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An improved compact formulation for the assortment optimization problem with small consideration sets

JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2025年

作者： Roberti, Roberto Salvagnin, Domenico Fischetti, Matteo Univ Padua Dept Informat Engn Padua Italy

We investigate the assortment optimization problem with small consideration sets, where customers belong to classes and choose according to the k-product non-parametric ranking-based choice model - i.e., each customer's preference list contains at most k products, and customers purchase the most preferred product among the ones offered in the assortment. This problem is known to be NP-hard even when k is equal to 2. The best approximation method from the literature has a performance guarantee of 2(1-1k)k-1(1k) and can find, empirically, assortments that are 0.3-0.5% within optimality when k equals 4 and there are 100 products and 10 000 customer classes. By building upon a compact mixed-integer linear programming model proposed, in the literature, for the full non-parametric ranking-based choice model, we propose an improved compact model that features a very tight continuous relaxation and can be easily solved with a general-purpose solver. An extensive set of computational experiments shows that our improved formulation can find provably optimal assortments of instances with up to 200 products, 100 000 customers classes, and k equal to 5, in a few minutes of runtime.

关键词： Assortment optimization choice models mixed-integer linear programming exact methods

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A hybrid local search algorithm for the continuous energy-constrained scheduling problem

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JOURNAL OF SCHEDULING 2025年第1期28卷 65-84页

作者： Brouwer, Roel van den Akker, Marjan Hoogeveen, Han Univ Utrecht Dept Informat & Comp Sci Utrecht Netherlands

We consider the continuous energy-constrained scheduling problem (CECSP). A set of jobs has to be processed on a continuous, shared resource. A schedule for a job consists of a start time, completion time, and a resource consumption profile. The goal is to find a schedule such that each job does not start before its release time, is completed before its deadline, satisfies its full resource requirement, and respects its lower and upper bounds on resource consumption during processing. The objective is to minimize the total weighted completion time. We present a hybrid local search approach, using simulated annealing and linear programming, and compare it to a mixed-integer linear programming (MILP) formulation. We show that the hybrid local search approach matches the MILP formulation in solution quality for small instances and is able to find a feasible solution for larger instances in reasonable time.

关键词： Continuous scheduling Resource-constrained scheduling mixed-integer linear programming Simulated annealing

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Optimal operation of hydrogen-based multi-energy microgrid integrating water network and transportation sector

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INTERNATIONAL JOURNAL OF HYDROGEN ENERGY 2025年 97卷 501-515页

作者： Khan, Muhammad Ahsan Rehman, Talha Kim, Hak-Man Incheon Natl Univ Dept Elect Engn 119 Acad Ro Incheon 22012 South Korea Incheon Natl Univ Res Inst Northeast Asian Super Grid 119 Acad Ro Incheon 22012 South Korea

To address the rising demand for hydrogen energy and its reliance with the water sector, this study presents an optimal scheduling framework fora multi-energy microgrid (MEMG) that integrates electric, thermal, water, and hydrogen energy networks. To this end, a mixed-integer linear programming (MILP) model is formulated to minimize both operational costs and emissions. A bi-variate piecewise McCormick envelope technique is utilized to manage the non-linear constraints associated with the water network. The model also incorporates the transportation sector, including electric and hydrogen vehicles (EVs, HVs), with vehicle-to-grid (V2G) technology, and models their associated uncertainties using Monte Carlo simulation (MCS). Additionally, the sale of oxygen as a by-product of the hydrogenation process is also considered. The case study shows significant economic and environmental benefits, with a 29.66% cost reduction and 22.26% emissions decrease from water network integration. Oxygen sales further reduce costs by 14.19%, and V2G technology contributes an additional 2.35% cost and 6.01% emissions reduction. The proposed linear approximation method achieved superior performance, with a root mean square error (RMSE) of 0.72 and a relative error of 2.132%.

