Single-objective Programming Model Research Articles

Optimal Decision on Pricing and Replenishment of Vegetable Products Based on Goal Planning

Developing replenishment and pricing plans has always been the key for fresh food supermarkets to gain more profits. This paper analyzes various situations and provides the optimal solution through Spearman correlation analysis, Lasso regression, goal programming and other methods and models. We use normality testing and box plots to present the distribution patterns of major categories and individual products from both vertical and horizontal perspectives. Establish a single objective programming model and solve it with Lingo to obtain a maximum profit of 98513 yuan for 7 days. The largest total replenishment amount is for the flower and leaf category, the smallest is for edible mushrooms, the highest average cost markup rate is for aquatic roots and stems, and the lowest is for cauliflower. This has certain reference value and theoretical significance for fresh food supermarkets to formulate replenishment and pricing plans.

Price And Replenishment of Vegetables Based on NARX Neural Network

The research on the replenishment and pricing of vegetable commodities is helpful for supermarket to make more scientific purchase and sale decisions. Based on this, this paper mainly uses NARX neural network to study the replenishment and pricing of vegetable commodities. Firstly, it preprocesses the missing and abnormal values of the data, constructs a correlation analysis model to study the relationship between the sales of various categories of vegetables, then establishes a NARX neural network model to solve the daily replenishment total, and finally constructs a single objective programming model to get the pricing strategy, which provides a theoretical basis for supermarket to make scientific pricing and replenishment decisions.

Artificial Intelligence in Market Segment Portfolio for Profit Maximization

This paper proposes an approach to select a market segment portfolio to maximize overall profit. The study first uses artificial intelligence algorithms to select the market segments with high profitability. The mathematical programming model is then used to identify the most profitable market segment portfolio. The single-objective programming model is used to find the optimal profit for the baseline condition, and a sensitivity analysis is performed to understand the impact of the variable changes on the results. Then, a multi-objective programming model helps to identify the best profit when the evaluated items reach extreme values. A sensitivity analysis is conducted to reveal the impact of the variable changes on the results. The above results are compared with those of the scoring method. It is found that the artificial intelligence algorithm combined with mathematical programming models can indeed find the market segmentation portfolio with better profits than the conventional methods.

Study on the optimal investment strategy based on single target PSO

With the development of science, technology and popularity of electronic transactions, quantitative investment transactions have become the focal point in the field of investment. In order to maximize returns during the investment period, we will build a single-objective PSO-based decision model based on asset price trend forecast data to develop a daily investment strategy. At first, we use price volatility as a risk factor and determine the risk level in combination with the application principle of ROC. Then, combined with the prediction results, we distinguish the gold market trading days and non-trading days, establish a single-objective programming model with the maximum daily net income as the goal. Finally, we use PSO algorithm to optimize the solution process. And we can get the daily optimal investment strategy and the final asset is $ 226648.42.

Unmanned Aerial Vehicles Rescue System Design and Traffic Model Planning

Unmanned Aerial Vehicles (UAV) are widely used in disaster relief and road exploration in recent years. This paper mainly studied the emergency response of UAVs after disasters. The UAV response system is mainly suitable for the distribution of necessities and road exploration after geological disasters and tsunamis in coastal areas. By analyzing the problem and making reasonable assumptions, the optimization model was established with the traffic planning theory, and MATLAB software was used to program and solve the problem. An optimal scheduling scheme was presented to solve these problems. The normalization method was used to select a highly capable UAV. Taking the minimum volume of idle space buffer material as the objective function and taking into account the constraints, such as payload of unmanned aerial vehicle, a single objective programming model was established. The results are as follows: Each International Standards Organization (ISO) cargo container has five UAVs B, one UAV C, one UAV F and one UAV H. It provides 188 days of relief requirements with ISO cargo containers’ space utilization of 71.4%. The research shows that the UAV response system has the functions of necessities distribution and road exploration after disasters, and can be used to deal with the emergency response after disasters in coastal areas, and has a wide range of applicability.

