key: cord-0063209-pcrtjeot authors: Naqvi, Mohammad Abbas; Amin, Saman Hassanzadeh title: Supplier selection and order allocation: a literature review date: 2021-05-17 journal: J DOI: 10.1007/s42488-021-00049-z sha: 1aae1d76d5baebc0164ac091fe7c24bd8f4f048b doc_id: 63209 cord_uid: pcrtjeot The goals of procurement managers in every industry usually are acquiring the right materials at the right time, at the right prices and quantities. To achieve these goals, the best suppliers should be selected. Supplier selection and order allocation have been studied extensively in the past. In this paper, we review the peer-reviewed journal publications in this area. The taxonomy in this research includes problem domain and operations research techniques. The problem domain is examined in three subcategories including Literature Reviews (LR), Deterministic Optimization (DO) models, and Uncertain Optimization (UO) models. Then, observations, recommendations, and future research directions in the field of supplier selection and order allocation are discussed. Purchasing and procurements are important activities in every organization. Supplier Selection and Order Allocation (SSOA) are prominent elements of purchasing and procurement . Both qualitative and quantitative factors such as quality, cost, and delivery time should be considered in the supplier selection problem . Therefore, supplier selection is a Multi-Criteria Decision-Making (MCDM) problem (Cheraghalipour and Farsad 2018; Moheb-Alizadeh and Handfield 2019) . Cost saving and minimization of risks can be achieved by using suitable supplier selection methods Arabsheybani et al. 2018) . Some authors have combined supplier selection and order allocation together to solve these two problems simultaneously (e.g., Babbar and Amin 2018) . Supplier selection and order allocation are very important in green supply chain management considering sustainability and environmental factors . Sustainable supplier selection encompasses cost, environmental, and social criteria and supplier's performance history Ghadimi et al. 2018) . Supplier selection is a strategic process in organizations, and plays a critical role in the success of them . Offering quantity discount is an important feature in the selection of the best suppliers. Therefore, each company can achieve low cost while allocating large volume orders to the suppliers . In this paper, the related peer-reviewed journal papers have been found and reviewed via search in globally recognised databases such as ScienceDirect (Elsevier), Taylor and Francis, and Google Scholar. The main keyword is "supplier selection and order allocation" which is used to search related papers published between 2015 and 2020. As a result, 92 articles are analysed. The majority of other literature review papers in this field just have focused on supplier selection, and order allocation has been ignored. In addition, they have been written some years ago, and there is a need to have an updated literature review paper about supplier selection and order allocation. The structure of our paper is new among those literature review papers. Considering uncertainty in the reviewed papers and reviewing the applied operations research techniques are other main characteristics of our paper. The other parts of this paper are as follows. The taxonomy and classification of the literature are provided in Section 2. Then, some observations and discussions are mentioned in Section 3. In addition, the related conclusions and future research avenues are provided in Section 4. Two dimensions are utilized in this review paper to categorize the papers. The first one is the problem domain. Besides, the second one is the operations research (optimization) methods. This classification is useful to analyze the supplier selection and order allocation problem based on both conceptual and mathematical viewpoints. The problem domain comprises three subsections: Literature Reviews (LR), Deterministic Optimization (DO) models, and Uncertain Optimization (UO) models. Table 1 includes the related papers. Some authors have published literature review papers in the field of supplier selection and order allocation. Govindan et al. (2015) reviewed green purchasing and green supplier selection process of some articles published between 1997 and 2011. They found that Analytic Hierarchy Process (AHP) is the most popular MCDM method for assessing green suppliers. In addition, Fuzzy AHP is very popular in the environmental management systems. Yildiz and Yayla (2015) reviewed 91 articles that have been published between 2001 and 2014 about supplier selection. They stated that quality and cost are the most significant criteria in the supplier selection problem. Wetzstein et al. (2016) reviewed several papers in the supplier selection field published between 1990 and 2015. They mentioned that there are future research avenues in considering green and sustainable factors. Karsak and Dursun (2016) reviewed 149 articles published between 2001 and 2013 concentrating nondeterministic analytical methods (i.e., stochastic/fuzzy) under imprecise data. Simić et al. (2017) examined the last 50 years (50th anniversary of fuzzy sets theory established by Lotfiali Askar Zadeh in 1965) of articles in supplier selection and evaluation that