关键词： Electric vehicles Hydrogen energy Hydrogen vehicles mixed-integer linear programming Multi-energy microgrid Water-energy nexus

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A Day-Ahead Optimal Battery Scheduling Considering the Grid Stability of Distribution Feeders

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ENERGIES 2025年第5期18卷 1067-1067页

作者： Mumtahina, Umme Alahakoon, Sanath Wolfs, Peter Cent Queensland Univ Rockhampton Qld 4701 Australia Cent Queensland Univ Gladstone Qld 4680 Australia

This study presents a comprehensive framework for optimizing energy management systems by integrating advanced methodologies for weather forecasting, energy cost analysis, and grid stability using a mixed-integer linear programming (MILP) algorithm. A novel approach is proposed for day-ahead weather forecasting, leveraging real-time data extraction from reliable weather websites and applying clear sky modeling to estimate photovoltaic (PV) generation with high accuracy. By automating weather data acquisition, the methodology bridges the gap between weather predictions and practical energy management, providing utilities with a reliable tool for operating and integrating renewable energy. The optimization framework focuses on minimizing the utility bill by analyzing a distribution feeder representative of Australia's energy infrastructure, incorporating time-of-use (TOU) and flat tariff systems across eight Australian states to simulate realistic energy costs. Furthermore, voltage constraints are applied within the optimization framework to maintain system stability and improve voltage profiles, ensuring both technical reliability and economic efficiency. The proposed framework delivers actionable insights for utility industries, enhancing the scheduling of battery energy storage systems (BESS) and facilitating the integration of renewable energy into the grid.

关键词： optimal scheduling battery energy storage system energy management system mixed-integer linear programming weather forecasting

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Asteroid mining: ACT&Friends’ results for the GTOC12 problem

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Astrodynamics 2025年第1期9卷 19-40页

作者： Dario Izzo Marcus Märtens Laurent Beauregard Max Bannach Giacomo Acciarini Emmanuel Blazquez Alexander Hadjiivanov Jai Grover Gernot Heißel Yuri Shimane Chit Hong Yam European Space Technology and Research Center Noordwijk2201 AZthe Netherlands European Space Operations Centre Darmstadt64293Germany Surrey Space Center University of SurreyGuildfordGU27XHUK School of Aerospace Engineering Georgia Institute of TechnologyAtlantaGeorgia30332USA Mission Design and Operations Group ispace inc.Sumitomo Fudosan Hamacho Building 3F3-42-3Nihonbashi HamachoChuo-kuTokyo103-0007Japan

In 2023, the 12th edition of Global Trajectory Competition was organized around the problem referred to as “Sustainable Asteroid Mining”. This paper reports the developments that led to the solution proposed by ESA’s Advanced Concepts Team. Beyond the fact that the proposed approach failed to rank higher than fourth in the final competition leader-board, several innovative fundamental methodologies were developed which have a broader application. In particular, new methods based on machine learning as well as on manipulating the fundamental laws of astrodynamics were developed and able to fill with remarkable accuracy the gap between full low-thrust trajectories and their representation as impulsive Lambert transfers. A novel technique was devised to formulate the challenge of optimal subset selection from a repository of pre-existing optimal mining trajectories as an integer linear programming problem. Finally, the fundamental problem of searching for single optimal mining trajectories (mining and collecting all resources), albeit ignoring the possibility of having intra-ship collaboration and thus sub-optimal in the case of the GTOC12 problem, was efficiently solved by means of a novel search based on a look-ahead score and thus making sure to select asteroids that had chances to be re-visited later on.

