The classical multi-level lot-sizing and scheduling problem formulations for process industries rarely address perishability issues, such as limited shelf lives of intermediate products. In some industries, ignoring t...
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The classical multi-level lot-sizing and scheduling problem formulations for process industries rarely address perishability issues, such as limited shelf lives of intermediate products. In some industries, ignoring this specificity may result in severe losses. In this paper, we start by extending a classical multi-level lot-sizing and scheduling problem formulation (MLGLSP) to incorporate perishability issues. We further demonstrate that with the objective of minimising the total costs (purchasing, inventory and setup), the production plans generated by classical models are often infeasible under a setting with perishable products. The model distinguishes different perishability characteristics of raw materials, intermediates and end products according to various industries. Finally, we provide quantitative insights on the importance of considering perishability for different production settings when solving integrated production planning and scheduling problems.
Due to the unpredictable nature of wind energy and non-coincidence between wind units output power and demand peak load, wind units is deemed as an unreliable source of energy. In order to compensate for the short-ter...
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Due to the unpredictable nature of wind energy and non-coincidence between wind units output power and demand peak load, wind units is deemed as an unreliable source of energy. In order to compensate for the short-term fluctuation of wind energy, deployment of energy storage (ES) units in various types have been introduced as a viable solution. This paper develops a stochastic mathematical model for the optimal allocation of ES units in active distribution networks (ADNs) in order to reduce wind power spillage and load curtailment while managing congestion and voltages deviation. Nonlinearities of the original formulation are converted to linear equivalents and the final model lies within the computationally tractable mixed-integer linear programming (MILP) fashion. The IEEE 33-bus 12.66 kV radial distribution test system is utilized to illustrate the effectiveness of the proposed methodology. It was found that the rated power and capacity of ES units are depends on wind units' location and penetration level, in such a way that ES units are allocated near wind units to absorb excessive wind energy as much as possible. Furthermore, the results indicate ES units are useful for other purposes such as voltage management issue even if the wind units are not allocated. (C) 2018 Elsevier Ltd. All rights reserved.
Modern electricity markets with large penetration of renewable energy resources require fair and accurate pricing methods to elicit generation flexibility and foster competition in electricity markets. This paper prop...
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Modern electricity markets with large penetration of renewable energy resources require fair and accurate pricing methods to elicit generation flexibility and foster competition in electricity markets. This paper proposes the fundamental theory and closed-form formulas for continuous-time locational marginal price (LMP) of electricity, which more accurately integrates the spatio-temporal variations of load and operational constraints of power systems in the electricity price calculation. This paper first formulates the network-constrained generation scheduling and pricing problems as continuous-time optimal control problems using two methods for modeling transmission network, i.e., Theta and generation shift factor (GSF) methods. The continuous-time network-constrained scheduling and pricing problems minimize in their objective functional the total operation cost of power systems over the scheduling horizon subject to generation and transmission constraints. The closed-form continuous-time LMP formulas are derived for each transmission network model, which explicitly include terms that reflect the simultaneous spatio-temporal impacts of transmission flow limits and intertemporal generation ramping constraints in LMP formation. A scalable and computationally efficient function space solution method is proposed that converts the continuous-time problems into mixedintegerlinearprogramming problems with finite-dimensional decision space. The proposed solution method enables high-fidelity solution of transmission-constrained scheduling and pricing problems in higher dimensional spaces, while including as a special case the current discrete-time solutions. The proposed models are implemented on a three-bus system and the IEEE reliability test system, where the proposed models showcase more accuracy in reflecting the impacts of fast net-load variations over discrete-time counterparts.
Aggregate production planning (APP) that is an important concept of supply chain management (SCM), is one of the tools to determine production rates, inventory levels, and workforce requirements for fulfilling custome...
