Total Cost Objective Function Research Articles

Computational model design for road to waterway transportation conversion efficiency improvement based on deep learning algorithm

Abstract Path planning for combined transportation can improve the irrationality in the carrier task so as to achieve the purpose of cost reduction and efficiency. This study takes economic efficiency as the starting point, takes the transportation time window as a constraint, and constructs the total cost objective function in the transportation process. The objective function of carbon emission in the transportation process is designed to address the green and low-carbon problem. The Ant colony algorithm is used to solve the multi-objective joint transportation model, aiming to obtain a green and efficient transportation path that meets the actual demand. The ACO algorithm shows good convergence performance in the transportation task from starting point O to ending point D. The ACO algorithm is capable of solving the transportation task from starting point O to ending point D after 130 iterations. After 130 iterations of the algorithm, the cost objective function value converged to 3427.8 RMB, and the carbon emission objective function value converged to 5534 kg after 90 iterations of the algorithm. Furthermore, the ACO algorithm’s Pareto solution set exhibits a uniform spatial distribution and excellent ductility and approximation effects. Assigning the same weights to cost, carbon emissions, and transportation time, the optimal solution 4 is obtained. The scheme from the starting point O via nodes 1, 2, and 6 to the end point D, through the joint transportation of road and waterway for 162 hours, a total of 5549 kg CO2, and the cost of transporting each ton of goods is 4093.9 yuan.

Multi-objective unit commitment with spinning reserve cost using hybrid method

<span lang="EN-US">Under the generation of electrical power, fuel consumption, and emission are emphasized in the thermal power industry. Based on this, emission and cost were considered objectives with inequality and equality constraints. The spinning reserve was replenished as one of the constraints. In this paper, the spinning reserve cost (SRC)was incorporated with the total cost objective function. The hybrid technique is steered to achieve minimal value which is the combination of the cuckoo search method and flower pollination algorithm. To predict the potential of the proposed technique, two systems are considered namely a four-unit system and an IEEE thirty-nine bus system. The obtained simulation outcome shows a better improvement with the proposed technique in optimal value.</span>

Robust Bi-Level Planning Method for Multi-Source Systems Integrated With Offshore Wind Farms Considering Prediction Errors

Considering the economy, reliability, and output characteristics of multiple power sources (MPS) and energy storage (ES) comprehensively, a multi-source system integrated with offshore wind farms (OWFs) and its construction cost, and operating and maintenance cost model are established. The system is mainly composed of OWFs, thermal power plants, gas turbine power plants, and pumped hydro storage plants. Given the economy of the power system and offshore wind power accommodation, a bi-level optimal capacity configuration and operation scheduling method is proposed for the multi-source system integrated with OWF clusters with the objective function of optimal total cost. Then, a robust bi-level planning method for the multi-source system integrated with OWFs considering the dual uncertainty of load and offshore wind power prediction is proposed, in which the upper and lower models are solved by an improved particle swarm optimization (PSO) algorithm and CPLEX solver, respectively. Based on the method, the cost-optimal capacity configuration and operation scheduling scheme of an MPS and ES can be obtained. Finally, an OWF group in Shandong Province is taken as an example to check the validity and feasibility of the proposed method.

Non-dominated Sorting Genetic Algorithm II and Particle Swarm Optimization for design optimization of Shell and Tube Heat Exchanger

Optimization methods are applied in Shell and Tube Heat Exchanger (STHE) design to reduce the cost of the device. Various existing optimization techniques such as Particle Swarm Optimization (PSO), Adaptive Range Genetic Algorithm (ARGA) are applied in the design of STHE. Existing optimization methods used in STHE design, have the limitation of lower convergence and easily trap into local optima. In this research, the hybrid method of Non-dominated Sorting Genetic Algorithm II (NSGA II) and PSO method is proposed to reduce the cost in STHE design. The NSGA II method is applied to improve the exploration and PSO method is applied to improve exploitation of search process. The hybrid method has objective function of total cost and overall heat transfer of the model to improve the performance. The NSGA II has strong exploration in the search due to the non-dominated search process and also provides good convergence. The PSO method is applied in the best solution of NSGA II and the PSO method has the advantage of strong exploitation that escapes from the local optima. The hybrid NSGA II-PSO method is tested on three test cases and is compared with existing optimization methods to analyze its performance. The result shows that the hybrid NSGA II-PSO method has a 4.85% lesser total cost in case 1 and 1.51% lesser total cost in case 2, when compared to the ARGA method.

