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This study considers a supply chain consisting of a commodity supplier and a final product manufacturer with uncertain demand. In addition to purchasing from the supplier through a forward contract, the manufacturer can adjust their inventory by trading the commodity in an online spot market after observing the actual demand. However, the spot market is imperfect in that transactions cannot be certainly realized and come with additional transaction costs. Furthermore, the spot price is volatile such that overly relying on the spot market is unwise. To investigate how the spot market affects the decisions and coordination in a supply chain, we develop a game-theoretical model incorporating spot trading. We derive the optimal ordering decision in a centralized supply chain, as well as the supplier's and manufacturer's equilibrium pricing and ordering decisions in a decentralized supply chain. The impact of the imperfect spot market on the optimal decisions and profits is analyzed. This study also demonstrates how the supply chain can be coordinated in the presence of an imperfect spot market. Finally, a numerical analysis is performed to examine the analytical results. Our results indicate that the spot market can generally improve the performance of the centralized supply chain and benefit the manufacturer in the decentralized one. However, it can be detrimental to the supplier. The supply chain can be coordinated by a revenue-sharing contract, and both parties' profits can be improved. Our findings suggest that the manufacturer could take advantage of the spot market, and the supplier should attempt to integrate or coordinate the supply chain to share the benefits of spot trading.

Probability weighting function (PWF) is the psychological probability of a decision-maker for objective probability, which reflects and predicts the risk preferences of decision-maker in behavioral decisionmaking. The existing approaches to PWF estimation generally include parametric methodologies to PWF construction and nonparametric elicitation of PWF. However, few of them explores the combination of parametric and nonparametric elicitation approaches to approximate PWF. To describe quantitatively risk preferences, the Newton interpolation, as a well-established mathematical approximation approach, is introduced to task-specifically match PWF under the frameworks of prospect theory and cumulative prospect theory with descriptive psychological analyses. The Newton interpolation serves as a nonparametric numerical approach to the estimation of PWF by fitting experimental preference points without imposing any specific parametric form assumptions. The elaborated nonparametric PWF model varies in accordance with the number of the experimental preference points elicitation in terms of its functional form. The introduction of Newton interpolation to PWF estimation into decision-making under risk will benefit to reflect and predict the risk preferences of decision-makers both at the aggregate and individual levels. The Newton interpolation-based nonparametric PWF model exhibits an inverse S-shaped PWF and obeys the fourfold pattern of decision-makers’ risk preferences as suggested by previous empirical analyses. First published online 17 April 2023

This study formulates an inventory model with limited storage capacity under the condition of order-size dependent trade credit. Shortages are allowed and partially backlogged. The objective of this study is to determine the optimal replenishment cycle length, the optimal fraction of no shortage, and whether retailers should choose to rent an extra warehouse to store more items, such that retailers’ total annual profit is maximized. We prove the global optimally of objective functions and derive the closed-form optimal solution. Some numerical examples are presented to illustrate the applicability of the proposed model. Sensitivity analysis is carried out and managerial insights are obtained. We find that if retailers’ own warehouse capacity is relatively small, they always benefit from enlarging order quantity and renting an extra warehouse; meanwhile, suppliers further prolong the credit period is beneficial for both parties. On the contrary, as retailers’ own warehouse capacity increases and exceeds the optimal order quantity under that of without capacity constraints, adopting the same replenishment strategy as that without capacity constraints is profitable for retailers. Our results also reveal that other model parameters (e.g., ordering cost, inventory holding cost, shortages cost, backordering rate, etc.) have a significant impact on retailers’ optimal decisions. First published online 17 November 2021

The bike rebalancing problem is one of the major operational challenges in the urban bike-sharing system, which involves the redistribution of bikes among stations to prevent stations from being empty or overloaded. This paper investigates a new bike rebalancing problem, which considers the collection of broken bikes in the multi-depot system. The proposed problem can be classified as a two-commodity vehicle routing problem with pick-up and delivery. An integer programming model is formulated to find the optimal vehicle assignment and visiting sequences with the minimum total working time and fixed cost of vehicles. A hybrid heuristic algorithm integrating variable neighborhood search and dynamic programming is proposed to solve the problem. The computational results show that the proposed method can find 26 best solutions out of 36 instances, while the CPLEX obtains 16 best solutions. Impact of broken bikes collection and distribution of depots is examined. Comparison of different practical strategies indicates that the number of vehicles can be significantly reduced by allowing multiple visits to depots. Allowing vehicles to return to different depots can help reduce the total working time.

