Minimizing weighted total earliness, total tardiness and setup costs

The paper considers a (static) portfolio system that satisfies adding-up contraints and the gross substitution theorem. The paper shows the relationship of the two conditions to the weak dominant diagonal property of the matrix of interest rate elasticities. This enables to investigate the impact of simultaneous changes in interest rates on the asset demands.

Approximation algorithms for capacitated stochastic inventory systems with setup costs

We develop the first approximation algorithm with worst-case performance guarantee for capacitated stochastic periodic-review inventory systems with setup costs. The structure of the optimal control policy for such systems is extremely complicated, and indeed, only some partial characterization is available. Thus, finding provably near-optimal control policies has been an open challenge. In this article, we construct computationally efficient approximate optimal policies for these systems whose demands can be nonstationary and/or correlated over time, and show that these policies have a worst-case performance guarantee of 4. We demonstrate through extensive numerical studies that the policies empirically perform well, and they are significantly better than the theoretical worst-case guarantees. We also extend the analyses and results to the case with batch ordering constraints, where the order size has to be an integer multiple of a base load.National Science Foundation (U.S.) (CMMI-1362619)National Science Foundation (U.S.) (CMMI-1131249)National Science Foundation (U.S.) (DMS-0732175)National Science Foundation (U.S.) (CMMI-0846554)National Science Foundation (U.S.) (FA9550-08-1–0369

Інформаційні технології алгоритмів мінімізації сумарного випередження і запізнення із налагодженнями

Розглядається інформаційне забезпечення алгоритмів розв’язання задач складання розкладів за критерієм мінімізації сумарного випередження і запізнення відносно директивних строків: при виконанні незалежних завдань одним приладом при наявності налагоджень, залежних від послідовності, та при виконанні груп завдань одним приладом із налагодженнями, незалежними від послідовності.Is considered informational support of algorithms of one machine scheduling problem of minimizing the total earliness and tardiness against due dates: for independent tasks with setup costs and for task groups with sequence independent setup costs

Optimal scheduling for charging electric vehicles with fixed setup costs.

The increasing popularity of electric vehicles (EV) will pose great challenge to the nation\u27s existing power grid by adding extra load during evening peak hours. This thesis develops a centralized optimal charging scheduling (OCS) model with a mixed integer nonlinear program to mitigate the negative impact of extra load from EVs on the power grid. The objective of the OCS model is to minimize the energy cost of the entire system and fixed setup costs for day-time charging, which essentially levels the load of the entire power grid throughout a day under the dynamic pricing environment. Furthermore, a rolling horizon heuristic algorithm is proposed as an alternative solution that addresses large scale OCS instances. Finally, when centralized scheduling is impractical, this thesis proposes a decentralized optimal charging heuristic using the concepts of game theory and coordinate search. Numerical results show that the optimal charging scheduling model can significantly lower the total energy cost and the peak-to-average ratio (PAR) for a power system. When compared to uncontrolled charging, the decentralized charging heuristic yields considerable energy savings as well, although not as efficient as the centralized optimal charging solutions

Foundations of Markov-Perfect Industry Dynamics. Existence, Purification, and Multiplicity

In this paper we show that existence of a Markov perfect equilibrium (MPE) in the Ericson & Pakes (1995) model of dynamic competition in an oligopolistic industry with investment, entry, and exit requires admissibility of mixed entry/exit strategies, con- trary to Ericson & Pakes's (1995) assertion. This is problematic because the existing algorithms cannot cope with mixed strategies. To establish a firm basis for computing dynamic industry equilibria, we introduce ¯rm heterogeneity in the form of randomly drawn, privately known scrap values and setup costs into the model. We show that the resulting game of incomplete information always has a MPE in cuto® entry/exit strate- gies and is computationally no more demanding than the original game of complete information. Building on our basic existence result, we first show that a symmetric and anonymous MPE exists under appropriate assumptions on the model's primitives. Sec- ond, we show that, as the distribution of the random scrap values/setup costs becomes degenerate, MPEs in cuto® entry/exit strategies converge to MPEs in mixed entry/exit strategies of the game of complete information. Next, we provide a condition on the model's primitives that ensures the existence of a MPE in pure investment strategies. Finally, we provide the first example of multiple symmetric and anonymous MPEs in this literature.

High Multiplicity Scheduling with Switching Costs for few Products

We study a variant of the single machine capacitated lot-sizing problem with sequence-dependent setup costs and product-dependent inventory costs. We are given a single machine and a set of products associated with a constant demand rate, maximum loading rate and holding costs per time unit. Switching production from one product to another incurs sequencing costs based on the two products. In this work, we show that by considering the high multiplicity setting and switching costs, even trivial cases of the corresponding "normal" counterparts become non-trivial in terms of size and complexity. We present solutions for one and two products.Comment: 10 pages (4 appendix), to be published in Operations Research Proceedings 201

On the P-Coverage Problem on the Real Line

In this paper we consider the p-coverage problem on the real line. We first give a detailed description of an algorithm to solve the coverage problem without the upper bound p on the number of open facilities. Then we analyze how the structure of the optimal solution changes if the setup costs of the facilities are all decreased by the same amount. This result is used to develop a parametric approach to the p-coverage problem which runs in O (pn log n) time, n being the number of clients.Economics ;