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Aggregate production planning (APP) that is an important concept of supply chain management (SCM), is one of the tools to determine production rates, inventory levels, and workforce requirements for fulfilling customer demands in a multi-period setting. Traditional APP models employ a single objective function to optimize monetary issues only. In this paper, we present a multi-objective APP model to analyze economic, social, environmental, and cultural pillars inclusively;moreover, each pillar includes several sub-pillars in the model. The resulting model includes an accurate representation of the problem with binary and continuous variables under sustainability considerations. We illustrate the effectiveness of the model in an appliance manufacturer and solve the problem using an exact solution method for multi-objective mixed-integerlinear programs (MOMILP). We find a large number of the non-dominated (ND) points in the objective function space and analyze their trade-offs systematically. We show how this framework supports multiple criteria decision making process in the APP problems in the presence of sustainability considerations. Our approach provides a comprehensive analysis of the ND points of sustainable APP (SAPP) problems, and hence, the trade-offs of objective functions are insightful to the decision makers.
Energy saving and environmental protection are important issues of today. Concerning the environmental and social need to increase the utilization of used products, this paper introduces two remanufacturing reverse lo...
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Energy saving and environmental protection are important issues of today. Concerning the environmental and social need to increase the utilization of used products, this paper introduces two remanufacturing reverse logistics (RL) network models, namely, the open-loop model and the closed-loop model. In an open-loop RL system, used products are recovered by outside firms, while in a closed-loop RL system, they are returned to their original producers. The open-loop model features a location selection with two layers. For this model, a mixed-integerlinear program (MILP) is built to minimize the total costs of the open-loop RL system, including the fixed cost, the freight between nodes, the operation cost of storage and remanufacturing centers, the penalty cost of unmet or remaining demand quantity, and the government-provided subsidy given to the enterprises that protect the environment. This MILP is solved using an adaptive genetic algorithm with MATLAB simulation. For a closed-loop RL network model, a special demand function considering the relationship between new and remanufactured products is developed. Remanufacturing rate, environmental awareness, service demand elasticity, value-added services, and their impacts on total profit of the closed-loop supply chain are analyzed. The closed-loop RL network model is proved effective through the analysis of a numerical example.
This paper addresses the problem of scheduling n identical jobs on a set of m parallel uniform machines. The jobs are subjected to conflicting constraints modelled by an undirected graph G, in which adjacent jobs are ...
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This paper addresses the problem of scheduling n identical jobs on a set of m parallel uniform machines. The jobs are subjected to conflicting constraints modelled by an undirected graph G, in which adjacent jobs are not allowed to be processed on the same machine. Minimising the maximum completion time in the schedule (makespan C-max) is known to be NP-hard. We prove that when G is restricted to complete bipartite graphs the problem remains NP-hard for arbitrary number of machines, however, if m is fixed an optimal solution can be obtained in polynomial time. To solve the general case of the problem, we propose mixed-integer linear programming (MILP) formulations alongside with lower bounds and heuristic approaches. Furthermore, computational experiments are carried out to measure the performance of the proposed methods. (C) 2019 Published by Elsevier Ltd.
Multi-manned assembly lines are commonly found in industries that manufacture large-size products (e.g. automotive industry), in which multiple workers are assigned to the same station in order to perform different op...
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Multi-manned assembly lines are commonly found in industries that manufacture large-size products (e.g. automotive industry), in which multiple workers are assigned to the same station in order to perform different operations simultaneously on the same product. Although the balancing problem of multi manned assembly lines had been modelled before, the previously presented exact mathematical formulations are only able to solve few small-size instances, while larger cases are solved by heuristics or metaheuristics that do not guarantee optimality. This work presents a new mixed-integer linear programming model with strong symmetry break constraints and decomposes the original problem into a new Benders' Decomposition Algorithm to solve large instances optimally. The proposed model minimises the total number of workers along the line and the number of opened stations as weighted primary and secondary objectives, respectively. Besides, feasibility cuts and symmetry break constraints based on combinatorial Benders' cuts and model's parameters are applied as lazy constraints to reduce search-space by eliminating infeasible sets of allocations. Tests on a literature dataset have shown that the proposed mathematical model outperforms previously developed formulations in both solution quality and computational processing time for small-size instances. Moreover, the proposed Benders' Decomposition Algorithm yielded 117 optimal results out of a 131-instances dataset. Compared to previously presented methods, this translates to 19 and 25 new best solutions reached for medium and large-size instances, respectively, of which 19 and 23 are optimal solutions. (C) 2019 Elsevier B.V. All rights reserved.
