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.

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.

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.

In this paper, we studied fuzzy linear fractional programming (FLFP) problems with trapezoidal fuzzy numbers where the objective functions are fuzzy numbers and the constraints are real numbers. In this study, in order to obtain the fuzzy optimal solution with unrestricted variables and parameters, a new efficient method for FLFP problem has been proposed. These proposed methods are based on crisp linear fractional programming and newly transformation technique is also used. A computational procedure has been presented to obtain an optimal solution. To show the efficiency of our proposed method a real life example has been illustrated.

Governments and customers are forcing the paper manufacturers to become more sustainable. Accordingly, there still exists a gap in the quantitative modeling of these issues. In this paper, this gap is covered through simultaneously considering economical, environmental and social impacts in the paper closed-loop supply chain network design. The proposed multi-objective, multi-echelon, multi-product and single-period model is composed of suppliers, plants, regional wholesalers, retailers, customer zones, collection sites, centralized collection points, recycling facilities, energy recovery and disposal centers.The objectives considered are minimization of total cost; environmental benefit through maximizing coverage of collected waste paper by opened centralized collection centers; and maximization of the social impact of the network in a way that would prefer the location of facilities in the less populated regions.The proposed model is applied to an illustrative example designed utilizing real data of the paper industry in East Azerbaijan of Iran and interactive fuzzy goal programming approach is used to solve the developed model. Sensitivity analysis of the proposed model is also performed by considering key parameters.

This paper presents a bi-objective capacitated hub arc location problem with single assignment for designing a metro network with an elastic demand. In the literature, it is widely supposed that the network created with the hub nodes is complete. In this paper, this assumption is relaxed. Moreover, in most hub location problems, the demand is assumed to be static and independent of the location of hubs. However, in real life problems, especially for locating a metro hub, the demand is dependent on the utility that is proposed by each hub. By considering the elasticity of demand, the complexity of solving the problem increases. The presented model also has the ability to compute the number of trains between each pair of two hubs. The objectives of this model are to maximize the benefits of transportation and establishing the hub facilities while minimizing the total transportation time. Furthermore, the bi-objective model is converted into a single objective one by the TH method. The significance of applicability of the developed model is demonstrated by a number of numerical experiments and some sensitivity analyses on the data inspired by the Qom monorail project. Finally, the conclusion is provided.

The fast changing and dynamic global business environment require companies to plan their entire supply chain from the raw material supplier to the end customer. In this paper, we design an integrated supply chain including multiple suppliers, multiple factories, multiple distributors, multiple customers, multiple products, and multiple transportation alternatives. A new multi-objective mixed-integer nonlinear programming model is proposed to deal with this facility location-allocation problem. It considers two conflicting objectives simultaneously, and then the problem is transformed into a multi-objective linear one. The first objective function aims to minimize total losses of the supply chain including raw material purchasing costs, transportation costs and establishment costs of factories and distributions. The second objective function is to minimize the sum deterioration rate of end products and raw materials incurred by transportation alternatives. Finally, the proposed model is solved as a single-objective, mixed-integer, programming model applying the Global Criteria Method. We test their model with numerical example and the results indicate that the proposed model can provide a promising approach to fulfill customer demand and design an efficient supply chain.

Delivering perishable products to customers as soon as possible and with the minimum cost has been always a challenge for producers and has been emphasized over recent years due to the global market becoming more competitive. In this paper a multi-objective mix integer non-linear programming model is proposed to maximize both profits of a distributer and the total freshness of the several products to be delivered to customers with respect to their demands and with consideration of different soft time windows for each customer, heterogeneous distribution fleet and customer selection option for the distributer. The proposed model is solved with TH method. The two genetic algorithm and simulated annealing algorithm are used to solve large-sized problems. Finally, their results are compared to each other when the optimization software becomes unable of solution representation.