Despite its recent introduction in literature, the Best–Worst Method (BWM) is among the most well-known and applied methods in Multicriteria Decision-Making. The method can be used to elicit the relative importance (weight) of the criteria as well as to get the priorities of the alternatives on the criteria at hand. In this paper, we will present an extension of the method, namely, the parsimonious Best–Worst-Method (P-BWM) permitting to apply the BWM to get the priorities of the alternatives in case they are in a large number. At first, the Decision-Maker (DM) is asked to give a rating to the alternatives under consideration; after, the classical BWM is applied to a set of reference alternatives to get their priorities used to compute, then, the priorities of all the alternatives under consideration. We propose also a procedure to select reference alternatives, possibly in cooperation with the DM, providing a well-distributed coverage of the rating range. The new proposal requires the DM a fewer number of pairwise comparisons than the original BWM. Another contribution of the paper is related to the comparison between BWM, P-BWM, the Analytic Hierarchy Process (AHP), and the parsimonious AHP in terms of the amount of preference information provided by the DM in each method to apply it. In addition to the standard approach, we propose one alternative way of inferring the priority vectors in BWM and P-BWM based on the barycenter of the space of alternatives priorities compatible with the preferences given by the DM. Finally, an experiment with university students has been conducted to test the new proposal. Results of the experiments show that P-BWM performs better than BWM in terms of capability to represent the DM's preferences and the difference between the results of the two methods is significant from the statistical point of view. The new proposal will permit to use the potentialities of the BWM to get the alternatives’ priorities in real-world decision-making problems where a large number of alternatives must be taken into account.

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As ports are experiencing heavier traffic, the pressure to improve port call processes is increasing. Port call optimization (PCO) is one of these improvement initiatives, enabling the arrival of vessels to the port just-in-time when the vessel services, like pilotage, towage, and mooring, are all readily available. Otherwise, vessels that sailed at full speed to arrive at the port may have to wait, idling at anchorage, occupying space, burning fuel, and leading to increased congestion. One of the main challenges in the implementation of PCO is determining the time at which availability of these services can be guaranteed. The paper addresses this challenge by presenting a model that jointly schedules vessels and service providers. It extends the current approaches to allow application to larger and busier ports, where repositioning times for pilots and tugboats is highly variable and vessels experience waiting times between services. The problem is formulated as a mixed-integer linear programming one and is modelled in continuous time. We test alternative scheduling strategies using three different objective functions, based on the current ‘first-come-first-serve’ approach, a minimal level of service, and the best capacity utilization. The model is applied on data made available by the Port of Rotterdam, and it provides a full-service schedule for vessels and service providers.

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Since the development of the best–worst method (BWM) in 2015, it has become a popular research focus in multi-criteria decision-making. The original optimization problem of the BWM is a nonlinear min–max model that can lead to multiple optimal solutions, while the linear model of the BWM produces a unique solution. The two models need to be solved by optimization software packages. In addition, although the linear model of the BWM can obtain a unique solution, it produces different feasible regions than the nonlinear model of the BWM, and it changes the objective function. This study aims to solve the nonlinear model of the BWM mathematically to obtain the analytical forms of the optimal solutions. First, we transform the original nonlinear model of BWM into an equivalent optimization model driven by the optimally modified comparison vectors. The equivalent BWM provides a solid basis for computing the analytical solutions. Second, for not-fully consistent pairwise comparison systems, we strictly prove that there is only one unique optimal solution with three criteria, and there might be multiple optimal solutions with more than three criteria. We further develop the analytical forms of these unique and multiple optimal solutions and the optimal interval weights. Third, we develop a secondary objective function to select a unique solution for the BWM. The secondary objective function retains all the characteristics of the original nonlinear model of the BWM, and we find the unique solution analytically. Finally, some numerical examples are examined, and a comparative analysis is performed to demonstrate the effectiveness of our analytical solution approach.@en