Analysis and Construction of EEMD Smart Model and Fuzzy Forecasting through Improved Bayesian Estimation

Different portfolio models will have a great impact on the model rate of return. In order to meet the data needs of portfolio investment forecasting, a big data generation method based on incremental Bayesian network model is proposed. Firstly, the fuzzy interval number is constructed by using the global GM (1pare 1) prediction model, then the fuzzy Mmurv model is established based on the interval fuzzy number, and the model is optimized based on the midpoint, radius and acceptability of the interval number, thus a single objective programming model with parameters is obtained. The future data is partially generated by using the time series generation algorithm, and the Bayesian network model trained by historical data is updated with the newly generated data. So that the updated Bayesian network can reflect the relationship between the variables and the laws contained in the new and old financial data in this period of time. And use the model to predict the amount of foreign direct investment absorbed by China in 2020, test the robustness and analyze the impact of major random events to show the reliability of the prediction. The analysis is carried out on multiple scales. The results show that the integration of IMF1 and IMF2 components through the white noise test can be regarded as the random impact of external factors; the cycle length of IMF3 component is about 3 years, which can be regarded as the inventory cycle caused by the change of enterprise inventory; the cycle length of IMF4 component is 5 years, which can be regarded as political cycle; the cycle length of IMF5 component is about 20 years, which can be regarded as construction cycle. The set of portfolio paths is generated by path search algorithm in Bayesian network, and the big data set with real data characteristics is generated according to the probability distribution of each path. The experimental results show that the method is feasible and ensures a certain accuracy. The forecast results show that the amount of foreign direct investment in China will continue to fluctuate seasonally and in a trend in recent years.

Efficient and sustainable closed-loop supply chain network design: A two-stage stochastic formulation with a hybrid solution methodology

In recent years, consumers and legislators have pushed companies to design their supply chain networks to consider environmental and social impacts as an important performance outcome. Due to the role of resource utilization as a key component of logistics network design, another primary goal of design is ensuring available scarce resources are used as efficiently as possible across all facilities. To address efficiency issues in a sustainable closed-loop supply chain network, a stochastic integrated multi-objective mixed integer nonlinear programming model is developed in this paper, in which sustainability outcomes as well as efficiency of facility resource utilization are considered in the design of a sustainable supply chain network. In doing so, efficiency is assessed using a bi-objective output-oriented data envelopment analysis model. A hybrid three-step solution methodology is presented that creates a linear form of the original mixed integer nonlinear programming problem using piecewise McCormick envelopes approach. In the second step, an aggregated single objective programming model is derived by exploiting the multi-choice goal programming. Finally, a Lagrangian relaxation algorithm is developed to effectively solve the latter stochastic single objective mixed integer linear programming problem. The application of the proposed approach is investigated with data drawn from a case study in the electronics industry. This case study illustrates how firms may balance sustainability and efficiency in the supply chain network design problem. Further, it demonstrates the integration of efficiency results in improving economic aspects of sustainability as well as social responsibility outcomes, but also highlights the trade-offs that exist between efficiency and environmental impacts.

The interval copula-measure Me based multi-objective multi-stage stochastic chance-constrained programming for seasonal water resources allocation under uncertainty

A copula-measure Me based interval multi-objective multi-stage stochastic chance-constrained programming (CMIMOMSP) model is proposed for water consumption optimization. It can conduct water allocation amid multiple users and multiple stages, and deal with the uncertainties presented as interval numbers, random fuzzy interval numbers, and stochastic variables. It improves upon multi-stage stochastic chance-constrained programming by introducing the multi-objective programming, and it can tradeoff the relationships amid economic benefit, full usage of water resources, and economic loss. It enhances the accuracy of copula function and conditional distribution function through proposing the interval functions. Besides, it can deal with the impact of the decision attitudes of managers on water allocation by formulating the function equation between water demand and the optimistic-pessimistic factor. The CMIMOMSP model is applied to a case study of the Heihe River Basin to verify its application. The results indicate that: (1) the optimistic-pessimistic factors have different degrees of positive influences on water allocation for industrial, domestic and ecological sectors; (2) the joint violated probability and optimistic-pessimistic factor have various range of impacts on agricultural water allocation; (3) tthe objective function values have different variation tendencies with the rise of joint violated probabilities and optimistic-pessimistic factors. Its robustness is enhanced by comparing it with the three single-objective programming models. The CMIMOMSP model can provide various water allocation schemes for managers with different risk attitudes in semi-arid and arid districts.

The least square pre-nucleolus for interval cooperative games based on anti-symmetric interval excess values

Considering both cardinal characteristics and double powers, the anti-symmetric interval excess value is defined. The least square pre-nucleolus for interval cooperative games is presented by making a single-objective programming model. We obtain the analytic expression of least square pre-nucleolus using Lagrange multiplier method, and construct an effective quadratic programming model to derive the least square pre-nucleolus of incomplete interval cooperative games. In addition, the application of least square pre-nucleolus in land pollution control is provided to show the validity of the proposed solution concepts.

