Programming Optimization Model Research Articles

Matheuristic approach and a mixed-integer linear programming model for biomass supply chain optimization with demand selection

It is crucial to identify alternative energy sources owing to the ever-increasing demand for energy and the other environmental problems associated with using fossil fuels. Biomass as a source of bioenergy is considered a promising alternative to fossil fuels. This study aims to optimize the biomass supply chain by developing an integrated model incorporating typical tactical supply chain decisions based on market or demand selection decisions. To this end, a novel mixed-integer linear programming (MILP) model is proposed to maximize the profit of the corresponding biomass supply chain and to commercialize electricity production by selecting electricity demand and making supply chain decisions regarding power plant operations, biomass feedstock purchase and storage, and biomass transport trucks. Owing to the intricacy of the MILP model, a fix-and-optimize-based solution strategy is developed and validated by applying it to several instances of a real-world case study. The results demonstrate that the proposed strategy can significantly reduce computational time while preserving high solution quality. Additionally, it helps improve planning and decision-making as it reveals the effect of essential biomass logistics characteristics on routing outcomes.

Exploring optimal pathways of the high-CO2 content natural gas source to chemicals and fuels using superstructure multi-objective optimization

This study aims to develop a mathematical formulation of superstructure multi-objective optimization to find optimal pathways of high-CO2 natural gas and PV-hydrogen to chemicals and fuels integrated with CO2 sequestration. A mixed-integer nonlinear programming optimization model is used to compete along 56 pathways in the superstructure optimization network. The model was developed with the general algebraic modeling system and computed with the standard branch and bound (SBB) solver to maximize annual net profit and minimize annual net CO2 emissions. The result shows the selected products in 2020 are liquefied natural gas, methanol, dimethyl ether, formic acid, and acetic acid, with annual net profits and net CO2 emissions of 38.17 million $/year and −8.47 million tons of CO2/year, respectively. In the projection analysis, the annual net profit growth results at a compounding annual growth rate of 7.85% per year between 2020 and 2060, while annual net CO2 emissions decrease until −16.37 million tons of CO2/year in 2060. In 2030, blue acetic acid will be selected via all separation processes. For 2050, the synfuel via partial membrane separation is selected. The other products, formic acid, methanol, and acetic acid via membrane separation (full and partial), will always be selected between 2020 and 2060. Therefore, this could be a future strategy for monetizing high–CO2–content natural gas sources with low-carbon process development.

An extended ε$\varepsilon $‐constraint method for a bi‐objective assortment optimization problem

AbstractThe paper deals with assortment optimization when customers purchase products using a nonparametric choice model. Each customer is presented with a preference list and will buy an available highest‐ranked offered product on the preference list. The paper presents a novel bi‐objective integer programming model for assortment optimization following a ranking‐based consumer choice model. The objectives are maximizing the expected revenue and maximizing customer satisfaction. This problem is recognized as an NP‐hard problem. After developing the bi‐objective model, an improved version of the augmented ‐constraint method is proposed to solve the problem and retrieve the Pareto‐optimal solutions. In each iteration, this algorithm solves a single‐objective linear integer programming sub‐problem. Our approach aims to obtain a complete set of Pareto‐optimal solutions. Finally, we present computational experiments on synthetic data. Several numerical illustrations are provided at the end to demonstrate the application of the proposed methodology. The computational results provide the decision‐makers with valuable information regarding the factors that mainly affect the solutions.

Efficient computational strategies for a mathematical programming model for multi-echelon inventory optimization based on the guaranteed-service approach

This paper presents a Multi-Echelon Inventory Optimization (MEIO) framework, based on the Guaranteed-Service Model (GSM), to allocate safety stocks across a supply chain with several locations and products, minimizing costs while meeting service level objectives. Extending previous work by Achkar et al. (2023), this paper enhances the Mixed-Integer Quadratically Constrained Program (MIQCP) with a highly efficient solution approach. The model introduces a piecewise linear approximation, significantly improving computational efficiency and the accuracy of the approximation for the fill rate function. It also introduces a different and more efficient approach to account for stochastic lead times using a discrete function. Moreover, an extension of the approach to account for non-normally distributed demands is proposed. The model is applied to several instances of a real-world case study from a pharmaceutical company, with more than 7300 product-location combinations, showing that optimal solutions can be obtained within few seconds of computational time.