Rapid growth and development of civil engineering in recent years inspire building enterprises to concentrate on construction contractor selection for achieving more construction quality and lower construction cost. The existing studies generally regard the process of selecting the best contractor as a multi-criteria group decision making problem. Few research studies addressed the contractor selection problem in the context of large-scale group decision making, which is common in practical scenarios in terms of major construction projects as a number of experts with diverse backgrounds are usually involved. On this basis, we establish a contractor selection framework under large-scale group decision making environment, which covers expert classification, consensus reaching process, collective decision matrix generation, and the ranking-oriented decision making method. We cluster expert group with K-means clustering method based on expertise levels, which are depicted by six features generated with an expertise identification approach. The consensus model manages consensus reaching process from both intra- and inter- layers and takes into account the interactions between them. After reaching agreements among experts, this paper utilizes the concept of proportional hesitant fuzzy linguistic term set to assemble intra-subgroup assessments for the reduction of information loss or distortion. Then, an aggregation process carries on as to gather subgroup assessments in which the subgroup weights are derived from their cluster centers and sizes in the use of the TOPSIS method. Finally, the well-established decision making tool integrating qualitative and quantitative criteria, ELECTRE III, is adapted to elicit the ranking of bidders. An illustrative study and a comparative analysis are performed to demonstrate the feasibility and effectiveness of the established multi-criteria group decision making approach.

With complexity and uncertainty having an increasing impact on the decision-making environment, much attention is being paid to the development and application of multiple criteria group decision-making (MCGDM) models owing to the potential for fully exploiting the diverse strengths and expertise of various members. In general, inevitable interactions among decision makers (DMs), when a number of DMs share similar knowledge and experiences, can have a significant impact on the management of decision information directly or indirectly related to DMs, and can easily lead to distorted and unconvincing decision outcomes. In order to model the MCGDM problem in which DMs share a similar background, a consolidated MCGDM model in the context of intuitionistic fuzzy sets (IFSs) is developed. First, we refine the constructive principles for intuitionistic fuzzy entropy (IFE) and use them as a basis to produce a novel IFE measure simultaneously factoring in the intuitionism and fuzziness of IFSs. With the aim of dealing with the impact on the specifications of the weights of DMs and criteria, an integrated method is then proposed based on the novel IFE measure, 2-additive fuzzy measure, and Choquet integral. Due to their capability of modeling effectively the interrelationships among arguments, the weighted intuitionistic fuzzy Bonferroni mean (WIFBM) and the weighted intuitionistic fuzzy geometric Bonferroni mean (WIFGBM) are introduced to fuse the individual evaluation values of alternatives on criteria. In addition, simple additive weighting based on the WIFBM or WIFGBM is applied to rank alternatives and select the best one. Finally, the feasibility and effectiveness of the proposed model are explored with a case study of an emergency plan decision-making problem accompanied with sensitivity and comparison analysis.

Deep Neural Networks (DNNs) has been dominating recent data mining related tasks with better performances. This article proposes a hybrid approach that exploits the unique predictive power of DNN and classical time series regression models, including Generalized Linear Model (GLM), Seasonal AutoRegressive Integrated Moving Average model (SARIMA) and AutoRegressive Integrated Moving Average with eXplanatory variable (ARIMAX) method, in forecasting time series in reality. For each selected time series regression model, three different hybrid strategies are designed in order to merge its results with DNNs, namely, Zhang's method, Khashei's method, and moving average filter-based method. The real seasonal time series data of patient arrival volume in a Hong Kong A&ED center was collected for the period July 1, 2009, through June 30, 2011 and is used for comparing the forecast accuracy of proposed hybrid strategies. The mean absolute percentage error (MAPE) is set as the metric and the result indicates that all hybrid models achieved higher accuracy than original single models. Among 3 hybrid strategies, generally, Khashei's method and moving average filter-based method achieve lower MAPE than Zhang's method. Furthermore, the predicted value is an important prerequisite of conducting the rostering and scheduling in A&ED center, either in the simulation-based approach or in the mathematical programming approach.

