On a Stackelberg Subset Sum Game

This contribution deals with a two-level discrete decision problem, a so-called Stackelberg strategic game: A Subset Sum setting is addressed with a set $N$ of items with given integer weights. One distinguished player, the leader, may alter the weights of the items in a given subset $L\subset N$, and a second player, the follower, selects a solution $A\subseteq N$ in order to utilize a bounded resource in the best possible way. Finally, the leader receives a payoff from those items of its subset $L$ that were included in the overall solution $A$, chosen by the follower. We assume that the follower applies a publicly known, simple, heuristic algorithm to determine its solution set, which avoids having to solve NP-hard problems. Two variants of the problem are considered, depending on whether the leader is able to control (i.e., change) the weights of its items (i) in the objective function or (ii) in the bounded resource constraint. The leader's objective is the maximization of the overall weight reduction, for the first variant, or the maximization of the weight increase for the latter one. In both variants there is a trade-off for each item between the contribution value to the leader's objective and the chance of being included in the follower's solution set. We analyze the leader's pricing problem for a natural greedy strategy of the follower and discuss the complexity of the corresponding problems. We show that setting the optimal weight values for the leader is, in general, NP-hard. It is even NP-hard to provide a solution within a constant factor of the best possible solution. Exact algorithms, based on dynamic programming and running in pseudopolynomial time, are provided. The additional cases, in which the follower faces a continuous (linear relaxation) version of the above problems, are shown to be straightforward to solve.Comment: 13 pages, 1 figur

Investigation of HNCO adsorption and hydrolysis on Fe-ZSM5

The adsorption of HNCO on Fe-ZSM5 was investigated in detail by DRIFT spectroscopy and compared to the adsorption on H-ZSM5, Al2O3, SiO2, Fe2O3/Al2O3 and Fe2O3/SiO2. At 150°C, HNCO adsorbs dissociatively on Fe-ZSM5 producing principally isocyanate species (-NCO) adsorbed on Al and Fe sites. In the presence of water the hydrolysis of the -NCO groups to NH3 was observed. Comparison of the DRIFT results with measurements of the catalytic activity of coated cordierite monoliths suggests that -NCO groups are likely intermediate species in the hydrolysis of HNCO over Fe-ZSM

Mass Vaccine Administration under Supply Uncertainty

The insurgence of COVID-19 requires fast mass vaccination, hampered by scarce availability and uncertain supply of vaccine doses and a tight schedule for boosters. In this paper, we analyze planning strategies for the vaccination campaign to vaccinate as many people as possible while meeting the booster schedule. We compare a conservative strategy and q-days-ahead strategies against the clairvoyant strategy. The conservative strategy achieves the best trade-off between utilization and compliance with the booster schedule. Q-days-ahead strategies with q < 7 provide a larger utilization but run out of stock in over 30% of days

On-line load balancing made simple: Greedy strikes back

AbstractWe provide a new approach to the on-line load balancing problem in the case of restricted assignment of temporary weighted tasks. The approach is very general and allows us to derive on-line algorithms whose competitive ratio is characterized by some combinatorial properties of the underlying graph G representing the problem: in particular, the approach consists in applying the greedy algorithm to a suitably constructed subgraph of G. In the paper, we prove the NP-hardness of the problem of computing an optimal or even a c-approximate subgraph, for some constant c>1. Nevertheless, we show that, for several interesting problems, we can easily compute a subgraph yielding an optimal on-line algorithm. As an example, the effectiveness of this approach is shown by the hierarchical server model introduced by Bar-Noy et al. (2001). In this case, our method yields simpler algorithms whose competitive ratio is at least as good as the existing ones. Moreover, the algorithm analysis turns out to be simpler. Finally, we give a sufficient condition for obtaining, in the general case, O(n)-competitive algorithms with our technique: this condition holds in the case of several problems for which a Ω(n) lower bound is known

Decisioni nella produzione flessibile: layout e gestione delle operazioni

Dottorato di ricerca in ricerca operativa. 11. ciclo. Supervisore e coordinatore Mario Lucertini.Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Competitive algorithms for the bicriteria k-server problem

In this paper we consider the bicriteria formulation of the well-known online k-server problem where the cost of moving k servers between given locations is evaluated simultaneously with respect to two different metrics. Every strategy for serving a sequence of requests is thus characterized by a pair of costs, and an online algorithm is said to be (c1, c2)-competitive in the strong sense if it is c1-competitive with respect to the first metric and c2-competitive with respect to the second one. We first prove a lower bound on c1 and c2 that holds for any online bicriteria algorithm for the problem.We then propose an algorithm achieving asymptotically optimal tradeoffs between the two competitive ratios. Finally, we show how to further decrease the competitive ratios when the two metrics are induced by the distances in a complete graph and in a path, respectively, obtaining optimal results for particular cases