Integrating reaction pathways and downstream separation network for optimal sustainable process route selection

Reducing the environmental impact of chemical production has become a critical objective due to carbon emission regulations and the challenges the carbon market poses. Downstream separation network optimization, which can improve process sustainability by using complex heat exchanger networks, applying advanced separation techniques, optimizing the design/operating parameters, etc., has been researched for many years. However, most optimization work focuses solely on downstream separation sections without considering the selection of raw materials and different reaction pathways. This work aims to develop a mixed integer nonlinear programming (MINLP) optimization model, which integrates reaction pathway selection and downstream separation optimization, to select the optimal sustainable process route for utilizing raw materials or producing products. The objective is to maximize/minimize the process profit/cost. Decision variables such as binary variables, which represent the selection of separation task, key component, heating utility, and continuous variables, which influence the separation mass/energy balance, are considered. By giving parameters like reaction conversion rate, selectivity, and raw material/product price, this optimization model can identify the optimal process route for producing a target product or utilizing a raw material. The optimization model was applied to two case studies: one-step isobutylene and methanol utilization and two-step 1,4-butanediol (BDO) production. The process routes, using isobutylene for pivalic acid production and methanol for gasoline production, have the highest process profit per carbon emission. And the process route, which uses acetylene for BDO production, leads to minimum process cost.

Tugboat Scheduling with Multiple Berthing Bases under Uncertainty

This study proposes a novel fuzzy programming optimization model for tugboat scheduling, directly considering multiple berthing bases, time windows, and operational uncertainties. The uncertainties in the required number of tugboats, the earliest start time, the latest start time, the processing time, and the start and end locations of each task are directly captured in the proposed fuzzy optimization model. The objective of the presented formulation is to minimize the total cost of fuel and delays. According to the characteristics of the problem, a Grey Wolf Optimization algorithm based on random probability encoding and custom genetic operators is proposed. The proposed algorithm, LINGO, the canonical Grey Wolf Optimization algorithm, and particle swarm optimization were used to compare and analyze the results of several examples. The results validate the efficiency of the proposed algorithm against the alternative exact and metaheuristics methods. Moreover, the findings from the conducted sensitivity analysis show the applicability of the developed fuzzy programming model for different confidence interval levels.

Batteries or silos: Optimizing storage capacity in direct air capture plants to maximize renewable energy use

Direct air capture (DAC) of carbon dioxide is among the technologies that is forecast to play a major role in achieving the global ambition to constrain atmospheric temperature rise to below two degrees Celsius by 2100. However, DAC is an energy intensive chemical process, whose designs are currently incompatible with intermittent renewable energy (RE) sources. This research develops a model to enable the flexible operation of DAC, to maximize RE usage. A new model of the chemical process flow of a liquid solvent DAC that includes silos to store CaCO3 and CaO is developed. A linear programming optimization model that minimizes energy costs while achieving the CO2 capture targets of the DAC plant is developed. Scenario analysis establishes the storage silo size and battery storage size needed to reduce renewable energy curtailment to zero for a given RE profile. Simulations with a representative 336-hour RE profile reveal that two silos of sizes 660 tons and 370 tons would be needed to support flexible DAC plant operations and reduce RE curtailment to zero. For the same profile, a 355 MWh/65 MW battery would be required to achieve zero renewable curtailment. The results demonstrate that flexible operation of DAC is achievable, and DAC plants can adapt to variable RE without the need for battery energy storage. Furthermore, considering the scale of storage needed to minimize RE curtailment in a commercial-scale DAC plant, the results suggest that using physical storage silos could be more cost-effective than using battery energy storage.

On Solution to ASUU Strike and Consolidated University Academic Salary Structure II (CONUASS II) in the Nigerian Universities Using Optimization Method

