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To select the best strategies in the presence of both deterministic and non‐deterministic data in uncertain environments, without relying on weight assignment by decision makers, this paper aims to propose an innovative approach, which is based on mathematical programming called chance‐constrained data envelopment analysis (CCDEA).

This paper proposes an innovative approach called CCDEA for strategy selection.

In summary, the approach presented in this paper has some distinctive contributions: the proposed model does not demand weights from maker; DEA analysis obtains the optimal weights for all inputs and outputs of each decision‐making unit without relying on the subjective judgment of decision makers; the proposed model considers multiple criteria for strategy selection; the paper makes a sufficient contribution to the practice of operations research. This paper is the first study which applies CCDEA for evaluating the strategies in uncertain environments; and the paper introduces a method for strategy selection in the presence of stochastic data.

To the best of the authors' knowledge, this paper is the first application of CCDEA to deal with strategy selection.

The purpose of this paper is to attempt to realize a distribution network optimization in supply chain using grey systems theory for uncertain information.

There is much uncertain information in the distribution network optimization of supply chain, including fuzzy information, stochastic information and grey information, etc. Fuzzy information and stochastic information have been studied in supply chain, however grey information of the supply chain has not been covered. In the distribution problem of supply chain, grey demands are taken into account. Then, a mathematics model with grey demands has been constructed, and it can be transformed into a grey chance‐constrained programming model, grey simulation and a proposed hybrid particle swarm optimization are combined to resolve it. An example is also computed in the last part of the paper.

The results are convincing: not only that grey system theory can be used to deal with grey uncertain information about distribution of supply chain, but grey chance‐constrained programming, grey simulation and particle swarm optimization can be combined to resolve the grey model.

The method exposed in the paper can be used to deal with distribution problems with grey information in the supply chain, and network optimization results with a grey uncertain factor could be helpful for supply chain efficiency and practicability.

The paper succeeds in realising both a constructed model of the distribution of supply chain with grey demands and a solution algorithm of the grey mathematics model by using one of the newest developed theories: grey systems theory.

Supplier selection problem is the key process in decision making of supply chain management. An effective selection of vendors is heavily responsible for the success of any organization. Vendor selection problem (VSP) reflects a more practical view when the decision makers involved in the problem are present on different levels. Moreover, vendor selection consists of various random parameters to be dealt with in real life. The purpose of this paper is to present a decentralized bi-level VSP where demand and supply are normal random variables and objectives are fuzzy in nature. Decision makers are present at two levels and are called as leader and follower. As the next purpose, this paper extends and presents a solution approach for fuzzy bi-level multi-objective decision-making model with stochastic constraints. Different scenarios have been developed within a real-life case study based on different sets of controlling factors under the control of leader.

This study uses chance-constrained programming and fuzzy set theory to generate the results. Stochastic constraints are converted into deterministic constraints using chance-constrained programming. Decision variables in the bi-level VSP are partitioned between the two levels and considered as controlling factors. Membership functions based on fuzzy set theory are created for the goals and controlling factors and are used to obtain the overall satisfactory solutions. The model is tested on a real-life case study of a textile industry and different scenarios are constructed based on the choice of leader’s controlling factors.

Results showed that the approach is quite helpful as it generates efficient results producing a good level of satisfaction for the decision makers of both the levels. Results showed that on choosing the vendors that are associated with worst values in terms of associated costs, vendor ratings and quota flexibilities as controlling factors by the leaders, the level of satisfaction achieved is highest. The level of satisfaction of solution is lowest for the scenario when the leader chooses to control the decision variables associated with vendors that are profiled with minimum vendor ratings. Results also showed that higher availability of materials and budget with vendors proved helpful in obtaining quota allocations. Different scenarios generate different results along with different values of satisfaction degrees and objective values which shows the flexible feature of the approach based on leader’s choice of controlling factors. Numerical results showed that the leader’s control can be effectively incorporated maintaining satisfaction levels of the followers under various scenarios or conditions.

The paper makes a certain contribution toward the study of vendor selection existing in a hierarchical manner under uncertain environment. A wide set of data of different factors is needed which can be seen as a limitation when the available time is short for the supplier selection process.

VSP which is generally adopted by most of the large organizations is characterized with hierarchical decision making. Moreover, dealing with the real-life concern, the data available for some of the parameters are not complete, representing an uncertainty of parameters. This study is quite helpful for decentralized VSP under uncertain environment to reduce the costs, improve profit margins and to create long-term relationships with selected vendors. The proposed model also provides an avenue to explore the decision making when the leader has control over some of the decision variables.

Reviewing the literature available, this is the first attempt to present a multi-objective VSP where the decision makers are at hierarchical levels considering uncertain parameters such as demand and supply as per the best knowledge of authors. This research further provides an approach to construct scenarios or different cases based on the choice of leader’s choice of controlling factors.

