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The multiple objective decision making problem arises when two or more non‐comparable objective functions are to be simultaneously optimised. There is a definite trend towards utilising interactive techniques for solving the multiple objective decision making problem. Interactive techniques allow the involvement of the DM throughout the decision process. In this paper we first provide a brief overview of multiple objective decision making, and then give a survey of literature dealing with interactive multiple objective decision making from 1965 to 1988.

Modelling of the multiproject cash flow decisions in a contracting firm facilitates optimal resource utilization, financial planning, profit forecasting and enables the inclusion of cash‐flow liquidity in forecasting. However, a great challenge for contracting firm to manage his multiproject cash flow when large and multiple construction projects are involved (manipulate large amount of resources, e.g. labour, plant, material, cost, etc.). In such cases, the complexity of the problem, hence the constraints involved, renders most existing regular optimization techniques computationally intractable within reasonable time frames. This limit inhibits the ability of contracting firms to complete construction projects at maximum efficiency through efficient utilization of resources among projects. Recently, artificial neural networks have demonstrated its strength in solving many optimization problems efficiently. In this regard a novel recurrent‐neural‐network model that integrates multi‐objective linear programming and neural network (MOLPNN) techniques has been developed. The model was applied to a relatively large contracting company running 10 projects concurrently in Hong Kong. The case study verified the feasibility and applicability of the MOLPNN to the defined problem. A comparison undertaken of two optimal schedules (i.e. risk‐avoiding scheme A and risk‐seeking scheme B) of cash flow based on the decision maker's preference is described in this paper.

Distribution network design involves a set of strategic decisions in supply chains because of their long-term impacts on the total logistics cost and environment. To incorporate a trade-off between financial and environmental aspects of these decisions, this paper aims to determine an optimal location, among candidate locations, of a new logistics center, its capacity, as well as optimal network flows for an existing distribution network, while concurrently minimizing the total logistics cost and gas emission. In addition, uncertainty in transportation and warehousing costs are considered.

The problem is formulated as a fuzzy multiobjective mathematical model. The effectiveness of this model is demonstrated using an industrial case study. The problem instance is a four-echelon distribution network with 22 products and a planning horizon of 20 periods. The model is solved by using the min–max and augmented ε-constraint methods with CPLEX as the solver. In addition to illustrating model’s applicability, the effect of choosing a new warehouse in the model is investigated through a scenario analysis.

For the applicability of the model, the results indicate that the augmented ε-constraint approach provides a set of Pareto solutions, which represents the ideal trade-off between the total logistics cost and gas emission. Through a case study problem instance, the augmented ε-constraint approach is recommended for similar network design problems. From a scenario analysis, when the operational cost of the new warehouse is within a specific fraction of the warehousing cost of third-party warehouses, the solution with the new warehouse outperforms that without the new warehouse with respective to financial and environmental objectives.

The proposed model is an effective decision support tool for management, who would like to assess the impact of network planning decisions on the performance of their supply chains with respect to both financial and environmental aspects under uncertainty.

This research attempts to present a solid transportation problem (STP) mechanism in uncertain and indeterminate contexts, allowing decision makers to select their acceptance, indeterminacy and untruth levels.

Due to the lack of reliable information, changeable economic circumstances, uncontrolled factors and especially variable conditions of available resources to adapt to the real situations, the authors are faced with a kind of uncertainty and indeterminacy in constraints and the nature of the parameters of STP. Therefore, an approach based on neutrosophic logic is offered to make it more applicable to real-world circumstances. In this study, the triangular neutrosophic numbers (TNNs) have been utilized to represent demand, transportation capacity, accessibility and cost. Then, the neutrosophic STP was converted into an interval programming problem with the help of the variation degree concept. Then, two simple linear programming models were extracted to obtain the lower and upper bounds of the optimal solution.

The results reveal that the new model is not complicated but more flexible and more relevant to real-world issues. In addition, it is evident that the suggested algorithm is effective and allows decision makers to specify their acceptance, indeterminacy and falsehood thresholds.

Under the transportation literature, there are several solutions for TP and STP in crisp, fuzzy set (FS) and intuitionistic fuzzy set (IFS) conditions. However, the STP has never been explored in connection with neutrosophic sets to the best of the authors’ knowledge. So, this work tries to fill this gap by coming up with a new way to solve this model using NSs.

This paper presents an interactive fuzzy satisfying method by assuming that the decision maker (DM) has fuzzy goals for each of the objective functions in multiobjective nonlinear programming problems. The fuzzy goals of the DM are quantified by eliciting the corresponding membership functions through the interaction with the DM. After determining the membership functions for each of the objective functions, in order to generate a candidate for the satisficing solution which is also a Pareto optimal, the DM selects an appropriate standing membership function and specifies his/her aspiration levels of achievement of the other membership functions, called constraint membership values. For the DM's constraint membership values, the corresponding constraint problem is solved and the DM is supplied with the Pareto optima] solution together with the trade‐off rates between a standing membership function and each of the other membership functions. Then by considering the current values of the membership functions as well as the trade‐off rates, the DM acts on this solution by updating his/her constraint membership values. In this way, the satisficing solution for the DM can be derived efficiently from among a Pareto optimal solution set by updating his/her constraint membership values. On the basis of the proposed method, a time‐sharing computer program is written and an application to regional planning is demonstrated along with the corresponding computer outputs.

The purpose of this paper is to extend a methodology for solving multi‐objective linear programming (MOLP) problems, when the objective functions and constraints coefficients are stated as interval numbers.

The approach proposed in this paper for the considered problem is based on the maximization of the sum of membership degrees which are defined for each objective of multi objective problem. These membership degrees are constructed based on the deviation from optimal solutions of individual objectives. Then, the final model based on membership degrees is itself an interval linear programming which can be solved by current methods.