Joint decision-making is one of the coordination mechanisms to address the inherent complexity of business-to-business (B2B) processes within a supply chain. Joint decision-making can be helpful to define shared goals and objectives, identify supply chain failures and opportunities, and consolidate supply chain success. Parties may benefit directly from a partnership's potential and synergies by collaboratively making decisions. However, specific business conditions need to be in place to enable joint decision-making. This paper investigates how companies in a dyadic relationship arrive at joint and individual supply chain decision-making structure. We examine the drivers, facilitators, and barriers of making joint as well as individual decisions within the supplier-buyer dyad and frame our arguments borrowing perspectives from resource dependency theory, transaction cost economics, collaboration theory, and social exchange theory. The paper presents a case study of Dutch high-tech companies, analysing experiences of supply chain managers via semi-structured interviews. High-tech firms often collaborate and share supply chain decisions due to the high-value capital equipment as well as a shared dependency on highly specific scarce resources. Our study provides new empirical insight into how firms cope with conflicting drivers, facilitators, and barriers in collaborations, controlling their decision-making structure. From the case study, we identify the combinations of facilitators and drivers that tend to promote the existence of joint decisions. We conclude with providing a list of suggestions for decision-makers and future research.

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Priorities in multi-criteria decision-making (MCDM) convey the relevance preference of one criterion over another, which is usually reflected by imposing the non-negativity and unit-sum constraints. The processing of such priorities is different than other unconstrained data, but this point is often neglected by researchers, which results in fallacious statistical analysis. This article studies three prevalent fallacies in group MCDM along with solutions based on compositional data analysis to avoid misusing statistical operations. First, we use a compositional approach to aggregate the priorities of a group of DMs and show that the outcome of the compositional analysis is identical to the normalized geometric mean, meaning that the arithmetic mean should be avoided. Furthermore, a new aggregation method is developed, which is a robust surrogate for the geometric mean. We also discuss the errors in computing measures of dispersion, including standard deviation and distance functions. Discussing the fallacies in computing the standard deviation, we provide a probabilistic criteria ranking by developing proper Bayesian tests, where we calculate the extent to which a criterion is more important than another. Finally, we explain the errors in computing the distance between priorities, and a clustering algorithm is specially tailored based on proper distance metrics.@en

This paper presents a new multi-criteria decision-making (MCDM) method, namely the ratio product model (RPM). We first overview two popular aggregating models: the weighted sum model (WSM) and the weighted product model (WPM). Then, we argue that the two models suffer from some fundamental issues mainly due to ignoring the ratio nature of the alternatives' scores with respect to the criteria and the importance weights of the criteria. Building on the notion of compositional data analysis, the developed RPM regards performance scores and criteria weights as compositions, which solves the issues around the WSM and WPM. Using several examples, we show that the WSM and WPM could lead to erroneous conclusions, whereas the RPM could lead to fully reliable conclusions. Since many MCDM methods rely on some aggregation approaches, the proposed method is a significant contribution to the field and puts forward the correct way to analyze decision problems while respecting the nature and constraints of the input data.@en

The Physical Internet (PI) is a paradigm-changing and technology-driven vision, which is expected to significantly impact the development of the freight transport and logistics (FTL) system of today. However, the development of the FTL system towards the PI creates much uncertainty for its current stakeholders. Ports are one of those stakeholders that are expected to be profoundly affected by these developments. However, research that focuses on port policy, under the uncertain developments towards the PI, is still lacking. By providing port authorities with insights and recommendations on robust policy areas, we address this void in literature. We conduct a scenario analysis in combination with multi-criteria decision analysis (MCDA) to determine the importance of port performance indicators and policy areas in different scenarios. The most significant, uncertain, and orthogonal factors for the development of the PI are technological development and institutional development. We find that for a proper alignment with the PI vision, in three out of four scenarios, ports should prioritize the implementation of digital solutions and standards, as opposed to an infrastructure focused policy.@en

Cooperation between vessel service providers can improve the performance of ports. However, the potential impact of such cooperation has not yet been quantitatively addressed in the literature. We present an assessment using a port simulation model where the exchange of information has been made explicit. Cooperation is modelled as information exchange between the pilotage and towage service providers for the deployment of pilots and tugboats. A first application of the model is shown for the case of Port of Rotterdam. We find that time savings of up to 30% in waiting times can be achieved, while both service providers improve their performance. These findings provide empirical confirmation of the expected benefits of cooperation in ports as voiced in the literature. Furthermore, the results underscore the importance of moving beyond an ad-hoc synchronizations of these services towards systematic cooperation, to the benefit of ports as well as the service providers.@en