We propose three strategies by which a professor of a university course can assign final letter grades taking into account the natural uncertainty in students' individual assignment and final numerical grades. The...
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We propose three strategies by which a professor of a university course can assign final letter grades taking into account the natural uncertainty in students' individual assignment and final numerical grades. The first strategy formalizes a common technique that identifies large gaps in the final numerical grades. For the second and third strategies, we introduce the notion of a borderline student, that is, a student who is close to, but below, the breakpoint for the next highest letter grade. Using mixed-integer linear programming and a tailor-made branch-and-bound algorithm, we choose the letter-grade breakpoints to minimize the number of borderline students. In particular, the second strategy treats the uncertainty implicitly and minimizes the number of borderline students, while the third strategy uses a robust-optimization approach to minimize the maximum number of borderline students that could occur based on an explicit uncertainty set. We compare the three strategies on realistic instances and identify overall trends as well as some interesting exceptions. While no strategy appears best in all cases, each can be computed in a reasonable amount of time for a moderately sized course. Moreover, they collectively provide the professor important insight into how uncertainty affects the assignment of final letter grades. (C) 2018 Elsevier B.V. All rights reserved.
This paper aims at proposing an optimization model for high voltage transformers' maintenance scheduling to minimize operational cost and risk. The focus of the paper is on the transformer fleet management, and no...
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This paper aims at proposing an optimization model for high voltage transformers' maintenance scheduling to minimize operational cost and risk. The focus of the paper is on the transformer fleet management, and not on a single transformer maintenance procedure or the evaluation of a single transformer failure risk. The proposed methodology takes as inputs the importance (e.g., based on the expected energy not supplied) and failure risk of each transformer (e.g., based on on-line Dissolved Gas Analysis), and the maintenance cost for each transformer. It also considers the main practical constraints in field interventions. As output, the proposed methodology provides the best timing for the maintenance of each transformer from the fleet of interest. The problem has been modeled as mixed-integer linear programming. Eleven months of real data from the Brazilian transmission system are used for setting up the recent history of outages. The following year data are employed to test the effectiveness of the optimization model. The output of the proposed fleet maintenance scheduling tool is the optimum viable intervention calendar for a power transformer fleet within a 52-week horizon. This proposal represents an innovative and robust solution, which can support the operational planning experts' decision-making process.
Improving energy efficiency has been one of main objectives in modern manufacturing enterprises. Various approaches aiming at efficient energy management have been proposed/developed, among which minimizing energy con...
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Improving energy efficiency has been one of main objectives in modern manufacturing enterprises. Various approaches aiming at efficient energy management have been proposed/developed, among which minimizing energy consumption by energy-sensible production scheduling techniques has emerged as a promising one. However, reported workshop models are quite simple and unrealistic. This paper studies a more realistic workshop model called ultra-flexible job shop (uFJS). In an uFJS, the sequence among operations for a job can be changed within certain constraints. To formulate this energy-efficient scheduling problem, a mixed-integer linear programming model was developed. To deal with large-sized problems, a specially designed genetic algorithm (GA) was subsequently proposed and implemented. Numerical results showed the proposed GA worked with decent effectiveness and efficiency. Finally, several comparative studies are carried out to further demonstrate its efficacy in terms of energy efficiency improvement. The advantage of the uFJS as compared to other relative simple workshop models is also shown. By considering the flexibility in operation sequencing in each job, the uFJS effectively integrates process planning and scheduling in discrete parts manufacturing system, thus providing a much larger solution space for more energy-efficient solutions. It therefore provides an excellent platform for decision-makers when developing energy-efficient techniques and strategies
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