multi-objective programming

The selection of human assets for teams significantly impacts the success and profitability of projects. Industrial Revolution 4.0 (4IR) and the post-COVID-19 conditions impose requirements on virtual collaboration, bots-human collaboration, and teleworking projects. The matrix-structured organization faces challenges in this process because it requires weighing various criteria from distinct perspectives. Accordingly, an inappropriate team selection process can result in high costs or failure. Team member competency criteria are identified based on 4IR, in this study. The study also evaluates the theory of generations based on the fact that project teams consist of members from different generations, each with unique characteristics. To this end, a multi-objective allocation model is presented that maximizes competency level while minimizing costs, considering the organizational structure, the 4IR, the post-COVID-19 era condition, and the generation theory. The study attempts to provide decision-makers in multiple-project organizations with a realistic picture to make a trade-off between the cost and competency level of teams. The linear best-worst method (BWM) is used to weigh the competency criteria. Regarding the developed bi-objective model, the Augmented ε- Constraint (AUGMECON) method is utilized to solve the problem. The model is also validated using the Iran Mall project. The findings indicate that younger generations have almost 1.3 more competence scores in virtual communication than older generations. Also, the organization should increase expenditures by 7.1% to reach the highest level of competency.

Population growth has led to more food demand, especially meat. Designing a supply chain, especially a meat one, is complicated due to the uncertainty of food demand and the perishability of meat. To this aim, we develop a multi-objective mixed-integer linear programming model. The developed model contains four echelons, i.e., farms, slaughterhouses, retailers, and customers. The first objective function minimizes the total costs, the second objective minimizes the distribution time, and the third objective minimizes the network's non-resiliency simultaneously. An enhanced version of the augmented ε-constraint method is employed to solve the suggested model, and a set of Pareto–optimal solutions is found. This study also explores the impact of using the robust possibilistic approach in modeling a supply chain network under uncertainty. Numerical experiments demonstrate that the robust optimization approach brings significantly superior outcomes in comparison to the conventional deterministic approach, and the model provides a practical and valuable tool for real-world supply chain challenges.

In line with growing global concerns regarding environmental and social issues, supply chaincorporations are improving their environmental and social performances. The optimal design of a closedloop supply network must conceive various aspects, leading to a multi-objective problem. This study developsa mixed-integer linear programming model to provide an integrated supply network with a particular focuson sustainability. Besides cost efficiency, energy consumption, and job creation are incorporated asadditional objective functions. This article uniquely introduces the training of supply chain employees as partof the developed model to address social responsibility. The Non-Dominated Sorting Genetic Algorithm-II(NSGA-II) and Multiple Objective Particle Swarm Optimization (MOPSO) are employed to solve the multiobjective problem. The numerical examples for cost and energy values are based on real data. The resultsdemonstrate the significant effect of returned product recovery on cost reduction in the network and changesin energy consumption at different levels. NSGA-II and MOPSO yield a set of optimal solutions that increasethe flexibility of decision-makers. Indeed, a set of Pareto solutions reveals a conflict between the objectivefunctions and allows the network to be highly effective in decision-making under different conditions andpolicies.

In this paper, we present a suitable extension of the approach described by Pieume et al. (2011) for solving multi-follower multi-objective linear bilevel programming problems. This problem is a special case of multi-follower bilevel linear programming problems, where each decision maker possesses several objective functions that in some cases, conflict with one another. We construct a multi-objective linear programming problem. Furthermore, we show that the multi-follower multi-objective linear bilevel programming problem can be reduced to optimize the top-level multi-objective linear programming problem over an efficient set. The proposed approach uses a Pareto-filter scheme, and obtains an approximate discrete representation efficient set unlike the fuzzy approaches that only obtain one efficient solution.  Ultimately, a numerical example is presented to illustrate the efficiency of the proposed approach.