Retracted] Optimization Algorithm of Logistics Transportation Cost of Prefabricated Building Components for Project Management

Because the traditional logistics transportation cost optimization algorithm of prefabricated building components has the problems of long transportation time and high transportation cost, a logistics transportation cost optimization algorithm of prefabricated building components for project management is proposed. A project management oriented prefabricated building component management system is built, the logistics and transportation process of prefabricated building components are analyzed, and the logistics vehicles of prefabricated building components under the time window are scheduled. According to the scheduling results, through the waiting unloading time cost, transportation cost, and penalty cost, the total cost objective function is built to obtain the optimal cost. The simulation results show that the proposed algorithm has the shortest logistics transportation time and the lowest transportation cost.

The impact of using a naïve approach in the limited-stop bus service design problem

The proven benefits of limited-stop services have captured the attention of researchers, especially during the last decade. However, to solve the limited-stop service design problem many existing works directly impose a capacity constraint to a total social cost objective function. This “naïve approach” implicitly assumes that passengers behave altruistically, basing their decisions on what is best for the whole system. Although this issue has been identified in earlier works, the magnitude of the error induced by this simplification has not been studied yet. The objective of this work is to measure this error and to understand how it misrepresents passenger flows and bus occupation rates. To measure this error gap, we optimize a set of test scenarios by applying a naïve approach, and then take the resulting design and obtain a benchmark passenger assignment using a simple behavioral model. We propose two main indicators to compare both passenger assignment: the total passenger deviation, and the total capacity deficit. This comparison reveals that the assignment of the naïve approach may indeed be unrealistic, and raises concerns that a network design based on the naïve approach might have severe problems when implemented. Thus, the work highlights the importance of taking the results of the naïve approach with caution and verify them with a passenger assignment model before their implementation.

Optimization of Pressure-Swing Distillation for iC5-Methanol Azeotropic Mixture Purification

Typical industrial technologies to produce tert-amyl methyl ether (TAME), a gasoline oxygenated additive, require some advanced purification process for methanol recovery from the reactor effluent, due to the presence of the iC5-methanol minimum boiling point azeotrope. Pressure-swing distillation (PSD) is widely used as an efficient method for separating pressure-sensitive azeotropic mixtures in industrial processes. However, it is well known that distillation units are responsible for the highest energy consumption in chemical separation facilities, reaching in some cases to 95% of the total energy cost. Thus, the objective of this work was to perform an optimization methodology of the main design and operational variables of the PSD process applied to the separation of the azeotropic iC5-methanol mixture, considering minimizing the objective function of total annual cost (TAC). For this purpose, Honeywell’s UniSim Design® Suite software was used to simulate the process flowchart and Matlab® was used to perform TAC optimization. The optimized PSD design revealed potential for saving of up to 12% per year in terms of TAC when compared to the non-optimized process, thus proving the feasibility of the optimization methodology for this specific process. Furthermore, it reinforces the main objective of the optimization technique that is to make chemical processes more economically competitive in the industrial sector.

Resilient planning strategies to support disruption-tolerant production operations

The challenge being addressed in this paper is how best to prepare production for the potential disruptive events in order to minimise the impact of these unexpected disturbances. In particular, the paper is focusing on two particular approaches to disruption preparation. The first examines the optimal location and quantity of inventory or “work-in-progress”. The second explores the role of inspection stations in providing timely warning of quality issues. A mathematical model of the operations of a production system is suggested, which covers several types of disruptions: resource breakdowns with unknown start time, product quality losses and random demand fluctuations. The optimal solution minimises a total cost objective function, which is made up of production costs, inventory holding costs, inspection costs, as well as penalty costs for the lost or uncompleted orders. As an output, the model gives the best location and quantity of inventory and the best location of inspection points for any arbitrary production system. The model is first formulated as an optimal control problem, and it is shown how to transform it to a quadratic integer programming problem. The approach was applied to study an industrial strength laboratory production system that reflects the actual industrial disruption scenarios experienced by an industrial collaborator in a key production facility. The optimal solution for this laboratory system is presented and its evaluation is shown under several scenarios with disruptions. The model was also tested on large scale production systems with up to 500 resources.