Optimization of environmental impacts of construction projects: a time–cost–quality trade-off approach

The construction industry and the implementation of civil projects are considered to be one of the causes of environmental pollution. Given the impacts and pollution created by the implementation of projects, it is necessary to identify the environmental impacts in order to reduce their effects. The purpose of this paper is to present a discrete time–cost–quality–environmental impacts trade-off problem for the construction industry with multiple execution modes for project activities in order to reduce the environmental impacts of the project implementation. A multi-objective planning model was developed in this problem to address the four objectives of minimizing time, cost, and environmental impacts and maximizing quality of the project implementation. Then, the problem was modeled as a single-objective programming model by converting the objective function to a constraint. The Leopold matrix method was used to evaluate environmental impacts. Finally, part of a rural water supply project was used as a practical example to demonstrate the applicability and efficiency of the model. The results of this study showed that the proposed method to optimize the aforementioned objectives is highly efficient, and planning and decision making in the early stages of a project to choose the method of doing the project activities will result in reducing costs, time, environmental impacts, and enhancing the quality of the project. By calculating the environmental impacts of project activities in each execution mode, project managers and stakeholders can take into account the environment around them, along with pursuing the economic, time, and quality objectives of the project, and minimize the project overall negative environmental impacts as a measurable amount. This research can help project managers choose the most appropriate method to execute their activities so that the project will ultimately be delivered with the least amount of time, cost, and environmental impact, and with the highest quality.

Sustainable supplier selection and order allocation: A novel multi-objective programming model with a hybrid solution approach

Sustainable supplier selection is the process of identifying the appropriate supply partners of an organization with the most beneficial monetary value, while diminishing the various effects of its operations on society and environment. Therefore, it plays a significant role in moving an organization toward sustainable development. Alongside sustainable supplier selection, assigning proper quantity of orders to suppliers satisfying sustainability criteria is another activity that should be simultaneously carried out in order to develop a comprehensive tool in sustainable supplier management. Meanwhile, the issue of sustainable supplier selection and order allocation has attracted limited attention in the literature. The present paper aims at developing an inclusive multi-objective mixed integer linear programming model, which accounts for multiple periods, multiple products and multimodal transportation, to evaluate suppliers and allocate order quantities. Furthermore, the developed model that includes all sustainability aspects also takes both shortage and discount conditions into account. A hybrid three-step solution methodology is then presented, using which the original multi-objective problem is firstly converted to a single objective model by ε-constraint method. In the second step, the current single objective programming model is solved using the Benders decomposition algorithm that in turn is accelerated by a variety of algorithmic enhancements. Finally, among all the Pareto optimal solutions of the original multi-objective programming problem, the preferable solution is intelligently selected based on the DEA super efficiency score of all purchasing firms as a decision support tool. The applicability of the proposed approach is illustrated by a real-world case study in automotive industry.

A group decision-making method considering both the group consensus and multiplicative consistency of interval-valued intuitionistic fuzzy preference relations

This paper investigates a group decision-making (GDM) method that considers group consensus and multiplicative consistency of interval-valued intuitionistic fuzzy (IVIF) preference relations (IVIFPRs). First, the mean and variance of IVIF values (IVIFVs) are defined and a ranking method for IVIFVs is proposed considering the risk attitude of the expert. Then, the group consensus is presented by the individual similarity between experts. An iteration algorithm is designed to improve the group consensus. A statistical comparative analysis validates this algorithm. Subsequently, a new multiplicative consistency of IVIFPR is defined based on the multiplicative consistency of interval fuzzy preference relation. Two single-objective programming models are established to extract the most optimistic and pessimistic interval priority weight vectors from an IVIFPR, respectively. In particular, if the feasible domains of these two models are empty, two adjusted programs are constructed to replace the originals. Combining the most optimistic and pessimistic interval priority weights, the IVIF priority weights are generated. Further, expert weights are derived from Markov model and used to derive the collective IVIFPR for generating the IVIF priority weights. Therefore, a new method is proposed to solve the GDM with IVIFPRs. Finally, two cases are analyzed to verify the effectiveness of the proposed method.

