Multi-choice Goal Programming Research Articles

A lateral resupply blood supply chain network design under uncertainties

The vibrant subject of blood banking and blood distribution is addressed where lateral resupply of blood products is allowed. In this paper, we studied a blood supply chain network design consisting of four conventional levels each of which corresponding to one entity in the real world: donors, blood collection facilities, blood centers, and hospitals. The blood supply chain network considered two important properties: ABO-Rh factors and shelf lives of blood products. Moreover, an integrated inventory system for sharing hospitals’ inventory levels is considered to investigate the two performance indicators of the network in terms of cross-matching and outdated units. This type of inventory system is known as “Lateral Resupply” permitting a hospital to satisfy its demand by the other hospitals’ inventories in the absence of the required product at the blood center and its excess in any hospital. The proposed mixed-integer mathematical programming model entails three objectives referring to the three underlying concepts of sustainability, additionally, to cope with uncertainties and multi objectiveness, a scenario-based optimization approach and revised multi-choice goal programming technique were employed, respectively. Finally, the results confirmed that the lateral resupply virtue improved the performance indicators.

An integrated FAHP-MCGP approach to project selection and resource allocation in risk-based internal audit planning: A case study

Effective audit planning could drive internal audit function to be the catalyst for company development by launching audit projects that protect and create organization value. In the risk-based internal audit planning process, once risk assessment is completed, audit projects should be selected and resources are allocated accordingly. However, an optimal annual audit plan cannot be realized based on subjective selection of projects and manual distribution of available hours merely. In the planning process, the risk level that can be mitigated by performing individual audit project is vague and there is also uncertainty with the time to be spent on each project. By developing a structured three-phase framework for risk-based audit planning, this paper proposes a novel approach that combines fuzzy analytic hierarchy process (FAHP) and multi-choice goal programming (MCGP) to fill the gap between prioritization and allocation technique. An exploratory estimation of risk reduction factor for each candidate project is performed using FAHP, and then MCGP assists in making a more informed choice so as to minimize the total deviations from predefined goals concerning the risk coverage, flexibility and optimal mix of project portfolio. A real case study of annual audit plan for a global internal audit team is presented to illustrate how the proposed FAHP-MCGP approach could be applied in practice. The results of this research indicate that the proposed FAHP-MCGP approach is a useful tool for selecting potential projects and allocating staff time during risk-based internal audit panning and has substantial practical application.

A robust optimization model of the field hospitals in the sustainable blood supply chain in crisis logistics

Crisis management is one of the significant challenges when a disaster occurs. Post disaster operations mainly focus on medical treatments. One of the general requirements of medical treatments of field hospitals in disaster is blood transfusion. This way, configuring a blood transfusion network to handle the appropriate assignments and distribution is proved to influence the type, number and severity of recent crises. Therefore, obtaining effective solutions, containing determining the optimal location of facilities of field hospitals, identifying the optimal capacity of facilities and transportation, blood transfusion routes to reduce costs and injustices in this area in times of crisis is essential. Hence, in this study, we proposed a model, intend for allocating blood types and regarding the lifetime of blood to tackle with field hospitals in the disaster sites. Furthermore, the coverage of the demand for blood types for the establishment of field hospitals and the balanced distribution of blood between these hospitals from the blood collection level to the establishment of field hospitals with optimal routing of blood transfusion at the lowest cost is considered. The proposed model for the crisis response management phase is modelled applying a multi-objective mathematical model under uncertain conditions. To cope with the uncertain data arisen in the disaster condition, the robust optimization approach is applied. Then, to solve the proposed model, a hybrid method based on Genetic Algorithm and Multi-Choice Goal Programming (GAMCGP) under uncertainty is developed. In addition, the proposed model is successfully applied to a real- world blood supply chain in Mazandaran, northern part of Iran, and the results validate the performance of the proposed model. It also proves that the suggested model can be considered as a new approach for blood supply chain tactical management in the crisis logistics.

A multi-objective distributionally robust model for sustainable last mile relief network design problem

Natural disasters not only inflict massive life and economic losses but also result in psychological damage to survivors, at times even causing social unrest. It is necessary to design a sustainable last mile relief network for distributing relief supplies regarding social factors, disaster relief efficiency as well as the economic cost of three perspectives in terms of sustainability. We establish a multi-objective distributionally robust optimization model for a sustainable last mile relief network problem that maximizes the equitable distribution of relief supplies and simultaneously minimizes the transportation time and operation cost. Under the partial probability information of uncertainties, such as the disaster situation, transportation time, freight, road capacity, and demand, we characterize the uncertain variables in an ambiguity set incorporating the bounds, means and the mean absolute deviations. Then, the bounds on the objective values and the safe approximations of the chance constraints are deduced under the ambiguity sets. Based on a revised multi-choice goal programming approach, we obtain a computationally tractable framework of the multi-objective model. To verify the effectiveness of the model and methods, a case study of the Banten tsunami is illustrated. The results demonstrate our proposed model can obtain a trade-off between the equitability, timeliness and economics for relief distribution in a relief network.