This study proposes a novel sustainable multi-objective agri-food supply chain in Mushroom industry due to the lack of economic, environmental, and social aspects that the prior studies neglected. The proposed study examines a four-echelon model including suppliers, intermediate manufacturers, final manufacturers and markets (plus secondary market). The model is also validated to provide insights into a relevant industry. The results indicated that investment in the oyster mushroom would lead to economic and social improvements. Moreover, investing in the button mushroom was observed to improve all three sustainability aspects. In the case of investing in the oyster and button mushroom, increasing the capacity of compost factories and sales price would lead to different results. Furthermore, the profitability of the supply chain was found to rise when waste is sold in the secondary market. Therefore, managers can adopt different strategies under different circumstances based on their priorities to raise supply chain profitability.

So far, numerous studies have been developed to evaluate the performance of “Decision-Making Units (DMUs)” through “Data Envelopment Analysis (DEA)” and “Network Data Envelopment Analysis (NDEA)” models in different places, but most of these studies have measured the performance of DMUs by efficiency criteria. The productivity is considered as a key factor in the success and development of DMUs and its evaluation is more comprehensive than efficiency evaluation. Recently, studies have been developed to evaluate the productivity of DMUs through the mentioned models but firstly, the number of these studies especially in NDEA models is scarce, and secondly, productivity in these studies is often evaluated through the “productivity indexes”. These indexes require at least two time periods and also the two important elements of efficiency and effectiveness in these studies are not significantly evident. So, the purpose of this study is to develop a new approach in the NDEA models using “Multi-Objective Programming (MOP)” method in order to measure productivity of DMUs through efficiency and effectiveness “simultaneously, in one stage, in a period, and interdependently”. “Simultaneous and single-stage” study provides the advantage of sensitivity analysis in the model. One case study demonstrates application of the proposed approach in the branches of a Bank. Using proposed approach revealed that it is possible for a branch to be efficient by considering its subdivisions separately but not be efficient by considering the conjunction between its subdivisions. In addition, a branch may be efficient by considering the conjunction between its subdivisions but not be productive. Efficient branches are not necessarily productive, but productive branches are also efficient.

Sustainable supply chain networks have attracted considerable attention in recent years as a means of dealing with a broad range of environmental and social issues. This paper reports a multi-objective mixed-integer linear programming (MILP) model for use in the design of a sustainable closed loop supply chain network under uncertain conditions. The proposed model aims to minimize total cost, optimize environmental impacts of establishment of facilities, processing and transportation between each level as well as social impacts including customer satisfaction. Due to changes in business environment the uncertainty existed in the research problem, in this paper the chance constrained fuzzy programming approach applied to cope with uncertainties in parameter of the proposed model. Then the proposed multi-objective model solves as single-objective model using LP-metric method.

This paper presents a novel formulation of the integrated bi-objective problem of project selection and scheduling. The first objective is to minimize the aggregated risk by evaluating the expected value of schedule delay and the second objective is to maximize the achieved benefit. To evaluate the expected aggregated impacts of risks, an objective function based on the Bayesian Networks is proposed. In the extant mathematical models of the joint problem of project selection and scheduling, projects are selected and scheduled without considering the risk network of the projects indicating the individual and interaction effects of risks impressing the duration of the activities. To solve the model, two solution approaches have been developed, one exact and one metaheuristic approach. Goal Programming method is used to optimally select and schedule projects. Since the problem is NP hard, an algorithm, named GPGA, which combines Goal Programming method and Genetic Algorithm is proposed. Finally, the efficiency of the proposed algorithm is assessed not only based on small size instances but also by generating and testing representative datasets of larger instances. The results of the computational experiments indicate that it has acceptable performance to handle large size and more realistic problems.

In this paper, we introduce a two stages model for allocation of injuries and medical supplies to medical centers. In the first stage a multi objective mathematical model allocates injured people from the affected neighborhood to medical centers. In the second stage a single objective linear model allocates medical supplies from the supply points to medical centers. The first stage’s objective is simultaneously minimizing the total relief time and costs and maximizing the level of matching the type of injury with the specialized field of the medical centers those injuries are sent. The second stage’s objective is to minimize the costs of allocating medical supplies to medical centers. An integrated model that combines the two previous models is presented and comparing the results with the two stages model. Proposed models are applied to one of the districts of Tehran to demonstrate their effectiveness. The case study includes two affected neighborhood and four medical centers and three supply points. ϵ-constraint method is used to produce the Pareto optimal solutions in a MOMP.