Collaborative decision making (CDM) with linguistic computational techniques has recently achieved significant advancements. Due to the widespread use of sophisticated linguistic constructions, such as generalized comparative linguistic expressions (GCLEs), additional information associated with subjective appraisals has been exploited with the aim of addressing accuracy improvements in multifarious CDM, given that partial information loss is almost inevitable while dealing with complex linguistic comprehension. This paper brings an innovative perspective into CDM from COmponent ANalysis with GCLEs (COANG) to formalize problems involved in making optimal choices, mainly in CDM problems with participants who are usually characterized by domain specificity. Consequently, the focus of this paper is on the domain-specific CDM (DSCDM) in which individual semantics should be built predominantly to model various implications of their decision appraisals with heterogeneity in the knowledgeable domain for the effort of computational reinforcements. The attitude orientation and strength are crucial decompositions to incorporate COANG into DSCDM to establish an elastic paradigm that puts forward individual perception comprehension ahead of exerting collective efforts. The DSCDM based on COANG model enables agents to turn complex challenges of sophisticated linguistic constructions into substantial opportunities by translating them into customized individual semantics (CIS), and CIS into useful insights for making better decisions and improving results. The potential advantages of the proposed COANG-based DSCDM framework are validated with a clinical psychological practice related to the severity assessment of symptoms of schizophrenia.

In recent years, hesitant multiplicative preference relation (HMPR) has been a powerful means to represent the evaluation information of decision makers during the pairwise comparison concerning alternatives. As the important parts of group decision making (GDM) issues with HMPRs, the consistency improving and consensus reaching processes have been researched by many scholars; however, the existing approaches present several limitations, including defining the consistency index depend on the other HMPR instead of the original HMPR, improving the consistency and consensus levels of HMPRs independently, and that the high computational complexity of the existing iterative algorithms. To overcome these drawbacks, this paper proposes a mathematical programming model to improve the consistency and consensus levels of HMPRs, simultaneously. First, a consistency index according to multiplicative consistency is put forward to compute the consistency degree of normalized HMPR (NHMPR) after the normalization procedure. Second, a programming model by minimizing the difference between the original NHMPR and the revised NHMPR is developed to obtain the acceptably consistent NHMPR; then, a consistency-based method is constructed to solve the decision making problems with an HMPR. Third, considering the GDM issues, a consistency- and consensus-based programming model is established to obtain the acceptably consistent and consensus NHMPRs, in which the original evaluation information can remain as much as possible. Fourth, the normalized hesitant multiplicative weighted geometric operator is introduced to fuse the revised NHMPRs and an algorithm for GDM is proposed with novel consistency improving and consensus reaching processes. Finally, two numerical examples are applied to show the practicality and advantages of the proposed approaches.

Tremendous effort has been exerted over the past few decades to construct multi-attribute decision functions with the capacity to model heterogeneous interrelationships among attributes. In this paper, we report an empirical study aiming to test whether or not considering interrelationships among attributes can benefit the representation of real preferences in multi-attribute ranking tasks. The generalized extended Bonferroni mean (GEBM) has recently been advocated as a promising and efficient tool for modeling heterogeneous interrelationships among attributes. We compare the GEBM with one of its most widely adopted competitors, simple additive weighting (SAW), in terms of their fitting quality when applied to preference elicitation. The attribute performances are manifested uniformly with the use of three widely-adopted utility measurements. Subsequently afterwards, the maximum split approach to establish the constraint objective function in regression for both the GEBM and the SAW to test whether or not all constraints resulting from the subject’s ranking can be fulfilled. On this bases, the number of fully or partly fitted subjects, consistency for subjects according to the better fitting model, and reliability of attribute weights learned by either the GEBM or the SAW are empirically examined in a bid to demonstrate the quantitative construction of fitting quality measurement. With the established fitting quality measurement, the necessity of taking heterogeneous interrelationships among attributes into account when constructing multi-attribute decision functions to represent real preferences can be analyzed. The main conclusion from the empirical study suggests that the relative performance of the two aggregation paradigms examined here depends on which fitting quality measurements are adopted. Researchers enthusiastic to discover the heterogeneous interrelationships among attributes when constructing multi-attribute decision functions might find the present results relevant when modeling actual preferences, and consequently this work should serve as a useful reference for enterprises and service providers seeking to strategically drive customer purchasing decisions.