A bi-objective supplier location, supplier selection and order allocation problem with green constraints: scenario-based approach

In this study, There is a mixed-integer nonlinear program (MINLP) for a two-echelon supply chain that focuses on supplier location, supplier selection and order allocation with green constraints. This bi-objective model is designed and modeled with the aim of coordinating inventory and transportation among suppliers and warehouses and tries to simultaneously meet the targets of minimizing total costs and carbon dioxide emissions of polluting gas in transportation. Since some of the important parameters in this model are considered uncertain, the scenario-based analysis is proposed to deal with uncertainty. Thirty numerical examples with different values and various sizes are solved by applying two methods of MODM, LP metrics, and Multi-choice goal programming with utility functions (MCGP-U) and their results are compared with one of the soft computing methods, Genetic algorithm. TOPSIS, Coefficient of Variation (CV) and One-way analysis of variance (ANOVA) methods are employed for the comprehensive comparison of these numerical examples. Finally, the sensitivity analysis method and Tornado diagram are applied to analyze the effect of variations of the model’s inputs on the results of the model.

A robust bi-objective mathematical model for disaster rescue units allocation and scheduling with learning effect

This paper proposes a novel bi-objective mixed-integer linear programming (MILP) model for allocating and scheduling disaster rescue units considering the learning effect. When a natural phenomenon (e.g., earthquake or flood) occurs, the presented decision support model is expected to help decision-makers of emergency relief centers to provide efficient planning for rescue units to minimize the total weighted completion time of rescue operations, as well as the total delay in rescue operations. The problem has some features in common with unrelated parallel machine scheduling (UPMS) problem and traveling salesman problem (TSP). To deal with the inherent uncertainty and bi-objective nature of the problem, an uncertainty-set based robust optimization technique and multi-choice goal programming (MCGP) with utility functions are applied. To demonstrate the applicability of the proposed model, a real case study in Mazandaran province in Iran is presented. The computational results confirm the high complexity of the problem and the significant impacts of the uncertainty on the solution. Moreover, the analytical results provide useful insights to decision-makers for disastrous situations.

Reverse logistics network design for medical waste management in the epidemic outbreak of the novel coronavirus (COVID-19)

The recent pandemic triggered by the outbreak of the novel coronavirus boosted the demand for medical services and protective equipment, causing the generation rate of infectious medical waste (IMW) to increase rapidly. Designing an efficient and reliable IMW reverse logistics network in this situation can help to control the spread of the virus. Studies on this issue are limited, and minimization of costs and the risks associated with the operations of this network consisting of different types of medical waste generation centers (MWGC) are rarely considered. In this research, a linear programming model with three objective functions is developed to minimize the total costs, the risk associated with the transportation and treatment of IMW, and the maximum amount of uncollected waste in MWGCs. Also, multiple functions that calculate the amount of generated waste according to the parameters of the current epidemic outbreak are proposed. Revised Multi-Choice Goal Programming method is employed to solve the multi-objective model, and a real case study from Iran is examined to illustrate the validation of the proposed model. The final results show that the model can create a balance between three considered objectives by determining the flow between centers, deciding to install two new temporary treatment centers, and allowing the network to only have uncollected waste in the first two periods in some MWGCs. Also, managerial insights for health organization authorities extracted from the final results and sensitivity analyses are presented for adequately handling the IMW network.

A fuzzy goal programming with interval target model and its application to the decision problem of renewable energy planning

Optimizing sustainable renewable energy portfolios is one of the most complicated decision making problems in energy policy planning. This process involves meeting the decision maker’s preferences, which can be uncertain, while considering several conflicting criteria, such as environmental, societal, and economic impact. In this paper, rather than using existing techniques, a novel multi-objective decision making (MODM) model, named fuzzy goal programming with interval target (FGP-IT), is proposed and constructed based on recent developments and concepts in fuzzy goal programming (FGP) and revised multi-choice goal programming (RMCGP). The model deals with decision making problems involving a high level of uncertainty by offering decision makers a more flexible way to formulate and express their preferences, namely, fuzzy interval target goals. The proposed method is used to optimize a hypothetical sustainable wind energy portfolio in Algeria. The results show that the FGP-IT model is capable of assisting decision makers with uncertain preferences in making such complicated decisions.

