Food waste contributes significantly to greenhouse emissions and represents a substantial portion of overall waste within hospital facilities. Furthermore, uneaten food leads to a diminished nutritional intake for pat...
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Food waste contributes significantly to greenhouse emissions and represents a substantial portion of overall waste within hospital facilities. Furthermore, uneaten food leads to a diminished nutritional intake for patients, that typically are vulnerable and ill. Therefore, this study developed mathematical models for constructing patient meals in a 1000-bed hospital located in Florida. The objective is to minimize food waste and mealbuilding costs while ensuring that the prepared meals meet the required nutrients and caloric content for patients. To accomplish these objectives, four mixed-integer programming models were employed, incorporating binary and continuous variables. The first model establishes a baseline for how the system currently works. This model generates the meals without minimizing waste or cost. The second model minimizes food waste, reducing waste up to 22.53 % compared to the baseline. The third model focuses on minimizing meal-building costs and achieves a substantial reduction of 37 %. Finally, a multi-objective optimization model was employed to simultaneously reduce both food waste and cost, resulting in reductions of 19.70 % in food waste and 32.66 % in meal-building costs. The results demonstrate the effectiveness of multi-objective optimization in reducing waste and costs within large-scale food service operations.
Optimization-based scheduling in the chemical industry is highly beneficial but also highly difficult due to its combinatorial complexity. Different modeling and optimization techniques exist, each with individual str...
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Optimization-based scheduling in the chemical industry is highly beneficial but also highly difficult due to its combinatorial complexity. Different modeling and optimization techniques exist, each with individual strengths. We propose Benders decomposition to integrate mixed-integer linear programming (MILP) and discrete-event simulation (DES) to solve flow shop scheduling problems with makespan minimization objective. The basic idea is to generate valid Benders cuts based on sensitivity information of the DES sub problem, which can be found in the critical paths of DES solutions. For scaled literature flow shops, our approach requires at least an order of magnitude fewer iterations than a genetic algorithm and provides optimality gap information. For a realworld case study, our approach finds good solutions very quickly, making it a powerful alternative to established methods. We conclude that the Benders-DES algorithm is a promising approach to combine rigorous MILP optimization capabilities with high-fidelity DES modeling capabilities.
This paper presents a scalable Model Predictive Control (MPC) algorithm for task scheduling and real time re-scheduling. The use case motivating the work is given by the problem of managing the integration activities ...
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This paper presents a scalable Model Predictive Control (MPC) algorithm for task scheduling and real time re-scheduling. The use case motivating the work is given by the problem of managing the integration activities involved in the final assembly of the Vega rocket at the European space center in Kourou, French Guiana. There are two main objectives. The algorithm shall suggest to the planning operators an optimized scheduling of the activities, i.e., one which minimizes the total completion time (the makespan), while satisfying all the applicable constraints. In addition, the algorithm shall provide in real time an update of the planning, in case some unforeseen events require a re-scheduling of the activities. While a standard application of mixed-integer optimization would not be feasible in practice due to the combinatorial complexity of the problem, the scalable MPC algorithm proposed in this paper retains all the flexibility and modelling power of optimization-based techniques, and is almost as fast as the state of the art scheduling heuristics, which in real scenarios can provide a sub-optimal solution in few seconds, or less. Extensive simulations on randomly generated realistic scenarios are carried out to validate the proposed approach. On average, the proposed MPC algorithm decreased by nearly 2% the makespan, compared to a state of the art scheduling heuristic, while having a comparable solving time, in the order of milliseconds, and while retaining (contrary to heuristics) all the flexibility and modelling power of the optimization based approaches (which took several hours to run on the test scenarios).
Multistage stochastic programming is a powerful tool allowing decision-makers to revise their decisions at each stage based on the realized uncertainty. However, organizations are not able to be fully flexible, as dec...
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Multistage stochastic programming is a powerful tool allowing decision-makers to revise their decisions at each stage based on the realized uncertainty. However, organizations are not able to be fully flexible, as decisions cannot be revised too frequently in practice. Consequently, decision commitment becomes crucial to ensure that initially made decisions remain unchanged for a certain period of time. This paper introduces partially adaptive multistage stochastic programming, a new optimization paradigm that strikes an optimal balance between decision flexibility and commitment by determining the best stages to revise decisions depending on the allowed level of flexibility. We introduce a novel mathematical formulation and theoretical properties eliminating certain constraint sets. Furthermore, we develop a decomposition method that effectively handles mixed-integer partially adaptive multistage programs by adapting the integer L-shaped method and Benders decomposition. Computational experiments on stochastic lot-sizing and generation expansion planning problems show substantial advantages attained through optimal selections of revision times when flexibility is limited, while demonstrating computational efficiency attained by employing the proposed properties and solution methodology. By adhering to these optimal revision times, organizations can achieve performance levels comparable to fully flexible settings.
Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based ...
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Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential mixed-integer linearization with trust region safeguard, computing feasible iterates via calls to a generic mixed-integer linear solver. Convergence to critical, possibly suboptimal, feasible points is established for arbitrary starting points. Finally, we present numerical applications in nonsmooth optimal control and optimal network design and operation.
Supply Chain Management (SCM) is one of the issues that scholars have studied for many years, both theoretically and practically, and given the subject's breadth and variety, it has received a great deal of resear...