In this paper, we applied dynamic programming model for optimization of Consolidated University Academic Salary Structure II (CONUASS II) for the overall interest of the academic staff and the Nigerian University System. Our focus was on the decision policy that would help to enhance the living condition of lecturers in the Nigerian universities thereby averting frequent strikes and disruption of academic calendars. The frequent and incessant strikes delay students and impacts negatively to their feature; hence, anything that could be done to stabilize the university education in Nigeria will contribute immensely to the economic growth and stability of the country. To achieve this, we applied dynamic programming and developed an optimal decision policy which was applied to obtain the best optimal policy needed for the highest ranking cadre in the academic to achieve optimal remuneration of at least twice their per annum salary with subsequent adjustment in the other cadres’ salaries accordingly. Applying the optimal decision policy, we obtained (1, 1, 1, 1, 1, 1, 2, 2, 0, 0) which optimizes the academic staff’s earning with a promotion to level 08 instead of remaining at bar with many steps. If this policy is implemented, a professor at the bar will grow to level 08 and will therefore earn up to at least double of his/her annual salary (N13,658,325) instead of the current stagnating salary of (N6,020,163) per annum at the bar. This will make the lecturers to be happy and discharge their duties with commitments and thereby addressing the perennial strikes in the Nigerian universities.

A Dynamic Programming Model for Joint Optimization of Electric Drayage Truck Operations and Charging Stations Planning at Ports

A Dynamic Programming Model for Joint Optimization of Electric Drayage Truck Operations and Charging Stations Planning at Ports

Veggies and PV: Optimization of Building-Integrated Agriculture in an Energy Hub

Building-integrated Agriculture (BIA) is the concept of utilizing façade surfaces for crop production. The potential is to reduce land-use and to increase the utility of built-up area. If outdoor building surfaces were to be used for farming, it results in a competition for sunlight between crops, solar renewable energy (such as photovoltaics, PV), and daylight access to illuminate indoor spaces. We therefore propose a coupled BIA and multi-energy systems model that can represent various energy sources (such as sunlight) and their conversion and storage (such as façade based crop production, PV, or electric batteries) in order to optimally meet demands for building energy and food. It is formulated as a mixed integer linear program (MILP) optimization model that describes the energy flows as an annual hourly time series. The model conducts a bi-objective minimization of monetary cost and carbon emissions, resulting in a Pareto front of optimal solutions. The model meets building energy demands for cooling, heating and electricity by an optimized energy technology portfolio, as well as nutritional demands for leafy vegetables of all occupants by either BIA or supermarket purchases. We apply our model to a residential case study in Singapore, which serves as an example for a high density city with already numerous community-driven and practiced BIA initiatives ongoing. Our results show that when minimizing cost, utilizing PV is more cost efficient on highly exposed surfaces such as the roof than BIA. However, for more shaded façade surfaces, crop production can be a cost and environmentally efficient addition to building design, as the annual vegetables demand of all occupants can be covered entirely by self-grown produce.

Train rescheduling and platforming in large high-speed railway stations

To deal with train delays in large high-speed railway stations, a multi-objective mixed-integer nonlinear programming (MO-MINLP) optimization model was proposed. The model used the arrival time, departure time, track occupation, and route selection as the decision variables and fully considered the station infrastructure layout, train operational requirements, and time standards as limiting factors. The optimization objective was to minimize train delays and reduce track and route adjustments. To realize the large-scale and rapid solution of the MO-MINLP model, this study proposed a rolling horizon optimization algorithm that used “half an hour” as a time interval and solved the rescheduling and platforming problem of each time interval step-by-step. In numerical experiments, 227 train movements under delay circumstances in Hangzhoudong station were optimized by using the proposed model and solution algorithm. The results show that the proposed MO-MINLP model could resolve route conflicts, compress unnecessary dwell times, and reduce train delays; the solution algorithm could efficiently increase the computational speed. The maximum solution time for optimizing the 227 train movements is 15 min 24 s.

Pari-Mutuel Betting Markets: Racetracks and Lotteries Revisited

This survey discusses the state of the art in research in racetrack and lottery investment markets. Market efficiency and the pricing of various wagers are studied along with new developments since the Thaler & Ziemba (1988) review. The weak form inefficient market pricing approach using stochastic programming optimization models changed racetrack betting from handicapping to a financial market allowing professional syndicates to operate as hedge funds. Topics discussed include arbitrage and risk arbitrage, syndicates, betting exchange rebates, behavioral biases, and fundamental and mispricing information in racetrack and lottery markets. Similar models can be used to successfully trade stock market anomalies. Supplemental Materials are included online.