Supply chain master planning considering material-financial flows

In this study, tactical decisions considering the material and financial flows in a supply chain have been made. To achieve these aims and some effective solutions, a multi-objective mathematical model proposed for an integrated supply chain master planning problem. The multi-product, multi-period and capacitated supply chain network has three objective functions. Two first objective functions are maximizing the net present value of manufacturing centers and suppliers’ cash flow, and the third one minimizes the market price of the final product. Besides we considered the market price as a key variable in the model and investigate its effects. Then, improved multi-choice goal programming is used to transform the multi-objective model to its single-objective one. To find out the appropriateness of the proposed model, the results of an industrial example are illustrated, and sensitivity analyses to evaluate the results are provided to obtain better insight and access to different aspects of the problem.

A hybrid genetic algorithm for integrating virtual cellular manufacturing with supply chain management considering new product development

The importance of issues such as responding to customers’ demand, reducing production costs and better flow of materials is clear for industry owners. Manufacturers need to be able to produce products with a lower cost and higher quality in the shortest possible time to deliver the products on time to customers. Also, production systems should be able to respond quickly to changes in product design and demand without significant investment. Hence, one of the ways for increasing productivity and having a strong presence in the competitive market is to integrate virtual cellular manufacturing (VCM) into the supply chain (SC) by taking into account the new product development concept. In this study, a multi-objective mathematical model is presented to the simultaneous integration of VCM with the SC and new product development. Given that the proposed model of this study is multi-objective, a multi-choice goal programming with a utility function (MCGP-U) has been used to solve the research problem. Also, the MCGP-U is implemented in a new hybrid genetic algorithm (GA), which is the integration of a GA and a variable neighborhood search (VNS), to tackle large-scale instances. Finally, a comparison is done between the results of MCGP-U and MCGP-GA-VNS.

Optimizing sustainable and renewable energy portfolios using a fuzzy interval goal programming approach

Determining the most sustainable renewable energy (RE) source portfolio that meets decision-maker preferences is a complicated and uncertain multi-criteria decision-making (MCDM) problem. The RE selection process involves meeting decision-makers’ (DMs) preferences wherein several conflicting criteria are present, such as environmental, societal, and economic. Fuzzy goal programming (FGP) is one of the most well-known techniques for dealing with uncertainty existing in MCDM problems. However, conventional FGP techniques suppose only one single coefficient (or parameter) for each decision variable. This paper proposes a novel multi-objective decision-making model called fuzzy interval goal programming (FIGP) to release the restrictions of FGP with single-coefficient modeling. The proposed model can formulate an interval coefficient for each decision variable. To formulate such a model, this study adopts the concept of multi-choice aspiration levels (MCALs) from the revised multi-choice goal programming (RMCGP) technique. Specifically, the integrated model considers various types of fuzzy goals in real-world problems and offers DMs more flexibility to express and formulate their preferences in terms of fuzzy interval goals. The proposed method is illustrated by selecting the optimal RE portfolio for electricity generation in Italy. The relevant renewables are biomass, solar photovoltaic (PV), tidal currents, and wind energy. An empirical analysis shows that the proposed methodology is capable of assisting the DMs in ascertaining the optimal portfolio of RE under a high level of uncertainty and in imprecise environments.

Sustainable feedstocks selection and renewable products allocation: A new hybrid adaptive utility-based consensus model

Nowadays, preferred compromise response of renewable energies' demands regarding the candidate sustainable feedstocks is a crucial issue for market change management. Thus, selecting the most suitable sustainable feedstock is a key factor for optimum renewable products allocation problem. To address the issue, this study proposes a hybrid adaptive framework based on consensus evaluation approach, weighting and ranking procedure, and preferred demand assignment under dynamic hesitant fuzzy sets. In this respect, the consensus evaluation approach is tailored regarding the direct and indirect feedback mechanisms to enhance the quality evaluation of candidate sustainable feedstocks under assessment criteria. Thereby, the weight of each criterion is determined based on the developed dynamic hesitant fuzzy entropy method and the candidate sustainable feedstocks are ranked with respect to developed dynamic hesitant fuzzy positive and negative ideal solutions. Then, a revised multi-choice goal programming model is extended regarding the dynamic hesitant fuzzy closeness indexes to attend to preferred compromise response of demand centers by optimum renewable products allocation. Meanwhile, the presented hybrid adaptive framework is implemented to a real case study to represent the applicability and efficiency of the proposed approach. Furthermore, a comparative analysis is provided by defining eight comparison indexes to compare the obtained results with two recent studies in relevant literature for representing the validation and verification of the proposed approach. The comparative analysis shows that the proposed approach versus the two other approaches has merits such as modeling of uncertainty, experts' weights, adaptive structure, unanimous agreement-based approach, and last aggregation framework. Finally, a sensitivity analysis is represented to show the sensitiveness and robustness of the obtained results from changing the criteria weights, goals values, and consensus elimination. Thereby, the sensitivity analysis indicates that the obtained ranking results are sensitive to sustainability criteria unlike the technical criterion.