Consumer goods supply chains are intensifying their efforts to develop and offer green products, in order to seize new business opportunities and improve profitability. A specific type of green products concerns marginal and development cost-intensive green products (MDIGPs), like electric vehicles. As greening these products affects both marginal and development costs, their design presents special challenges, especially within the context of uncertain demand. This paper formulates the joint product pricing-ordering-greening decision problem in the supply chains of MDIGPs and examines the impact of demand uncertainty. A sequential game-theoretic framework is developed, providing analytical expressions of the optimal solutions for the stochastic model. A bargaining game on the wholesale price between supply chain members is proposed to coordinate decisions. We compare the optimal decisions numerically in the stochastic and deterministic cases and find that, although demand uncertainty creates inefficiency in the green supply chain, it might positively impact product greenness and prices. Given the impact of the unit-variable greening costs of MDIGPs, we are able to identify cases where–contrary to common belief–demand uncertainty does not always lead firms to reduce greenness or increase prices.

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This study introduces a general framework, called Bi-sided facility location, for a wide range of problems in the area of combined facility location and routing problems such as locating test centres and designing the network of supermarkets. It is based on a multi-objective optimisation model to enhance the service quality which the clients received, called client-side, and enhance the interconnection quality and eligibility among the centres, called center-side. Well-known problems such as k-median and k-centre for the client-side and the travelling salesman problem for the centre-side are taken into account in this paper. After discussing the complexity of this kind of combination, we propose a heuristic approximation algorithm to find approximation Pareto-optimal solutions for the problem. The algorithm is an efficient local search utilising geometric objects such as the Voronoi diagram and Delaunay triangulation as well as algorithms for computing approximation travelling salesman tour. In addition to the comprehensive theoretical analysis of the proposed models and algorithm, we apply the algorithm to different instances and benchmarks, and compare it with NSGA-II based on set coverage and spacing metrics. The results confirm the efficiency of the algorithm in terms of running time and providing a diverse set of efficient trade-off solutions. Highlights: Introducing a general bi-side location model considering centres and clients’ utilities Discussing and proving the NP-hardness of the model in the general framework Considering two instances; k-centre and k-median for client-side and TSP for centre-side Proposing an efficient geometric-based algorithm for solving the problems Implementing, testing, and comparing the proposed algorithm on several benchmarks.@en

To design a bioethanol supply chain, along with the transportation and operational costs, it is vital to consider more factors categorized into three sustainability pillars (i.e. economy, social and environment). In this paper, to develop a mathematical model for bioethanol supply chain (BSC), we propose a two-phase methodology; in the first phase, using a sustainable framework of attributes contributing to the facility location selection in the BSC network, we calculate the sustainability score of alternatives through employing the best-worst method (BWM). Then, considering the results of the multi-attribute step as the parameters of an objective function called the sustainability value function, we develop a bi-objective multi-level bioethanol supply chain model. To solve the proposed model, a Nested bi-objective Optimization Genetic Algorithm (NbOGA) is introduced in this research. Finally, we evaluate the performance of the presented BSC model and the algorithm for a real-world problem. The results show that using the proposed structure, both sustainability attributes and transportation costs are appropriately satisfied in the BSC network.@en

The best-worst method (BWM) is a multicriteria decision-making (MCDM) method to derive the relative importance (weight) of a set of criteria used to evaluate a set of alternatives. Several models (e.g., nonlinear, linear, Bayesian, and multiplicative) have been developed to find the weights based on the provided pairwise comparisons, conducted among the criteria, by the decision-maker(s)/expert(s). The existing BWM models, however, do not handle interactions that might exist between the criteria encountered in a decision problem. In this study, a nonadditive BWM is developed that considers possible interactions between the criteria. To this end, we use the Choquet integral, one of the most widely accepted techniques, to incorporate criteria interactions. A nonlinear optimization model is introduced to minimize the maximum deviation of the obtained weights from the provided pairwise comparisons, considering the information about the interactions between the criteria. We then introduce a linear variant of the nonadditive BWM and discuss its property compared to the nonlinear model. The applicability of the proposed approach is demonstrated through a real-world case study of a battery-powered electric vehicle (BEV) selection problem.@en