Optimization Model and Application for Agricultural Machinery Systems Based on Timeliness Losses of Multiple Operations

Present agricultural practices confront issues such as mismatches between tractors and implements, imprecise machinery allocation, and excessive machinery investment. Optimization of agricultural machinery systems was a potent remedy for these concerns. To address inaccuracies in calculating objective functions and the incompleteness of constraints in existing models for agricultural machinery system optimization, a comprehensive mixed integer nonlinear programming (MINP) model for agricultural machinery system optimization was established. The model introduced timeliness loss costs for multiple key operations across various crops into the objective function, and constraints were enhanced by including operation sequence constraints and boundary constraints on initiation and completion dates of those key operations. Taking corn and soybeans as examples, timeliness loss functions of sowing and harvesting operations were derived through experiments. Solving the MINP model by Lingo (V.14.0) software, improvements in total power, workload per unit power, and total operational costs were shown when comparing the optimized machinery system through the MINP model against current systems. When the model omitted considerations for timeliness loss functions and operation sequence constraints, issues arose including an increase in total operational costs and an inversion of operation sequence. The model’s application in devising machinery allocation plans for production units of various operational scales revealed a gradual decrease in total power and costs per unit area with expanding scale, approaching stability when scale exceeded 1600 hm2. This study enriches theory and methodology for optimizing agricultural machinery systems, provides theoretical and technological underpinnings for rational machinery acquisition, and promotes the high-quality progression of comprehensive agricultural mechanization.

An Optimal Operation Strategy for Collaborative Flexibility Provision of a Carbon Capture and Utilization Process With Wind Energy

Improving power system flexibility by responsive demand is essential for integrating wind energy with a high level of variability in power systems. Carbon dioxide-based chemical processes as energy-intensive industrial loads may offer a vast potential of new forms of flexible operation due to their existing control infrastructure and storage capabilities. However, a collaborative decision model is needed for optimal energy sharing among the chemical plant and the grid under the variations and uncertainties of wind power. This study develops an optimal two-stage stochastic programming model for a novel flexible operation strategy of the chemical process coupled with wind turbines. In the proposed control scheme, a small-scale wind farm provides the power input of a chemical plant. Wind turbines are connected to the grid and actively participate in the day-ahead energy and reserve markets, considering the chemical plant as a source of flexibility. An equivalent scenario-based model of the proposed optimization problem is suggested using the Group Method of Data Handling (GMDH) for a data-driven prediction of stochastic variables. Simulation results demonstrate the effectiveness and significance of the proposed approach for an optimal and collaborative contribution in ancillary market of a carbon dioxide-based chemical plant supplied by wind energy.

A second-order conic approximation to solving the optimal power flow problem in bipolar DC networks while considering a high penetration of distributed energy resources

This article presents an optimal power flow (OPF) formulation based on the branch flow model for bipolar DC grids with asymmetric loading. The proposal considers the power injection formulation of the OPF to obtain the branch flow model equations that allow solving the power flow problem in bipolar DC networks. Furthermore, a nonlinear programming (NLP) optimization model is deduced and transformed into a second-order conic programming one, which involves convex optimization and guarantees a global optimum for the relaxed model, the uniqueness of this solution, and fast convergence. Finally, an approximation based on balanced operation is proposed to simplify the OPF. Several case studies in two test systems composed of 21 and 85 nodes with a bipolar structure demonstrate that the proposal is accurate, fast, and close to the exact solution of the NLP model when compared with competitive literature reports. All optimization models were implemented in the Python language.

Service Function Chaining to Support Ultra-Low Latency Communication in NFV

Network function virtualization (NFV) has the potential to fundamentally transform conventional network architecture through the decoupling of software from dedicated hardware. The convergence of virtualization and cloud computing technologies has revolutionized the networking landscape, offering a wide range of advantages, including improved flexibility, manageability, and scalability. The importance of network capability in enabling ultra-low latency applications has been greatly amplified in the current era due to the increased demand for emerging services such as autonomous driving, teleoperated driving, virtual reality, and remote surgery. This paper presents a novel and efficient methodology for service function chaining (SFC) in an NFV-enabled network that aims to minimize latency and optimize the utilization of physical network resources, with a specific focus on ultra-low latency applications. In our proposed methodology, we offer flow prioritization and an adjustable priority coefficient factor (µ) to reserve a portion of physical network resources exclusively for ultra-low latency applications in order to optimize the deployment paths of these applications further. We formulate the SFC deployment problem as an integer linear programming (ILP) optimization model. Furthermore, we propose a set of heuristic algorithms that yield near-optimal solutions with minimal optimality gaps and execution times, making them practical for large-scale network topologies. Performance evaluations demonstrate the effectiveness of our proposed methodology in enabling ultra-low latency applications in an NFV-enabled network. Compared to existing algorithms, our proposed methodology achieves notable enhancements in terms of the end-to-end delay (up to 22 percent), bandwidth utilization (up to 28 percent), and SFC acceptance rate (up to 13 percent).