Customer relationship management and new product development in designing a robust supply chain

New product development is a basic requirement for any company to survive in the competitive market. Most of the organizations realized that relying solely on the traditional competitive levers, such as increasing the quality, reducing costs, and distinguished provision of goods and services is not enough anymore. In addition to the aforementioned competitive advantages, a company needs to introduce new products and out-phase the old ones at the right time. In this research, the design of a supply chain network considering new product development is investigated. Here, the notion of customer relationship management is incorporated into the proposed mathematical model. Moreover, product demand that is inherently uncertain in the real situations is embedded in the proposed robust model. Objectives of new products development, and customer satisfaction along with maximization of the profit is considered in the model. Moreover, an improved multi-choice goal programming method is implemented to solve the model. Finally, the model performance is evaluated for a real-world case.

Weighted-additive fuzzy multi-choice goal programming (WA-FMCGP) for supporting renewable energy site selection decisions

This paper proposes a novel weighted-additive fuzzy multi-choice goal programming (WA-FMCGP) model for the imprecise decision context wherein several conflicting goals are present but each goal has multiple-choice aspiration levels (MCALs) and, around them, the fuzzinesses are expressed in terms of membership functions (MFs). The main contribution of this model is its use of an objective function that minimises the weighted-additive summation of the normalised deviations; thus, the model can adopt any minimisation process from any goal programming (GP) variant. The advantages of this FGP-MCGP (fuzzy GP – multi-choice GP) model are shown by using it to solve a numerical example from F-MODM (fuzzy MODM) literature and comparing the results with those of a recent FP-MCGP (fuzzy programming – multi-choice GP) study. The application of the model is also verified using real data (i.e., it can model and support renewable energy site selection (RESS) where the decision context is imprecise). As WA-FMCGP is largely a MODM model, through its application, this study also provides a supplementary method in contrast to the multi-attribute decision-making (MADM) model applications used thus far for RESS.

Multi-objective flexibility-complexity trade-off problem in batch production systems using fuzzy goal programming

Several factors change the flexibility and the complexity of production systems. The flexibility of the production system means to meet the changing needs of the customers. As flexibility increases the complexity also increases. In this paper, a multi-objective linear programming is proposed to model the trade-off of the complexity and flexibility of a batch production system (BPS). Strategic, tactical and operational decision variables have been considered. Seven objective functions of the proposed model are assumed as flexibility and complexity. Sixteen tactical decision variables are defined to determine the level of the dimensions of flexibilities and complexities. Thirty-four operational decision variables are defined to tune the shop-floor operations. Several sets of constraints considering aspects of flexibility and complexity as well as the conditions of batch production systems have been considered. As the achievement to the objective functions is not possible simultaneously, and there is no unique and concise relation between these objective functions in a typical batch production system so, a fuzzy goal programming (FGP) approach is proposed to solve the model. Moreover, goal programming (GP), Fuzzy GP, multi-choice goal programming (MCGP) and fuzzy MCGP are proposed and used to compare the performance of solution procedures. The superior solution approach among GP, MCGP, FGP, and FMCGP is FMCGP which concurrently considers several aspiration levels for objective functions, maximization of the achievement level of objective functions, and satisfying uncertain preference of fuzzy objectives. An evolutionary algorithm, called non-dominated sorting genetic algorithm (NSGA-II) and a random weighted version of FMCGP are customized to regenerate several non-dominated designs for flexibility-complexity trade-off problem in BPS. The results are promising and the proposed model is capable to set the strategic, tactical and operational variables of a BPS.

A robust bi-objective programming approach to environmental closed-loop supply chain network design under uncertainty

Imposition of strict environmental protection acts and the imperative need of the best possible allocation of resources have given birth to the concept of low carbon logistics. Environmental laws force the manufacturers to extend their existing supply chains to form a closed-loop supply chain (CLSC) through the setup of an efficient recovery system. In this paper, a multi-objective robust optimisation model is proposed for the design of CLSC network under uncertainty. First, a deterministic bi-objective mixed integer linear programming (BOMILP) model is developed for designing a CLSC network. Then, the robust counterpart of the proposed BOMILP is presented to cope with the real-world uncertainty. The first objective aims to maximise the total profit generated in the CLSC network and the second objective minimises the environmental pollution of the CLSC network. The proposed bi-objective model is solved using a multi-choice goal programming (MCGP) approach.