An operation synchronization model for distribution center in E-commerce logistics service

This paper is among the first that proposes a synchronization measurement model for the distribution centre operation synchronization (DCOS) problem, which aims to ensure the E-commerce order’s punctuality and synchronization at the same time. The main motivation of DCOS is that the intensified competition in E-commerce market makes efficient E-commerce logistics service extremely important, which means saving logistics cost and ensuring customer service at the same time. The synchronized operation may be a possible solution to ensure efficient order transhipment in the distribution center and to save cost. We thus introduce a measurement approach that is able to address the distribution center operation synchronization (DCOS) problem such as the trade-off relationship between synchronization and punctuality. In order to get persuasive conclusions, we adopt data from a real practice case and apply CPLEX to get the optimal solution. Our computational results show that considering the asynchronous cost in the total cost objective function will greatly improve the operation synchronization in the distribution center, by saving the storage space, the equipment, and the labour resources. And if the storage cost is in a reasonable range, the synchronized operation can be realized while the punctuality is also optimized. It is found in our case that the most efficient way to improve distribution center operation is expanding inbound operation capacity.

A novel approach to district heating and cooling network design based on life cycle cost optimization

Piping layout, material, and dimension choices are essential in determining the initial capital costs and full operating costs of a district heating and cooling (DHC) network. While common practice aims to minimize initial capital costs or, in some cases, operational costs, this paper introduces a novel method for designing DHC network layouts for minimum total life-cycle cost by introducing additional engineering design parameters related to pipe sizing, heat losses, and pumping energy. The proposed mixed-integer linear programming solution satisfies the thermal and hydraulic constraints on the network while minimizing the objective function of total cost over the lifetime of the network. The method is tested with three case studies. Results show improvement in reducing total life-cycle costs of the network compared to approaches that consider only capital or operating costs and exclude network dimensioning.

The Fast and the Robust: Trade‐Offs Between Optimization Robustness and Cost in the Calibration of Environmental Models

AbstractEnvironmental modelers using optimization algorithms for model calibration face an ambivalent choice. Some algorithms, for example, Newton‐type methods, are fast but struggle to consistently find global parameter optima; other algorithms, for example, evolutionary methods, boast better global convergence but at much higher cost (e.g., requiring more objective function calls). Trade‐offs between accuracy/robustness versus cost are ubiquitous in numerical computation, yet environmental modeling studies have lacked a systematic framework for quantifying these trade‐offs. This study develops a framework for benchmarking stochastic optimization algorithms in the context of environmental model calibration, where multiple algorithm invocations are typically necessary. We define reliability as the probability of finding the desired (global or tolerable) optimum from random initial points and estimate the number of invocations to find the desired optimum with prescribed confidence (here 95%). A robust algorithm should achieve consistently high reliability across many problems. A characteristic efficiency metric for algorithm benchmarking is defined as the total cost (objective function calls over multiple invocations) to find the desired optimum with prescribed confidence. This approach avoids the pitfalls of existing approaches that compare costs without controlling the confidence in algorithm success. A case study illustrates the framework by benchmarking the Levenberg‐Marquardt and Shuffled Complex Evolution (SCE) algorithms over three catchments and four hydrological models. In 8 of 12 scenarios, Levenberg‐Marquardt is more efficient than SCE—by sacrificing some of its speed advantage to match SCE reliability through more invocations. The proposed framework is easy to apply and can help guide algorithm selection in environmental model calibration.

Analyzing optimum thickness for combination of two thermal insulation materials for building walls

This paper reports an approach for analyzing optimum thickness for combination of two thermal insulation materials for walls of residential buildings on the basis of life cycle cost. Two thermal insulation materials for achieving contrast purposes can be use as a solution in many applications e.g. if fire resistant material added with Expanded polystyrene (EPS) to improve its fire resistance property, its thermal conductivity increases, where as if we select glass wool as thermal insulation material it has higher thermal conductivity but better fire resistant, thus if we wish to achieve high thermal resistance with better fire resistance at low cost we can use in place of single thermal insulation material a combination of two thermal insulation materials. In order to determine optimum thickness for combination of two thermal insulation materials there is a need to develop an approach, through which optimum insulation thickness for different combination of two thermal insulation materials on the basis of life cycle cost can be analyzed. To study the effect of fraction of one thermal insulation on optimum thermal insulation thickness proposed approach is applied to insulate external wall of a residential building envelope in heating application. Developed total cost objective function analyzed with the help of surface plot. In order to apply the developed approach EPS and glass wool are considered as thermal insulation materials. Through this approach optimum thickness for combination of two thermal insulation materials can be analyzed on the basis of life cycle cost in order to select best combination of thermal insulation materials as per requirement.

