The electricity production of a thermal generator is often constrained by the available fuel supply. These fuel constraints impose a maximum bound on the energy output over multiple time periods. Fuel constraints are increasingly important in electricity markets because of two main reasons. First, as more natural gas-fired generators join the deregulated market, there is often competition for natural gas supply from other sectors (e.g., residential and manufacturing heating). Second, as more environmental and emission regulations are being placed on fossil fuel-fired generators, fuel supply is becoming more limited. However, there are few studies that consider the fuel constraints in the unit commitment problem from the perspective of computational analysis. To address the challenge faced by an independent power producer with a limited fuel supply, we study a fuel-constrained self-scheduling unit commitment (FSUC) problem where the production decisions are coupled across multiple time periods. We provide a complexity analysis of the FSUC problem and conduct a comprehensive polyhedral study by deriving strong valid inequalities. We demonstrate the effectiveness of our proposed inequalities as cutting planes in solving various multistage stochastic FSUC problems. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: K. Pan was supported in part by the Research Grants Council of Hong Kong [Grant 15501920]. F. Qiu was supported in part by the U.S. Department of Energy Advanced Grid Modeling Program [Grant DE-OE0000875]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information [ https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1235 ] or is available from the IJOC GitHub software repository ( https://github.com/INFORMSJoC ) at [ http://dx.doi.org/10.5281/zenodo.6896199 ].

We present a framework for obtaining fully polynomial time approximation schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone single-period cost functions. This framework is developed through the establishment of two sets of computational rules, namely, the calculus of $K$-approximation functions and the calculus of $K$-approximation sets. Using our framework, we provide the first FPTASs for several NP-hard problems in various fields of research such as knapsack models, logistics, operations management, economics, and mathematical finance. Extensions of our framework via the use of the newly established computational rules are also discussed.

Machine identification of discrete event systems (DES) addresses the issue of identifying an unknown system based on externally observed sample path of the unknown system. Online Modeling Refinement studies the continuing machine identification process in the context when the observed sample path is updated incrementally. While machine identification problem for fixed length sample path is NP-complete, the computational requirement for the proposed online modeling refinement algorithm is maintained at minimal by taking the structure similarity between successive accumulated observed sample paths. In addition to the computational advantage, the proposed algorithm also guarantees the identification results of the system models "converge" to the unknown DEDS model as the incrementally observed sequence get "long" and "rich" enough.

Abstract Consider a network G = (V,E) with distinguished vertices s and t, and with k different costs on every edge. We consider the problem of finding k disjoint paths from s to t such that the total cost of the paths is minimized, where the jth edge‐cost is associated with the jth path. The problem has several variants: The paths may be vertex‐disjoint or arc‐disjoint and the network may be directed or undirected. We show that all four versions of the problem are strongly NP‐complete even for k = 2. We describe polynomial time heuristics for the problem and a polynomial time algorithm for the acyclic directed case.

We consider the multidepot capacitated vehicle routing problems and analyze the tour partitioning heuristics for different versions of the model. We prove that the worst-case ratios of the heuristics are bounded by some fixed numbers. Examples are provided to show that the worst-case bounds are tight or asymptotically tight for almost all versions. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.