Unified Multiobjective Optimization Scheme for Aeroassisted Vehicle Trajectory Planning

In this work, a multiobjective aeroassisted trajectory optimization problem with mission priority constraints is constructed and studied. To effectively embed the priority requirements into the optimization model, a specific transformation technique is applied and the original problem is then transcribed to a single-objective formulation. The resulting single-objective programming model is solved via an evolutionary optimization algorithm. Such a design is unlike most traditional approaches where the nondominated sorting procedure is required to be performed to rank all the objectives. Moreover, in order to enhance the local search ability of the optimization process, a hybrid gradient-based operator is introduced. Simulation results indicate that the proposed design can produce feasible and high-quality flight trajectories. Comparative simulations with other typical methods are also performed, and the results show that the proposed approach can achieve a better performance in terms of satisfying the prespecified priority requirements.

A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees

This paper aims to develop a new hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making (MCGDM) with hesitant fuzzy truth degrees and incomplete criteria weight information. In this method, the types of assessment information on criteria are expressed by Atanassov intuitionistic fuzzy sets, hesitant fuzzy sets, trapezoidal fuzzy numbers, intervals and real numbers, respectively. Firstly, the distances of each alternative to positive ideal solution (PIS) and negative ideal solution (NIS) are calculated. Then the hesitant fuzzy positive ideal group consistency index (HFPGCI) and hesitant fuzzy positive ideal group inconsistency index (HFPGICI), the hesitant fuzzy negative ideal group consistency index (HFNGCI) and hesitant fuzzy negative ideal group inconsistency index (HFNGICI) are defined, respectively. To derive the PIS, NIS and the criteria weights simultaneously, a new four-objective hesitant fuzzy mathematical programming model is constructed by minimizing the HFPGICI and HFNGICI as well as maximizing the HFPGCI and HFNGCI. Using the geometric-mean score functions of hesitant fuzzy sets, the four-objective programming model is transformed to a single objective program to resolve. Subsequently, the relative closeness degrees of alternatives for each decision maker (DM) are obtained and applied to derive the individual ranking order of alternatives. To generate the collective ranking order of alternatives, a multi-objective assignment model is established and converted into a single objective programming model to resolve. Thus, a new hesitant fuzzy mathematical programming method is proposed to solve hybrid MCGDM. Finally, a real example is provided to demonstrate the applicability and validity of the proposed method.

Solving multi-objective portfolio optimization problem using invasive weed optimization

Portfolio optimization is one of the important issues for effective and economic investment. There is plenty of research in the literature addressing this issue. Most of these pieces of research attempt to make the Markowitz’s primary portfolio selection model more realistic or seek to solve the model for obtaining fairly optimum portfolios. In this paper, P/E criterion and Experts’ Recommendations on Market Sectors have been added to the primary Markowitz mean-variance model as two objectives. The P/E ratio is one of the important criteria for investment in the stock market, which captures the current expectations of the market activists about different companies. Experts’ Recommendations for different Market Sectors, on the other hand, captures the experts’ predictions about the future of the stock market. There are many solving methods for the portfolio optimization problem, but almost none of them investigates Invasive Weed Optimization algorithm (IWO). In this research, the proposed multi-objective portfolio selection model has been transformed into a single-objective programming model using fuzzy normalization and uniform design method. Some guidelines are given for parameter setting in the proposed IWO algorithm. The model is then applied to monthly data of top 50 companies of Tehran Stock Exchange Market in 2013. The proposed model is then solved by three methods: (1) the proposed IWO algorithm, (2) the Particle Swarm Optimization algorithm (PSO), and (3) the Reduced Gradient Method (RGM). The non-dominated solutions of these algorithms are compared with each other using Data Envelopment Analysis (DEA). According to the comparisons, it can be concluded that IWO and PSO algorithms have the same performance in most important criteria, but IWO algorithm has better solving time than PSO algorithm and better performance in dominating inefficient solutions, and PSO algorithm has better results in total violation of constraints.