Factors driving the choice of shipper firms for services of logistics service providers have long been recognized in the freight transportation literature. However, the willingness among shippers to choose flexible transportation services, where the service package can be adapted during planning and execution, has received less attention. In particular, little is known about the contextual circumstances under which shippers would be inclined to select such flexible transportation service. In this study, experimental scenarios and discrete choice modeling are used to investigate the willingness among shippers to use flexible transportation services. We estimate multinomial logit, mixed logit, and latent class models for a sample of nearly 200 global shipper firms and calculate willingness-to-pay measures for flexibility. The findings indicate that flexible services are essential in demand-volatile markets. Since logistics services may provide external flexibility for shipper firms, we also study which related internal flexibilities in supply chains drive these choices. In particular, our findings show that it is mainly the volume flexibility of shippers that mediates the choice of flexible transportation services.@en

This study aims to develop a Multi-Attribute Decision-Making (MADM) method, the Best-Worst Tradeoff method, which draws on the underlying principles of two popular MADM methods (the Best-Worst Method (BWM) and the Tradeoff). The traditional Tradeoff procedure, which is based on the axiomatic foundation of multi-attribute value theory, considers the ranges of the attributes, but decision-makers/analysts find it hard to check the consistency of the paired comparisons when using this method. The traditional BWM, on the other hand, uses two opposite references (best and worst) in a single optimization, which not only frames the elicitation process in a more structured way, but helps decision-makers/analysts check the consistency. However, the BWM does not explicitly considers the attributes ranges in the pairwise comparisons. The method proposed in this study uses the “consider-the-opposite-strategy” and accounts for the range effect simultaneously. Specifically, the decision-maker considers the ranges of the attributes and provide two pairwise comparison vectors, then an optimization model is designed to determine the optimal weights of the attributes based on these two vectors. After that, consistency thresholds are constructed to check the consistency of the judgements. Finally, a case study is used to examine the feasibility of the proposed method.@en

In this study, the existence of anchoring bias—people's tendency to rely on, evaluate, and decide based on the first piece of information they receive—is examined in two multi-attribute decision-making (MADM) methods, simple multi-attribute rating technique (SMART), and Swing. Data were collected from university students for a transportation mode selection. Data analysis revealed that the two methods, which have different starting points, display different degrees of anchoring bias. Statistical analyses of the weights obtained from the two methods show that, compared to Swing (with a high anchor), SMART (with a low anchor) produces lower weights for the least important attributes, while for the most important attributes, the opposite is true. Despite their differences in anchoring bias, analytical approaches supported by empirical studies suggest that both methods (SMART and Swing) overweigh the less important attributes and underweigh the more important attributes. As such, we examined whether the best-worst method (BWM), which has two opposite anchors in its procedure (a possible promising anchoring debiasing strategy), could produce results that are less prone to anchoring bias. Our findings show that the BWM is indeed able to produce lower weights (compared to SMART and Swing) for the less important attributes and higher weights for the more important attributes. This study shows the vulnerability of MADM methods with a single anchor and supports the idea that MADM methods with multiple (opposite) anchors, like BWM, are less prone to anchoring bias.@en

This paper introduces an advisory-based time slot management system (TSMS) to control truck arrivals at seaport terminals with the aim to reduce congestion at terminal gates. A modeling framework is proposed, developed, and applied to assess the impact of a truck arrival shift for a case study in the Port of Rotterdam. This system is designed to apply control policies on truck inflow while taking the behavioral aspect of truck operating companies (TOCs) into account. Discrete choice modeling is used to infer the time-of-day preferences of TOCs for container pick-ups from the exchange of information between port and hinterland stakeholders. These preferences are used to shift truck arrivals to the off-peak period which consequently reduces the high waiting time of trucks at terminals gates. To evaluate the effectiveness of the designed TSMS, a simulation platform that resembles terminal operations has been developed using discrete-event simulation. For the allocation of trucks to a certain time of day, a choice-based stochastic assignment heuristic is designed to approximate the optimum configuration of the truck arrival shift policy experiment. The optimum truck arrival shift design shows that significant gain can be obtained even at a low shift rate.