The purpose of the current study is to select suppliers and determine their order allocation in a way that the performance of the sustainability of the supply process gets optimized on the whole. In this research, after reviewing the literature and investigating the supply chain of the case study (Iran Khodro’s supply chain) through Delphi method, a set of evaluation criteria related to the performance of the suppliers in economical, social and environmental terms was identified. In the next stage, by using the identified criteria, the multi-objective mathematical integer programming was presented to solve the problems of suppliers’ selection and order allocation. The suggested mathematical programming in this research is designed to be multi-product, single-period and multiple sourcing. Fuzzy TOPSIS method is applied to calculate the qualitative parameters that are used in the suggested mathematical programming. Ultimately, the mathematical model suggested in the research will be solved by two methods, i.e. Epsilon Constraint Method and Weighted Sum Method. Moreover, the total value of the sustainable purchasing (TVSP) will be calculated for both cases. Comparing these two methods indicates that in this research the results of weighted sum method are better than those epsilon constraint method.

In this research, a hierarchical location-allocation problem is modeled in a queue framework. The queue model is considered as M/M/1/k, in which system capacity is finite, equals to k. This is the main contribution of the current research. Customer's enters to the system in order to find the service according to a Poisson. In this problem, the hierarchical location-allocation model is considered in two levels. Also, the model has two objective functions: maximizing the total number of demand coverage and minimizing the waiting time of customers in queues to receive services. After modeling and verifying the validity of the presented model, it is solved using NSGA II and MOPSO meta-heuristics.

This paper proposes an innovative procedure of finding efficient facility location–allocation (FLA) schemes, integrating data envelopment analysis (DEA) and a multi-objective programming (MOP) model methodology. FLA decisions provide a basic foundation for designing efficient supply chain network in many practical applications. The procedure proposed in this paper would be applied to the FLA problems where various conflicting performance measures are considered. The procedure requires that conflicting performance measures classified as inputs to be minimized, or outputs to be maximized. Solving an MOP problem generates diverse alternative FLA schemes along with multi-objective values. DEA evaluates these schemes to generate a relative efficiency score for each scheme. Then, using stratification DEA, all of these FLA schemes are stratified into several levels, from the most efficient to the most inefficient levels. A case study is presented to demonstrate the effectiveness and efficiency of the proposed integrating method. We observe that the combined approach in this paper performs well and would provide many insights to academians as well as practitioners and researchers.

Data envelopment analysis (DEA) is a nonparametric approach to estimate relative efficiency of Decision Making Units (DMUs). DEA is one of the best quantitative approaches and balanced scorecard (BSC) is one of the best qualitative methods to measure efficiency of an organization. Since simultaneous evaluation of network performance of the quad areas of BSC model is considered as a necessity and separate use of DEA and BSC is not effective and leads to miscalculation of performance, integrated DEA-BSC model is applied. Regarding to multi-objective nature of the proposed model, two techniques including goal programming and weighted average method are used to solve such problems. At the end of the study, based on data relating to indexes of quad areas of BSC model, the results of the mentioned methods are compared. Besides assessing validation of the proposed model, the overall efficiency and each of the different stages of BSC are obtained. So that, finding a model for decision making units in various stages of BSC is the innovation of this research study.

In this study, the response phase of the management of natural disasters is investigated. One of the important issues in this phase is determining the distribution areas and timely distribution of relief to affected areas in which transportation routing is of a critical matter. In the event of disasters, especially flood and earthquake, terrestrial transportation is not that much easy due to the damage to many infrastructures. For this reason, we propose that delivering relief from the distribution areas to disaster stricken places should be done simultaneously by terrestrial as well as aerial transportation modes to increase route reliability and reduce travel time. In this study, for relief allocation after earthquake, we offer a mixed-integer nonlinear open location-routing model in uncertainty condition. This model includes several contradictory objectives and variety of factors such as travel time, total costs, and reliability. In order to solve this model, a hybrid solution by combining robust optimization and fuzzy multi-objective programming has been used. The performance and effectiveness of the offered model and solution approach has been investigated through a case study on the earthquake in East Azerbaijan, Iran. Our computational results show the solution we have offered for real problems has been effective.