Scheduling aerial resource operations for the extinction of large-scale wildfires

The significant increase in large-scale wildfire events in recent decades, caused primarily by climate change, has resulted in a growing number of aerial resources being used in suppression efforts. Present-day management lacks efficient and scalable algorithms for complex aerial resource allocation and scheduling for the extinction of such fires, which is crucial to ensuring safety while maximizing the efficiency of operations. In this work, we present a Mixed Integer Linear Programming (MILP) optimization model tailored to large-scale wildfires for the daily scheduling of aerial operations. The main objective is to achieve a prioritized target water flow over all areas of operation and all time periods. Minimal target completion across individual areas and time periods and total water output are also maximized as secondary and ternary objectives, respectively. An efficient and scalable multi-start heuristic, combining a randomized greedy approach with simulated annealing employing large neighborhood search techniques, is proposed for larger instances. A diverse set of problem instances is generated with varying sizes and extinction strategies to test the approaches. Results indicate that the heuristic can achieve (near)-optimal solutions for smaller instances solvable by the MILP, and gives solutions approaching target water flows for larger problem sizes. The algorithm is parallelizable and has been shown to give promising results in a small number of iterations, making it applicable for both night-before planning and, more time-sensitive, early-morning scheduling.

Optimization of Signal Timing for Urban Expressway Exit Ramp Connecting Intersection.

To alleviate the traffic problems of congestion and queue overflow on a mainline at the intersection of an urban expressway exit ramp articulation during peak hours, a bi-level programming optimization model of signal timing is proposed. The lower-level optimization objective is to maximize the capacity of the expressway exit ramp that articulates with the entrance road, while the upper-level optimization objective is to minimize the average vehicle delay and the number of stops per vehicle, taking into account the queue length in the direction of the ramp and other directions. The particle swarm optimization algorithm is selected to solve the proposed model, applied to a real case, and is validated using MATLAB and VISSIM simulation platforms. The simulation results show that the average vehicle delay and the number of stops per vehicle in the exit ramp on the expressway are reduced by 22.09% and 18.60%, while those in the intersection area are reduced by 20.96% and 17.19%, respectively. The conclusion indicates that the signal timing scheme obtained by this method can effectively improve the traffic efficiency at the intersection of the exit ramp on the expressway and alleviate the problem of congestion and the overflow of the exit ramp back to the mainline.

New mixed integer fractional programming problem and some multi-objective models for sparse optimization

We propose a novel Mixed-Integer Nonlinear Programming (MINLP) model for sparse optimization based on the polyhedral k-norm. We put special emphasis on the application of sparse optimization in Feature Selection for Support Vector Machine (SVM) classification. We address the continuous relaxation of the problem, which comes out in the form of a fractional programming problem (FPP). In particular, we consider a possible way for tackling FPP by reformulating it via a DC (Difference of Convex) decomposition. We also overview the SVM models and the related Feature Selection in terms of multi-objective optimization. The results of some numerical experiments on benchmark classification datasets are reported.

Coordinated planning of charging swapping stations and active distribution network based on EV spatial‐temporal load forecasting

AbstractElectric vehicles (EVs) charging swapping stations (CSSs), as well as multi‐functional integrated charging and swapping facilities (CSFs), have become important to reduce the impact of e‐mobility on the electric power distribution system. This paper presents a coordinated planning optimization strategy for CSSs/CSFs and active distribution networks (AND) that includes distributed generation. The approach is based on the application of a specifically developed spatial‐temporal load forecasting method of both plug‐in EVs (PEVs) and swapping EVs (SEVs). The approach is formulated as a mathematical programming optimization model that provides the location and sizing of new CSSs, the best active distribution network topology, the required distributed generation, and substation capacities. The developed model is solved using CPLEX, and its characteristics and performances are evaluated through a realistic case study.