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Contemporary innovations in freight transportation and logistics are instrumental in achieving more integrated, efficient, and sustainable services in the global market. While much attention is going to how contemporary innovations, including technology-enabled and management innovations, change the supply of services, little work is done on depicting their changing relationship with freight transportation demand. We present findings from a comprehensive study among Global Fortune 500 companies aimed at understanding what drives the demand for modern transportation services. We investigate the importance of three key service attributes that are growing in importance, i.e., operational control of transport mode, service flexibility and ancillary value-added services. We measure the influence of contextual factors on the choice of service, including supply chain strategy, demand volatility, internal flexibility and industry type. This leads to recommendations for shippers on how they can adjust their supply chains in the future to benefit from new freight services. Our findings also stress the need for the logistics industry to adopt modern service choice approaches.@en

The Physical Internet (PI), a new vision for the future of the global freight transport and logistics system, describes a geographical hierarchy of interconnected networks of networks, from the urban, to the national, the continental, and the global level. Like today, in PI the maritime ports will fulfil roles as continental and global hubs. Differently than ports today, however, decisions to split and bundle cargo across ships and other modes will not be made solely on the basis of long-term agreements by ports, but rather ever more dynamically and in real-time, aiming to reconsolidate shipments within the port area. This implies a need to reconsider the currently used information systems (ISs), and to gain understanding of future requirements to satisfy their needs. We exploit a design science research (DSR) approach to shape these requirements. Among the many components of future ISs, we study ports’ track-and-trace (T&T) capability. The proposed information architecture (IA) enables to integrate T&T capability in PI ports by means of information carried on PI containers into the logistics chain via an open interface platform, which also supports interoperability among the various actors’ ISs. The design is based on the Reference Architecture Model for Industry 4.0 (RAMI 4.0). This model supports the analysis of PI ports in key dimensions along with hierarchical logistics entities, which could be used as a blueprint for IAs of PI ports, globally. We provide insights into the approach's applicability by means of the illustrative case of Teesport, located in Northeast England (United Kingdom).

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Revenue and inventory management play a crucial role in the operational efficiency of food supply chains. The current study investigates dynamic pricing and inventory control policies in a two-level Food Supply Chain (FSC) of growing and deteriorating inventory that involves a rearing farm as the supplier and a retailer where these slaughtered items are prone to deterioration. The rearing farm breeds newborn animals, then slaughters them and sends the items to the retailer. The negative impact of overbreeding is taken into account to preserve the items’ quality and decrease food waste on the supply side. The model is analyzed under decentralized and centralized supply chain scenarios with a profit-sharing contract as the coordination tool in the centralized case. An analytic solution approach based on non-linear convex programming is developed to solve the problem. The developed structure is illustrated through experimental results with a real estimated growth function for broiler chickens. Sensitivity analysis is carried out to investigate the impact of different input parameters. It is shown that the centralized supply chain scenario not only enhances the profit of the supplier and the retailer but also is more desirable for the customers as the selling price of the items decreases in this setting. The results provide decision-makers of each echelon with insights into the features of the studied FSC, including their most influential input parameters, the areas that require further attention, and managerial suggestions under different scenarios.

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The purpose of this paper is to streamline the supply of corn, one of the key ingredients in the production of bioethanol. Using a comprehensive sustainable framework of criteria (including social, economic, and environmental dimensions), the potential locations of corn cultivation in Iran are examined from a multi-criteria decision analysis perspective. To this end, we need to find the importance of the relevant evaluation criteria and a ranking method to rank the potential locations. Best worst method (BWM) is used to determine the weight of the criteria presented in the framework based on the opinion of a sample of Iranian experts, after which the ‘preference ranking organization method for enrichment evaluations II’ (PROMETHEE II) is applied to ranking the different provinces of Iran. To improve the ranking results, we extend the PROMETHEE II by employing a set of piecewise linear value functions, for which the performance of alternatives with respect to the criteria calculated by the piecewise linear value functions is used to determine the amount of deviation in the first step of PROMETHEE II. The results of the hybrid methodology indicate that the presence of water, land cost and air pollution are the most important factors determining the ranking of the alternatives, and that Kordestan is the best province for corn cultivation in Iran.

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