of the utility function of the TU game modeling congestion, there are cases for which the Shapley value associated with an arc is negative, meaning that its average marginal contribution to the network utility is negative.

In the theory of congestion games, the Braess’ paradox shows that adding one resource to a network may sometimes worsen, rather than improve, the overall network performance. Here the paradox is investigated under a cooperative game-theoretic setting, in contrast to the non-cooperative one typically adopted in the literature. A family of cooperative games on networks is considered, whose utility function, defined in terms of a traffic assignment problem and the associated Wardrop equilibrium, expresses the average quality of service perceived by the network users.