Sample average approximation for a two-echelon inventory system with service-level constraints

We propose a sample-average-approximation-based simulation optimisation approach for solving a two-echelon inventory problem containing a total cost objective function and multiple service-level constraints. Some necessary parameter settings and conditions are provided to achieve the stopping condition in practice and the convergence to the optimal solution. The approach takes into account the stochastic nature of the objective and constraint performance measures, and allows the customer demands to occur with a random size and all events to occur at random points in time (including the stochastic lead times). Experimental studies are performed to evaluate the efficiency of the developed algorithms and other existing solution approaches.

Strategies of refueling, sailing speed and ship deployment of containerships in the low-carbon background

Abstract To solve the problems of refueling, ship speed determination and ship deployment of containerships, based on the nonlinear relationship between ship sailing speed, fuel consumption and carbon emissions, a corresponding nonlinear mixed integer programming model is developed by taking container transportation cost, fuel consumption cost and carbon emissions cost in multiple service routes as the total cost objective function, and ship refueling ports, refueling amounts, sailing speed and ship deployment quantities in the route as decision variables. The optimal solution can be obtained by transforming the nonlinear discrete mixed integer programming model into a nonlinear continuous programming model. The proposed model is applied to an Asia-Europe service route of China Shipping (Group) Company. The results show that the optimal refueling policy, speed selection and ship deployment can be determined using the proposed model and solution method. The impact of fuel price, container transportation quantity, ship tanker capacity and carbon tax rate on ship refueling strategy, speed and deployment is investigated. Some insights obtained from example analysis are provided.

Effect of multi-recycle streams on triple-column pressure-swing distillation optimization

Different structures of multi-recycle triple-column pressure-swing distillation (TCPSD) are synthesized and explored. Acetonitrile/methanol/benzene ternary mixture is set as a case to identify the applicability of different multi-recycle TCPSD flowsheets. Four multi-recycle flowsheets are analyzed and compared with convention TCPSD process and rigorous steady-state simulations are implemented using Aspen Plus. Operating parameters are optimized by using the sequential iterative optimization procedure when the split fraction changes with the objective function of minimum total annual cost. Two structures are found that distillate compositions surpass the distillation boundaries at finite reflux ratios. However, the results show that different multi-recycle TCPSD processes are feasible.

An Application of ‘Willingness to Pay’ Method as a Quantifier for Environmental Impact Assessment

The preservation/restoration of natural environment is frequently entailing excessive cost (paid by people through taxation) while it is a source of additional income for both, the State and the people, due to tourism. Since the evaluation of this good cannot be in market terms, it is applied here in a modified version of the CVM (Contingent Valuation Method), which is used in experimental economics in order to investigate the significance that people put on this good and how much they might be WTP (Willing to Pay) for supporting activities concerning the preservation/restoration of Lake Kastoria. The WTP dependence on (i) external diseconomies; (ii) the expectations for property values’ rise as a result of the restoration; (iii) the proximity of interviewees’ residence to the lake; (iv) the opinion of the interviewee on the time and money spent to visit the lake; (v) the time and money the interviewees spent to visit the lake, as well as other dependencies (all taken as independent variables) are estimated by means of logit, probit, logistic and linear regression models. The optimal concentration Copt of a pollutant in the environment can be determined as an equilibrium point in the tradeoff between (i) environmental cost, due to impact on man/ecosystem/economy; and (ii) economic cost for environmental protection, as it can be expressed by Pigouvian tax. These two conflict variables are internalized within the same techno-economic objective function of total cost, which is minimized. In this work, the first conflict variable is represented by a WTP index. A methodology is developed for the estimation of this index by using fuzzy sets to count for uncertainty. Implementation of this methodology is presented, concerning odor pollution of air round an olive pomace oil mill.

