Optimal Lower Bounds for Anonymous Scheduling Mechanisms

We consider the problem of designing truthful mechanisms on m unrelated machines, to minimize some optimization goal. Nisan and Ronen [Nisan, N., A. Ronen. 2001. Algorithmic mechanism design. Games Econom. Behav. 35 166–196] consider the specific goal of makespan minimization, and show a lower bound of 2, and an upper bound of m. This large gap inspired many attempts that yielded positive results for several special cases, but very partial success for the general case: the lower bound was slightly increased to 2.61 by Christodoulou et al. [Christodoulou, G., E. Koutsoupias, A. Kovács. 2010. Mechanism design for fractional scheduling on unrelated machines. ACM Trans. Algorithms (TALG) 6(2) 1–18] and Koutsoupias and Vidali [Koutsoupias, E., A. Vidali. 2007. A lower bound of 1+phi for truthful scheduling mechanisms. Proc. 32nd Internat. Sympos. Math. Foundations Comput. Sci. (MFCS)], while the best upper bound remains unchanged. In this paper we show the optimal lower bound on truthful anonymous mechanisms: no such mechanism can guarantee an approximation ratio better than m. Moreover, our proof yields similar optimal bounds for two other optimization goals: the sum of completion times and the lp norm of the schedule.United States-Israel Binational Science FoundationIsrael. Ministry of ScienceGoogle Inter-University Center for Electronic Markets and Auction

A New Lower Bound for Deterministic Truthful Scheduling

We study the problem of truthfully scheduling $m$ tasks to $n$ selfish unrelated machines, under the objective of makespan minimization, as was introduced in the seminal work of Nisan and Ronen [STOC'99]. Closing the current gap of $[2.618,n]$ on the approximation ratio of deterministic truthful mechanisms is a notorious open problem in the field of algorithmic mechanism design. We provide the first such improvement in more than a decade, since the lower bounds of $2.414$ (for $n=3$) and $2.618$ (for $n\to\infty$) by Christodoulou et al. [SODA'07] and Koutsoupias and Vidali [MFCS'07], respectively. More specifically, we show that the currently best lower bound of $2.618$ can be achieved even for just $n=4$ machines; for $n=5$ we already get the first improvement, namely $2.711$; and allowing the number of machines to grow arbitrarily large we can get a lower bound of $2.755$.Comment: 15 page

An Improved Randomized Truthful Mechanism for Scheduling Unrelated Machines

We study the scheduling problem on unrelated machines in the mechanism design setting. This problem was proposed and studied in the seminal paper (Nisan and Ronen 1999), where they gave a 1.75-approximation randomized truthful mechanism for the case of two machines. We improve this result by a 1.6737-approximation randomized truthful mechanism. We also generalize our result to a $0.8368m$-approximation mechanism for task scheduling with $m$ machines, which improve the previous best upper bound of $0.875m(Mu'alem and Schapira 2007)

A characterization of 2-player mechanisms for scheduling

We study the mechanism design problem of scheduling unrelated machines and we completely characterize the decisive truthful mechanisms for two players when the domain contains both positive and negative values. We show that the class of truthful mechanisms is very limited: A decisive truthful mechanism partitions the tasks into groups so that the tasks in each group are allocated independently of the other groups. Tasks in a group of size at least two are allocated by an affine minimizer and tasks in singleton groups by a task-independent mechanism. This characterization is about all truthful mechanisms, including those with unbounded approximation ratio. A direct consequence of this approach is that the approximation ratio of mechanisms for two players is 2, even for two tasks. In fact, it follows that for two players, VCG is the unique algorithm with optimal approximation 2. This characterization provides some support that any decisive truthful mechanism (for 3 or more players) partitions the tasks into groups some of which are allocated by affine minimizers, while the rest are allocated by a threshold mechanism (in which a task is allocated to a player when it is below a threshold value which depends only on the values of the other players). We also show here that the class of threshold mechanisms is identical to the class of additive mechanisms.Comment: 20 pages, 4 figures, ESA'0

Prior-Independent Mechanisms for Scheduling

We study the makespan minimization problem with unrelated selfish machines under the assumption that job sizes are stochastic. We design simple truthful mechanisms that under various distributional assumptions provide constant and sublogarithmic approximations to expected makespan. Our mechanisms are prior-independent in that they do not rely on knowledge of the job size distributions. Prior-independent approximation mechanisms have been previously studied for the objective of revenue maximization [Dhangwatnotai, Roughgarden and Yan'10, Devanur, Hartline, Karlin and Nguyen'11, Roughgarden, Talgam-Cohen and Yan'12]. In contrast to our results, in prior-free settings no truthful anonymous deterministic mechanism for the makespan objective can provide a sublinear approximation [Ashlagi, Dobzinski and Lavi'09].Comment: This paper will appear in Proceedings of the ACM Symposium on Theory of Computing 2013 (STOC'13

Value creation in production: Reconsideration from interdisciplinary approaches

This paper presents reconsideration of value creation in production from various aspects of value viewpoints in several disciplines such as production engineering, social sciences, and human sciences. The focal point of investigations is value co-creation by the provision of products and services in and for society. In the past, some methods of social sciences and others proved to be useful in making production more efficient. At present, such methods must help to realise value creation. In fact, production must become more effective in response to human needs in social, economic, and environmental dimensions. Along with the theoretical apparatus, this paper presents some case studies indicating the importance of value creation in production, followed by future perspectives of value co-creation in production