关键词： GTOC low thrust asteroid mining machine learning mixed-integer linear programming nonlinear programming

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On a fair and risk-averse urban air mobility resource allocation problem under demand and capacity uncertainties

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NAVAL RESEARCH LOGISTICS 2025年第1期72卷 111-132页

作者： Sun, Luying Deng, Haoyun Wei, Peng Xie, Weijun Virginia Tech Dept Ind & Syst Engn Blacksburg VA USA Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA George Washington Univ Dept Mech & Aerosp Engn Washington DC USA

Urban air mobility (UAM) is an emerging air transportation mode to alleviate the ground traffic burden and achieve zero direct aviation emissions. Due to the potential economic scaling effects, the UAM traffic flow is expected to increase dramatically once implemented, and its market can be substantially large. To be prepared for the era of UAM, we study the fair and risk-averse urban air mobility resource allocation model (FairUAM) under passenger demand and airspace capacity uncertainties for fair, safe, and efficient aircraft operations. FairUAM is a two-stage model, where the first stage is the aircraft resource allocation, and the second stage is to fairly and efficiently assign the ground and airspace delays to each aircraft provided the realization of random airspace capacities and passenger demand. We show that FairUAM is NP-hard even when there is no delay assignment decision or no aircraft allocation decision. Thus, we recast FairUAM as a mixed-integer linear program (MILP) and explore model properties and strengthen the model formulation by developing multiple families of valid inequalities. The stronger formulation allows us to develop a customized exact decomposition algorithm with both benders and L-shaped cuts, which significantly outperforms the off-the-shelf solvers. Finally, we numerically demonstrate the effectiveness of the proposed method and draw managerial insights when applying FairUAM to a real-world network.

关键词： fairness mixed-integer linear programming resource allocation risk-averse urban air mobility

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Optimal reactive operation of general topology supply chain and manufacturing networks under disruptions

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AICHE JOURNAL 2025年第0期

作者： Ovalle, Daniel Pulsipher, Joshua L. Ye, Yixin Harshbarger, Kyle Bury, Scott Laird, Carl D. Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA Univ Waterloo Dept Chem Engn Waterloo ON Canada Dow Chem Co USA Core R&D Lake Jackson TX USA Dow Chem Co USA Supply Chain Innovat Midland MI USA Dow Chem Co USA Core R&D Midland MI USA

Supply and manufacturing networks in the chemical industry involve diverse processing steps across different locations, rendering their operation vulnerable to disruptions from unplanned events. Optimal responses should consider factors such as product allocation, delayed shipments, and price renegotiation, among other factors. In such context, we propose a multiperiod mixed-integer linear programming model that integrates production, scheduling, shipping, and order management to minimize the financial impact of such disruptions. The model accommodates arbitrary supply chain topologies and incorporates various disruption scenarios, offering adaptability to real-world complexities. A case study from the chemical industry demonstrates the scalability of the model under finer time discretization and explores the influence of disruption types and order management costs on optimal schedules. This approach provides a tractable, adaptable framework for developing responsive operational plans in supply chain and manufacturing networks under uncertainty.

关键词： supply chain optimization disruptions mixed-integer linear programming operation scheduling

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Resilient pharmaceutical supply chains: Assessment of stochastic optimization strategies for process uncertainty integration in network design problems

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COMPUTERS & CHEMICAL ENGINEERING 2025年 195卷

作者： Sarkis, Miriam Shah, Nilay Papathanasiou, Maria M. Imperial Coll London Sargent Ctr Proc Syst Engn London SW72BB England Imperial Coll London Dept Surg & Canc London SW72BB England

In recent years, the market boom of next-generation therapies and vaccines has pressured the pharmaceutical industry to rapidly scaleup capacity to meet societal needs. Manufacturers catering for these markets reported shortages due to unforeseen demand trends and a crucial uncertainty in capabilities of platforms still under development. In this work, we present an optimization-simulation framework for the design of resilient supply chains to manufacturing uncertainty. Given previously quantified probability distributions of process parameters, we formulate stochastic optimization problems integrating process uncertainty via a sampling-based methodology. Stochastic programming results in networks of higher optimal costs compared to deterministic approaches. Furthermore, stochastic designs ensure product supply meets target demands under simulated uncertainty and result in a larger probability of achieving lower costs per dose. The optimization- simulation framework is used to test solution stability for a varying number of optimization scenarios, highlighting that the minimum number of samples to guarantee stability is problem-specific, thus motivating the investigation of scenario reduction techniques to ensure stability of scenario sets a priori. Overall, the cost-supply benefits of integrating manufacturing uncertainty are quantified, demonstrating the scope for its consideration in strategic planning problems in the sector.