To obtain reliable results in a qualitative multi-attribute group decision-making (MAGDM) problem, how to retain the evaluation information as much as possible and how to determine the reasonable weights of experts and attributes are two important issues. Proportional hesitant fuzzy linguistic term set (PHFLTS) is beneficial for retaining evaluation information as it would consider the linguistic terms and corresponding proportional information simultaneously. However, PHFLTS is a relatively new concept. Some novel manipulations, such as comparison, arithmetic operations, aggregation operators, and cosine similarity and distance measures are defined in this study with the purpose of improving the completeness and applicability of PHFLTS. Furthermore, cosine similarity measure-based weight determination model and entropy measure-based weight determination model under proportional hesitant fuzzy linguistic (PHFL) environment are constructed to derive the objective weights of experts and those of attributes as well. Subsequently, an integrated weighting model is proposed to determine the comprehensive weights of experts and attributes. Based on the defined operational laws for PHFLTS and comprehensive weighting model, two MAGDM methods, PHFL aggregation operator-based method and extended PHFL-VIKOR method, are developed to deal with MAGDM problems with PHFL information. To demonstrate the applicability, efficiency, and advantages of the proposed MAGDM methods, an illustrative example and a comparison example are provided.

Interval-valued Pythagorean fuzzy sets (PFSs), as an extension of PFSs, have strong potential in the management of complex uncertainty in real-world applications. This study aims to develop several interval-valued Pythagorean fuzzy Frank power (IVPFFP) aggregation operators with an adjustable parameter via the integration of an isomorphic Frank dual triple. First, a special automorphism on unit interval is introduced to construct an isomorphic Frank dual triple; and this triple is further applied on the definition of interval-valued Pythagorean fuzzy Frank operational laws. Second, two IVPFFP aggregation operators with the inclusion of an adjustable parameter are defined on the basis of the proposed operational laws, and several instrumental properties are then investigated. Furthermore, some limiting cases of the proposed IVPFFP operators are analyzed with respect to the varying adjustable parameter values. Finally, an IVPFFP aggregation operator-based multiple attribute group decision-making model is developed with a practical example furnished to demonstrate its feasibility and efficiency. The power that the adjustable parameter exhibits has been leveraged to affect the final decision results, and the proposed IVPFFP operators are compared with three selected aggregation operators to demonstrate their advantages provided with a practical example.

In this paper, we propose an extension of hesitant fuzzy sets, i.e., proportional hesitant fuzzy sets (PHFSs), with the purpose of accommodating proportional hesitant fuzzy environments. The components of PHFSs, which are referred to as proportional hesitant fuzzy elements (PHFEs), contain two aspects of information provided by a decision-making team: the possible membership degrees in the hesitant fuzzy elements and their associated proportions. Based on the PHFSs, we provide a novel approach to addressing fuzzy multi-attribute group decision making (MAGDM) problems. Different from the traditional approach, this paper first converts fuzzy MAGDM (expressed by classical fuzzy numbers) into proportional hesitant fuzzy multi-attribute decision making (represented by PHFEs), and then solves the latter through the proposal of a proportional hesitant fuzzy TOPSIS approach. In this process, preferences of the decision-making team are calculated as the proportions of the associated membership degrees. Finally, a numerical example and a comparison are provided to illustrate the reliability and effectiveness of the proposed approach.

As a safety and reliability analysis technique, failure mode and effects analysis (FMEA) has been used extensively in several industries for the identification and elimination of known and potential failures. However, some shortcomings associated with the FMEA method have limited its applicability. This study aims at presenting a comprehensive FMEA model that could efficiently handle the preference interdependence and psychological behavior of experts in the process of failure modes ranking. In this model, a linguistic variable expressed by the interval-valued Pythagorean fuzzy number (IVPFN) is utilized by experts to provide preference information with regard to failure modes’ evaluation and risk factors’ weight. Then, to depict the interdependent relationships between experts’ preferences, the Bonferroni mean operator is extended to IVPFN to aggregate the experts’ preference. Subsequently, an extended TODIM approach in which the dominance degree of failure modes is calculated by grey relational analysis is utilized to determine the risk priority of failure modes. Finally, a practical example concerning the risk assessment of a nuclear reheat valve system is provided to demonstrate the effectiveness and feasibility of the presented method. In addition, a sensitivity analysis and comparison analysis are conducted, and the results show that the preference interdependence and psychological behavior of experts have an important effect on the risk priority of failure modes.