The efficiency of the solutions obtained by the proposed method is proved. It is shown that the obtained solution by the proposed method for an interval multi objective problem is Pareto optimal.

The proposed method can be used in modeling and analyzing of uncertain systems which are modeled in the context of multi objective problems and in which required information is ill defined.

The paper proposed a novel and well‐defined algorithm to solve the considered problem.

This study aims to create a model for defining the best supplier for a company and allocating order that considers sustainability criteria beyond the traditional selection criteria.

In this paper, sustainable supplier Selection and order allocation (SSS and OA) problem is managed based on a multiobjective linear programming (MOLP) model that incorporates sustainability dimensions. First, an interval type-2 fuzzy analytic hierarchy process (FAHP) method is applied for the main criteria and subcriteria to determine the weight of the selected criteria. Then, these values are used to convert the proposed MOLP model into a single-objective model.

The economic criterion (0.438) was the most important criterion for SSS in the agricultural machinery sector, followed by the social criterion (0.333) and the environmental criterion (0.229).

The results show that the proposed framework can be utilized by the agricultural machinery industry for SSS and OA.

The proposed framework provides to develop an integrated model by interval type-2 fuzzy sets for SSS and OA, taking into account the relationships between qualitative and quantitative evaluation criteria with different priorities. The validity of the developed model is confirmed by a case study of the agricultural machinery industry in Turkey.

An interactive multiple criteria method for managerial decision support is presented. The approach used is aimed at meeting some of the key requirements placed on multiple criteria decision making (MCDM) tools by a “soft” systems view on managerial reality. This is based on two concepts: similarity of aspirations and the graphical conflict zones, and solves some of the reported difficulties in directional search methods.

This study aims to investigate a reliability-level demand-oriented pharmaceutical supply chain design with maximal anticipated demand coverage. Different hospitals with the particular reliability value associated with the various pharmaceutical items (PIs) are considered. An inter-connected multi-period supply chain comprising manufacturers, distribution centers, hospitals and patients is assumed for the smooth flow of health-care items, enhancing supply chain reliability. A reliability index for PIs is depicted to highlight product preference and facilitate hospitals’ service levels for patients.

A mixed-integer multi-objective programming problem that maximizes maximal demand coverage minimizes the total economic costs and pharmaceutical delivery time is depicted under intuitionistic fuzzy uncertainty. Further, a novel interactive neutrosophic programming approach is developed to solve the proposed pharmaceutical supply chain management (PSCM) model. Each objective’s marginal evaluation is elicited by various sorts of membership functions such as linear, exponential and hyperbolic types of membership functions and depicted the truth, indeterminacy and falsity membership degrees under a neutrosophic environment.

The proposed PSCM model is implemented on a real case study and solved using an interactive neutrosophic programming approach that reveals the proposed methods’ validity and applicability. An ample opportunity to generate the compromise solution is suggested by tuning various parameters. The outcomes are evaluated with practical managerial implications based on the significant findings. Finally, conclusions and future research scope are addressed based on the proposed work.

The propounded study has some limitations that can be addressed in future research. The discussed PSCM model can be merged with and extended by considering environmental factors such as the health-care waste management system, which is not included in this study. Uncertainty among parameters due to randomness can be incorporated and can be tackled with historical data. Besides, proposed interactive neutrosophic programming approach (INPA), various metaheuristic approaches may be applied to solve the proposed PSCM model as a future research scope.

The strategy advised is to provide an opportunity to create supply chains and manufacturing within India by helping existing manufacturers to expand, identifying new manufacturers, hand-holding and facilitating, teams of officers, engineers and scientists deployed and import only if necessary to meet timelines. Thus, any pharmaceutical company or organization can adopt the production and distribution management initiatives amongst hospitals to strengthen and enable the pharmaceutical company while fighting fatal diseases during emergencies. Finally, managers or policy-makers can take advantage of the current study and extract fruitful pieces of information and knowledge regarding the optimal production and distribution strategies while making decisions.

This research work manifests the demand-oriented extension of the integrated PSCM design with maximum expected coverage, where different hospitals with pre-determined reliability values for various PIs are taken into consideration. The practical managerial implications are explored that immensely support the managers or practitioners to adopt the production and distribution policies for the PIs to ensure the sustainability in supply chain design.

Although the modern portfolio theory (MPT) asset allocation framework can be adopted to enable decision making for international and direct real estate investing, and that many institutional investors adopt it to support their decision making, this framework can be enhanced to capture the multi‐causal factors influencing international and direct real estate investing. The purpose of this paper is to explain how a fuzzy decision‐making approach is a more intuitive, yet rigorous alternative in this regard.

This paper is concerned with the model formation and estimation of a unique fuzzy tactical asset allocation (FTAA), which in turn comprises the FTAA flexible programming model and the FTAA robust programming model.

Both these FTAA models enhance the classical, Markowitz MPT portfolio theory on asset allocation through making it more intuitively appropriate for decision making in international and direct real estate investing.

These two FTAA models achieve the benefits of intuitively greater risk diversification by city or real estate sector and enable effective risk management. These two short‐run fuzzy models would be accepted and more such models would emerge as an effective extension of quadratic programming optimization, as more computable software programs of this kind are widespread.

Fuzzy approaches to asset allocation in the short run, are limited by some drawbacks. Fuzzy models possess the common feature of converting the equality function under quadratic programming optimization into inequality functions. Such inequality optimization replaces the point solution of the MPT TAA optimization problem, obtained through the rigid intersection of all functions, via a generalized or intuitive answer over a defined space of alternatives. The product of the fuzzy process with fuzzy inputs, in the form of fuzzy outcome is in actual fact a more natural and intuitive approach to asset optimization.