关键词： Supply chain optimization mixed-integer linear programming Stochastic programming Manufacturing uncertainty Monte Carlo Sampling

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Generalized Optimal Scheduling of Cluster Tools With Reentrance and Residency Time Constraints

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2025年第1期55卷 307-318页

作者： Li, Xin Educ Univ Hong Kong Dept Math & Informat Technol Hong Kong Peoples R China

Cluster tools have been widely used in the semiconductor industry. In previous work, singe-arm and dual-arm cluster tools are dealt with separately. When considering residency time constraints, algorithms for scheduling robot moving sequences are mainly developed based on backward and swap strategies, respectively. How about the performance of other robot moving sequences is still an open problem. The present work addresses general conditions by considering all feasible robot moving sequences-beyond backward- and swap-based strategies. In addition, both dual-arm and single-arm cluster tools with reentrance are handled simultaneously. To solve this, the problem is first divided into two parts-the basic one without reentrance and reentrant operations. Based on detailed analysis of all available robot operations in a cluster tool, mixed-integer programming formulations are developed for both parts. Subsequently, both illustrative examples and randomly generated instances are tested to validate the efficiency of the proposed approach. Results of one example show improvement comparing to previous work. Another two examples-not scheduled previously-are scheduled well by the proposed approach. Meanwhile, the flexibility of operations obtained by the proposed model is demonstrated by an example with six processing modules and 12 stages in a dual-arm cluster tool. Additionally, more randomly generated instances are tested more to validate the proposed approach and analyze computation time.

关键词： Generalized formulation mixed-integer linear programming reentrance residency time single-arm and dual-arm cluster tools

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Effects on the Unit Commitment of a District Heating System Due to Seasonal Aquifer Thermal Energy Storage and Solar Thermal Integration

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ENERGIES 2025年第3期18卷 645-645页

作者： Verheyen, Joana Thommessen, Christian Roes, Juergen Hoster, Harry Univ Duisburg Essen Chair Energy Technol D-47048 Duisburg Germany Lagom Energy GmbH D-47057 Duisburg Germany Hydrogen & Fuel Cell Ctr ZBT GmbH D-47057 Duisburg Germany

The ongoing transformation of district heating systems (DHSs) aims to reduce emissions and increase renewable energy sources. The objective of this work is to integrate solar thermal (ST) and seasonal aquifer thermal energy storage (ATES) in various scenarios applied to a large DHS. mixed-integer linear programming (MILP) is used to develop a comprehensive model that minimizes operating costs, including heat pumps (HPs), combined heat and power (CHP) units, electric heat boilers (EHBs), heat-only boilers (HOBs), short-term thermal energy storage (TES), and ATES. Different ATES scenarios are compared to a reference without seasonal TES (potential of 15.3 GWh of ST). An ATES system with an injection well temperature of about 55 degrees C has an overall efficiency of 49.8% (58.6% with additional HPs) and increases the integrable amount of ST by 178% (42.5 GWh). For the scenario with an injection well temperature of 20 degrees C and HPs, the efficiency is 86.6% and ST is increased by 276% (57.5 GWh). The HOB heat supply is reduced by 8.9% up to 36.6%. However, the integration of an ATES is not always economically or environmentally beneficial. There is a high dependency on the configurations, prices, or emissions allocated to electricity procurement. Further research is of interest to investigate the sensitivity of the correlations and to apply a multi-objective MILP optimization.

关键词： district heating systems mixed-integer linear programming seasonal aquifer thermal energy storage solar thermal systems

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