The ascendancy of vertical marketing structures as total systems has brought about considerable interest in designing distribution systems. Various administered and co‐operative alignments have been successful in the marketplace by enabling lower total costs through central buying practices and by producing a more predictable demand pattern. As these planned systems begin to create de facto competition among individual firms, the need for methods of discovering optimal vertical arrangements will increase. One method of finding optimal arrangements of interacting phenomena is by modelling—and linear programming techniques have been found to be particularly useful. The transportation problem or distribution model was one of the first applied special cases of linear programming. Mathematical solutions to this “special case” of linear programming began appearing in the literature during World War II. Since that time, the management science literature has been replete with significant contributions in the transportation area such as those of Hitchcock, Dantzig, Chames and Cooper, and Orden.

Supply chain (SC) research has boomed over the past two decades. Significant contributions have been made to the field from various analytical and decision-making perspectives. This paper, a comprehensive bibliometric study, aims to identify the key research contributors, institutions and themes.

A comprehensive knowledge domain visualization of over 1,000 articles, published between 2000 and 2022, is carried out to construct a bird’s eye view of the field in terms of research production, key authors, main publication outlets, geographic disparity of the contributions and emerging research trends. Additionally, collaboration patterns among researchers and institutions are mapped to highlight the communication networks underlying research initiatives.

Results show an explosive growth in the number of articles tackling supply chain optimization (SCO) issues with a significant concentration of the contributions in a relatively small cluster of authors, journals, institutions and countries. Among the many important findings, our analysis indicates that mixed-integer linear programming is the most commonly used model, while robust optimization is the method of choice for handling uncertainty. Furthermore, most SC models are developed at only one level of the organizational hierarchy and consider only one planning horizon. The importance of developing integrated SCO systems is key for future research.

The study fills the optimization techniques gap that exists in SC management bibliometric studies and presents a thematic map for the SCO research highlighting the various research foci.

The purpose of this study is to develop a holistic optimization model for an integrated sustainable fleet planning and closed-loop supply chain (CLSC) network design problem under uncertainty.

A novel mixed-integer programming model that is able to consider interactions between vehicle fleet planning and CLSC network design problems is first developed. Uncertainties of the product demand and return fractions of the end-of-life products are handled by a chance-constrained stochastic program. Several Pareto optimal solutions are generated for the conflicting sustainability objectives via compromise and fuzzy goal programming (FGP) approaches.

The proposed model is tested on a real-life lead/acid battery recovery system. By using the proposed model, sustainable fleet plans that provide a smaller fleet size, fewer empty vehicle repositions, minimal CO₂ emissions, maximal vehicle safety ratings and minimal injury/illness incidence rate of transport accidents are generated. Furthermore, an environmentally and socially conscious CLSC network with maximal job creation in the less developed regions, minimal lost days resulting from the work's damages during manufacturing/recycling operations and maximal collection/recovery of end-of-life products is also designed.

Unlike the classical network design models, vehicle fleet planning decisions such as fleet sizing/composition, fleet assignment, vehicle inventory control, empty repositioning, etc. are also considered while designing a sustainable CLSC network. In addition to sustainability indicators in the network design, sustainability factors in fleet management are also handled. To the best of the authors' knowledge, there is no similar paper in the literature that proposes such a holistic optimization model for integrated sustainable fleet planning and CLSC network design.

This paper provides a theoretical framework for application of Chance-Constrained Programming (CCP) in situations where the coefficient matrix is random and its elements are not normally distributed. Much of the CCP literature proceeds to derive deterministic equivalent in computationally implementable form on the assumption of “normality”. However, in many applications, such as air pollution control, right skewed distributions are more likely to occur. Two types of models are considered in this paper. One assumes an exponential distribution of matrix coefficients, and another one uses an empirical approach. In case of exponential distributions, it is possible to derive exact “deterministic” equivalent to the chance-constrained program. Each row of the coefficient matrix is assumed to consist of independent, exponentially distributed random variables and a simple example illustrates the complexities associated with finding a numerical solution to the associated deterministic equivalent. In our empirical approach, on the other hand, simulated data typically encountered in air pollution control are provided, and the data-driven (empirical) solution to the implicit form of deterministic equivalent is obtained. Post-optimality analyses on model results are performed and risk implications of these decisions are discussed. Conclusions are drawn and directions for future research are indicated.

The purpose of this paper is to develop a computer aided decision‐making model for flexible manufacturing system (FMS) situations when multiple conflicting objectives are addressed by the management.

It is assumed that the problem is the managerial level schedule rather than the operational schedule. As a tool, goal programming has been employed for measuring the trade‐offs among the objectives. As a safeguard, the level of the reliability of the constraints associated with the random coefficients is taken into consideration. As an optimization technique, the approach of chance constrained programming which has been an operational way for introducing probabilistic constraints into the collection of the linear programming and goal programming problem constraints is stated and mathematically formulated.

The approach of chance constrained programming is suitable to introduce management concerns about the reliability of the constraints of the problem in the FMS.

The paper gives an overview of the FMS and proposes a goal programming model for the analysis of problem. The proposed model acknowledges the randomness of customer demands for better standardization of production planning and inventory management systems. By the fact that customer demands are not always deterministic the hypothesis that sale level for each period is normally distributed is imposed. A sample example problem is provided to show how the proposed model can work.