Robust Design of Dynamic Cell Formation Problem Considering the Workers Interest

To enhance agility and quick responding to customers' demand, manufacturing processes are rearrenged according to different systems. The efficient execution of a manufacturing system depends on various factors. Among them, cell design and human issue are the pivotal ones. The proposed model designs cellular manufacturing systems using three objective functions from three different perspectives, to reflect a more realistic picture of the cell formation problem. This paper presents a model with the goals of maximizing the total value of grouping efficacy and minimizing the total costs and total non-interest workers in cells in a dynamic environment for several consecutive periods. The main idea of the proposed model is enhancing cell efficiency through an assigning the group of workers who have a mutual interest in working with each other. For solving the current model, the revised multi-choice goal programming method has been employed. Finally, computational results and sensitivity analysis are discussed.

Topology design of remote patient monitoring system concerning qualitative and quantitative issues

Piecewise linear functions have been used to model and solve non-linear problems in science, social science, and technology fields since the 1950′s. Multi-choice goal programming (MCGP) has been widely used to solve multiple objective decision-making (MODM) problems in which each goal mapping with multiple aspiration levels is allowed, expanding the original feasible region to obtain better solutions in the MODM problems. This paper integrates the efficient S-shaped penalty method, arbitrary piecewise linear utility functions, trapezoidal utility functions, and MCGP to solve a topology design problem in a remote patient monitoring system (RPMS) by providing universal senior citizen coverage in which quantitative (e.g., patient satisfaction-related cost) and qualitative (e.g., satisfaction) issues are considered simultaneously. In addition, some novel utility functions such as the force utility function, indicator utility function, and arbitrary utility function are proposed to improve the usefulness of MCGP in the field of management science. These proposed utility functions can be easily used to model qualitative issues in real-world problems. A topology design problem for an RPMS is demonstrated to justify the feasibility, usefulness, and compatibility of the proposed methods. Further, sensitivity analysis and managerial implications are provided using an RPMS in Taiwan.

Order allocation and procurement transport planning in apparel supply chain: A utility-based possibilistic-flexible programming approach

The purpose of this paper is to study the integrated decisions of the physical supply channel on the global scale including the supplier selection, order allocation, and transportation planning under uncertainty. In detail, this study addresses the supply decision-making problem in a multi-source, multi-product, and multi-mode transportation in accordance with the price discounts. To this end, a multi-objective mixed integer linear programming model is developed to jointly determine the best suppliers, and purchasing quantities along with the number and type of transportation modes. Three important objective functions, i.e., total logistics costs, total late deliveries and total value of purchasing are optimized in our proposed mathematical model. Then, a fuzzy multi-choice goal programming model with the utility function is presented to solve the multi-objective formulation. A novel flexible-possibilistic programming approach is proposed to cope with the epistemic uncertainty and the flexibility of constraints based on the expected value and chance constraint programming concept. Finally, a numerical study in the apparel supply chain is carried out to show the model usefulness and the solution algorithm effectiveness.

Resilient supplier selection in logistics 4.0 with heterogeneous information

Supplier selection problem has gained extensive attention in the prior studies. However, research based on Fuzzy Multi-Attribute Decision Making (F-MADM) approach in ranking resilient suppliers in logistic 4.0 is still in its infancy. Traditional MADM approach fails to address the resilient supplier selection problem in logistic 4.0 primarily because of the large amount of data concerning some attributes that are quantitative, yet difficult to process while making decisions. Besides, some qualitative attributes prevalent in logistic 4.0 entail imprecise perceptual or judgmental decision relevant information, and are substantially different than those considered in traditional suppler selection problems. This study develops a Decision Support System (DSS) that will help the decision maker to incorporate and process such imprecise heterogeneous data in a unified framework to rank a set of resilient suppliers in the logistic 4.0 environment. The proposed framework induces a triangular fuzzy number from large-scale temporal data using probability-possibility consistency principle. Large number of non-temporal data presented graphically are computed by extracting granular information that are imprecise in nature. Fuzzy linguistic variables are used to map the qualitative attributes. Finally, fuzzy based TOPSIS method is adopted to generate the ranking score of alternative suppliers. These ranking scores are used as input in a Multi-Choice Goal Programming (MCGP) model to determine optimal order allocation for respective suppliers. Finally, a sensitivity analysis assesses how the Supplier's Cost versus Resilience Index (SCRI) changes when differential priorities are set for respective cost and resilience attributes.