An Application of ‘Willingness to Pay’ Method as a Quantifier for Environmental Impact Assessment

The preservation/restoration of natural environment is frequently entailing excessive cost (paid by people through taxation) while it is a source of additional income for both, the State and the people, due to tourism. Since the evaluation of this good cannot be in market terms, it is applied here in a modified version of the CVM (Contingent Valuation Method), which is used in experimental economics in order to investigate the significance that people put on this good and how much they might be WTP (Willing to Pay) for supporting activities concerning the preservation/restoration of Lake Kastoria. The WTP dependence on (i) external diseconomies; (ii) the expectations for property values’ rise as a result of the restoration; (iii) the proximity of interviewees’ residence to the lake; (iv) the opinion of the interviewee on the time and money spent to visit the lake; (v) the time and money the interviewees spent to visit the lake, as well as other dependencies (all taken as independent variables) are estimated by means of logit, probit, logistic and linear regression models. The optimal concentration Copt of a pollutant in the environment can be determined as an equilibrium point in the tradeoff between (i) environmental cost, due to impact on man/ecosystem/economy; and (ii) economic cost for environmental protection, as it can be expressed by Pigouvian tax. These two conflict variables are internalized within the same techno-economic objective function of total cost, which is minimized. In this work, the first conflict variable is represented by a WTP index. A methodology is developed for the estimation of this index by using fuzzy sets to count for uncertainty. Implementation of this methodology is presented, concerning odor pollution of air round an olive pomace oil mill.

Integrating drivers’ differences in optimizing green supply chain management at tactical and operational levels

Green Supply Chain Management (GSCM) has attained a huge attention by researchers in the last few decades. However, the effect of human aspects (e.g. drivers’ differences) in designing and managing green supply chains (GSCs) has been ignored despite the fact of their crucial importance in adopting and achieving optimal green strategies. In this paper, a novel approach is developed for integrating drivers’ differences to examine their effect on fuel consumption and CO2 emissions, denoted by a Green Driving Index (GDI), in optimizing green supply chain at the tactical and operational management levels. More specifically, a more realistic mixed integer nonlinear programming model is proposed to deal with multi-site, multi-product, and multi-period Aggregate Production Planning (APP) setting with different levels of drivers and different types of vehicles. The proposed model aims to minimize the total cost and CO2 emissions across the supply chain. Also, it aims to derive optimal assignments between vehicles, drivers, and the destinations as well as an optimal selection and training of the selected drivers. Two formulations of the problem are developed. Specifically, the first formulation minimizes a single objective function of total costs across the supply chain while considering the greenhouse gas (GHG) limits in the constraints whereas the second formulation minimizes a bi-objective function (total costs and GHG). A numerical study and sensitivity analyses are conducted to confirm the verification of the two proposed formulations. The results demonstrate that as CO2 emissions allowable limits become stricter, the model selects drivers having higher GDIs. The results indicate that the drivers’ differences should be considered in GSCM to generate realistic plans with minimum costs and minimal CO2 emissions.

Balancing Push and Pull Strategies within the Production System

This paper presents an approach for achieving a trade-off between pull and push production control principles. A mathematical model of the operation of a production system is suggested, which incorporates different options for inventory control strategies. The model covers several types of disruptions: resource breakdown, product quality loss and demand fluctuation. The optimal solution minimizes the total cost objective function and can be push, one of the classic pull control systems (kanbans, conwip, basestock) or any possible combination/superimposition of them. The approach is illustrated in an example, for which optimal pull/push combination is found and its evolution is shown under several scenarios with disruptions.

Two Stage Optimal Capacitors Placement and Sizing Using Differential Evolution Particle Swarm Optimization

Installing capacitors in a large unbalanced electrical distribution system will indeed improves the performance of the system in terms of its voltage profile and real power loss stability. However, determining the suitable locations for capacitors installation with an appropriate sizing in an unbalanced electrical distribution system involves an intricate process. This impediment can be resolved by implementing an optimal capacitors placement and sizing. The proposed technique is a highly nonlinear optimization problem which requires discrete and multi-dimensional control variables of capacitor locations and sizes. This paper proposed a new artificial intelligence approach used to reduce the total line real power loss and total real power consumption while maintaining the voltage profile along the feeders. It was done by integrating the circuitry schematic diagram of an unbalanced electrical distribution system modeled in SIMULINK® software with the computational programming based differential evolution particle swarm optimization (DEPSO) for optimal capacitors placement and sizing developed under the MATLAB® software. In this study, pre-selection of the capacitor locations can be considered as the first stage of the proposed concept and it is commenced prior to the optimization process performed by the DEPSO algorithm considered as the second stage of the proposed concept. A modified IEEE 13-bus unbalanced radial distribution system is used verify effectiveness of the proposed technique in solving the problem. The results will be discussed notably through comparative studies on the objective function of total cost and performance of the DEPSO technique.