Uncertain and multi-objective programming models for crop planting structure optimization

Crop planting structure optimization is a significant way to increase agricultural economic benefits and improve agricultural water management. The complexities of fluctuating stream conditions, varying economic profits, and uncertainties and errors in estimated modeling parameters, as well as the complexities among economic, social, natural resources and environmental aspects, have led to the necessity of developing optimization models for crop planting structure which consider uncertainty and multi-objectives elements. In this study, three single-objective programming models under uncertainty for crop planting structure optimization were developed, including an interval linear programming model, an inexact fuzzy chance-constrained programming (IFCCP) model and an inexact fuzzy linear programming (IFLP) model. Each of the three models takes grayness into account. Moreover, the IFCCP model considers fuzzy uncertainty of parameters/variables and stochastic characteristics of constraints, while the IFLP model takes into account the fuzzy uncertainty of both constraints and objective functions. To satisfy the sustainable development of crop planting structure planning, a fuzzy-optimizationtheory-based fuzzy linear multi-objective programming model was developed, which is capable of reflecting both uncertainties and multi-objective. In addition, a multiobjective fractional programming model for crop structure optimization was also developed to quantitatively express the multi-objective in one optimization model with the numerator representing maximum economic benefits and the denominator representing minimum crop planting area allocation. These models better reflect actual situations, considering the uncertainties and multi-objectives of crop planting structure optimization systems. The five models developed were then applied to a real case study in Minqin County, north-west China. The advantages, the applicable conditions and the solution methods of each model are expounded. Detailed analysis of results of each model and their comparisons demonstrate the feasibility and applicability of the models developed, therefore decision makers can choose the appropriate model when making decisions.

The design of an activity buffer that minimises project delay

The theory of constraint (TOC) has long been applied to planning project schedules, and critical chain and buffer management are both developed to reduce the impact of future project uncertainties. Several models are proposed for the project activity buffers, including: 1) the cut and paste method proposed by Goldratt, in 1997; 2) the square root error method proposed by Newbold, in 1998; 3) the adaptive procedure with density proposed by Tukel in 2005. This study proposes a multi-objective mathematical programming model that enables project managers to concurrently maximise the on time delivery of project activities. The multi-objective model is consolidated into a single-objective programming model using a fuzzy membership function. Maximising the value of this membership function leads to the maximisation of the probability of on time completion for all project activities. The model is applied to a real case and the result shows that the proposed fuzzy model determines the duration of activities, which ensures that a project can be completed with the highest probability compared to other methods.

Planning of inexact bi-level programming for coupling control of solid waste management and GHG emissions

In this study, based on inexact bi-level programming method, an optimization model (IBLP-GC the contribution of landfill facilities to GHG emissions would remain predominant, while the composting and incineration facilities would be large proportion of system management cost. Further comparative analysis between the inexact bi-level programming and two inexact single-objective programming models indicated that lower system cost would correspond to higher GHG emissions, then leading to a lower resource utilization rate; a potential approach to synchronously mitigate GHG emissions and minimize system cost may be landfilling gas utilization. Compared with the a couple of single-objective models, the proposed IBLP-G&C model can provide compromised schemes under an integrated consideration of environmental impact and economic efficiency under uncertainty.

Credibilistic multi-period portfolio optimization model with bankruptcy control and affine recourse

Avoiding the possibility of bankruptcy during the investment horizon is very important to multi-period portfolio management. This paper considers a multi-period fuzzy portfolio selection problem with bankruptcy control. A multi-period portfolio optimization model imposed by a bankruptcy control constraint in fuzzy environment is proposed on the basis of credibility theory. In the proposed model, a linearly recourse policy is used to reflect the influence of historical predication basis on current portfolio decision. Three optimization objectives, viz., maximizing the terminal wealth and minimizing the cumulative risk and the cumulative uncertainty of the returns of portfolios over the whole investment horizon, are taken into consideration. For solving the proposed model, a fuzzy programming approach is applied to transform it into a single objective programming model. Then, a hybrid particle swarm optimization algorithm is designed for solution. Finally, an empirical example is presented to illustrate the application of the proposed model and solution comparisons are also given to demonstrate the effectiveness of the designed algorithm.

Game-theory Model based on Carrier Sense Multiple Access Protocol in Wireless Network

In order to solve game-theory model problem based on carrier sense multiple access protocol with collision avoidance in wireless network, a game-theory-based general and compatible modeling process is proposed, where the transmission probability of a node in a slot time is regarded as mixed game and network performance parameter M is taken as revenue function of game so as to build M rounds non-cooperative mixed strategy game with N gamers. After performing M rounds game, it will acquire M Nash-equilibria which is not equal to each other, and then these Nash-equilibria are taken as the input of single objective programming model with many constraints so as to obtain compromise equilibria. Finally, a minimum contention window based on compromise equilibria is designed. The throughput and successful transmission rate are analyzed through the simulation, and the simulation experiment results show our proposed modeling process has the more throughputs and the lower drop performance than the existing methods.