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Supply Chain Management (SCM) is one of the issues that scholars have studied for many years, both theoretically and practically, and given the subject's breadth and variety, it has received a great deal of research and is still the focus of a great deal of study. An integrated production and distribution scheduling problem in a single customer mode for the "production for an ordering" system in a supply chain is a subproblem of SCM. In this problem, a manufacturer receives orders from a customer and processes them on a machine then sends them to the customer in batches. Sending batches of orders will reduce delivery costs but may increase the lateness of some orders. The goal is to sequence the processing of tasks and determine their classification for delivery so that the total weight of tasks and delivery costs are minimized. In this paper, two new linear programming models, including mixed-integer programming (MIP) and mixed-integer Nonlinear programming (MINP) models, as well as a new Heuristic Algorithm (HA), are proposed to solve this Np-hard problem. In order to evaluate the performance of these three methods, computational tests have been performed using the experimental design of 8340 different case studies to show their effectiveness and speed in solving production and distribution scheduling problems in SCM. The experimental results show the efficiency of the HA that could solve 45.13% of problems with a maximum solving time of 0.05917s which is much faster than MIP and MINLP.
The Periodic Event Scheduling Problem (PESP) is the central mathematical tool for periodic timetable optimization in public transport. PESP can be formulated in several ways as a mixed-integer linear program with typi...
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The Periodic Event Scheduling Problem (PESP) is the central mathematical tool for periodic timetable optimization in public transport. PESP can be formulated in several ways as a mixed-integer linear program with typically general integer variables. We investigate the split closure of these formulations and show that split inequalities are identical with the recently introduced flip inequalities. While split inequalities are a general mixed-integer programming technique, flip inequalities are defined in purely combinatorial terms, namely cycles and arc sets of the digraph underlying the PESP instance. It is known that flip inequalities can be separated in pseudo-polynomial time. We prove that this is best possible unless P=NP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {P}=\hbox {NP}$$\end{document}, but also observe that the complexity becomes linear-time if the cycle defining the flip inequality is fixed. Moreover, introducing mixed-integer-compatible maps, we compare the split closures of different formulations, and show that reformulation or binarization by subdivision do not lead to stronger split closures. Finally, we estimate computationally how much of the optimality gap of the instances of the benchmark library PESPlib can be closed exclusively by split cuts, and provide better dual bounds for five instances.
In recent years, the flex-route transit (FRT) has become increasingly popular due to its convenience, especially in scenarios where transportation demands are sparse or dispersed. However, due to growing concerns abou...
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In recent years, the flex-route transit (FRT) has become increasingly popular due to its convenience, especially in scenarios where transportation demands are sparse or dispersed. However, due to growing concerns about greenhouse gas emissions, reducing the energy consumption of vehicle travel has emerged as a critical issue. To this end, this paper aims to address the flex-route transit operational planning problem with energy consumption (FRTOPP-EC) through a mixed-integer programming (MIP) formulation. The objective is to minimize the energy consumption of all deployed vehicles by optimising their routes. Given the computationally intractable nature of FRTOPP-EC, we develop a branch-and-price (BAP) algorithm to solve it exactly. To tackle the pricing problem efficiently arising in the proposed algorithm, a tailored label correcting algorithm (LCA) is designed. Computational experiments are conducted using benchmark instances derived from a real-life system of FRT. The results indicate that our BAP algorithm outperforms the commercial solver (e.g. CPLEX) in terms of solution quality, the size of problems it can solve, and computational efficiency. Furthermore, comparative results with the commonly used heuristic insertion algorithm (HIA) underscore the superior effectiveness of our BAP algorithm. Finally, extension experiments are discussed to offer managerial insights for employers.
Multi-beam antenna and beam hopping technologies are an effective solution for scarce satellite frequency *** of the primary challenges accompanying with Multi-Beam Satellites(MBS)is an efficient Dynamic Resource Allo...
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Multi-beam antenna and beam hopping technologies are an effective solution for scarce satellite frequency *** of the primary challenges accompanying with Multi-Beam Satellites(MBS)is an efficient Dynamic Resource Allocation(DRA)*** paper presents a learning-based Hybrid-Action Deep Q-Network(HADQN)algorithm to address the sequential decision-making optimization problem in *** using a parameterized hybrid action space,HADQN makes it possible to schedule the beam pattern and allocate transmitter power more *** pursue multiple long-term QoS requirements,HADQN adopts a multi-objective optimization method to decrease system transmission delay,loss ratio of data packets and power consumption load *** results demonstrate that the proposed HADQN algorithm is feasible and greatly reduces in-orbit energy consumption without compromising QoS performance.
In this paper, we investigate the problem of finding a robust baseline schedule for the project scheduling problem under uncertain process times. We assume that the probability distribution for the duration is unknown...
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In this paper, we investigate the problem of finding a robust baseline schedule for the project scheduling problem under uncertain process times. We assume that the probability distribution for the duration is unknown, but an estimate is given along with an interval in which this time can vary. At most Gamma of the tasks will deviate from the estimated time. We present two approaches to solving this problem. The first approach treats the problem of determining the earliest guaranteed finish times and can be solved in polynomial time by an extension of the critical path method. The second is a two-stage approach that determines the baseline schedule in the first stage and an adaptation to the scenario in the second stage. We show strong NP-hardness of the second stage problem and introduce a novel formulation. From this formulation we derive an exact algorithm and three heuristics. A computational study on benchmark instances shows that the heuristics perform well on larger instances.
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