are based on fuzzy sets theory, fuzzy models, and fuzzy hybridization. The authors combined individual and integrated approaches to effectively review the fuzzy supplier selection methods. The authors selected 54 papers published in the reputable journals. Alkahtani and Kaid (2018) studied some journal papers published between 1995 and 2018 focusing on supplier selection. They provided information about the trends, the research gaps, and the selection criteria in the supplier selection field. Ocampo et al. (2018) reviewed 240 articles from peer-reviewed journals published between 2006 and 2016 focusing on the applications of different approaches for supplier selection and evaluation which include individual and hybrid methods. The authors indicated that the novel methods in the literature include uncertainty, risk analysis, and sustainability factors. Aouadni et al. (2019) reviewed 270 articles published between 2000 and 2017 about supplier selection and order allocation. In their paper, about 17 %, 9 %, and 7 % of the reviewed papers were about AHP, TOPSIS, and ANP methods, respectively. They mentioned that Wong (2020) fuzzy multiple-objective programming is a popular method in this area. In addition, some papers have used genetic algorithm to determine the orders. Chai and Ngai (2019) reviewed SSOA papers published among 2013 and 2018. They brought to light that MCDM methods and optimization are the most popular techniques for supplier selection and order allocation. In this part, deterministic optimization methods for supplier selection and order allocation are discussed. We provide some information about the publications that have received several citations. Other publications are written and mentioned in the following table. Sodenkamp et al. (2016) used a novel approach (trade-off mechanism) because the current multi-objective methods were not capable to create positive and negative performance synergies. Bohner and Minner (2017) disscussed a mixed-integer linear programming model for solving the intricate issue of supplier selection by having a backup supplier who is not cost effective. However, it minimizes the risk related to the stock out condition. Nourmohamadi studied purchasing decision-making through a TOPSIS method and a multi-choice goal programming model. In addition, they developed rough set theory and grey system. Moheb-Alizadeh and Handfield (2019) constructed a multiobjective optimization model for a manufacturer of automobile transmission systems for order allocation considering minimization of the CO 2 emissions. Nazeri et al. (2019) proposed a multi-objective model to test effective ranking in military's SSOA for outsourcing of hazardous materials. Wang et al. (2020) implemented carbon emission trading schemes using analytic network process-integer programming model and stipulated approach. They minimized cost and carbon emissions. The deterministic optimization models of supplier selection and order allocation are classified in Table 2 according to the multiple elements (sets) including parts, products, periods, suppliers, and scenarios. In some papers, it has been assumed that the parts can be assembled to make a product. Products usually represent the final products that can be sold in the markets. In addition, some papers have considered different periods such as months in their mathematical models. Besides, multiple potential suppliers have been considered by some authors. Furthermore, some authors have assumed different scenarios to analyze the problem under uncertainty. In this part, we mention some important publications that have developed uncertain optimization models and have received several citations. Other papers are mentioned in the following two tables. The paper of Azadnia et al. (2015) has been cited by more than 200 papers in Google Scholar. In this article, the authors introduced sustainable supplier selection by adding occupational health and safety management system. Those subcriteria are important components in sustainable supplier criteria. The authors utilized a fuzzy AHP and a rule based weighted fuzzy approach. They selected a sustainable supplier using a multi-product lot sizing order model. Çebi and Otay (2016) proposed a two-stage fuzzy method including fuzzy MULTIMOORA and fuzzy goal programming for the supplier selection and order allocation problem. They considered green supplier selection in the beverage industry. Govindan and Sivakumar (2016) studied the selection of the best supplier by minimizing the greenhouse gas emissions using a fuzzy TOPSIS and a multi-objective method. They determined the ranks of the green suppliers, and they classified the potential suppliers. Pazhani et al. (2016) proposed a mathematical model to find the optimal inventory level and showed that cost could be minimized if the transportation cost is considered in the objective. They also discussed the benefits of the integrated inventory management system approach comparing the sequential approach for solving the supplier selection problem. Ghorabaee et al. (2017) stated that a novel EDAS technique and interval type-2 fuzzy sets lead to a good multi-criteria green supplier selection model. Hamdan and Cheaitou (2018) proposed a novel two-stage QFD model and an optimization model for SSOA. They solved the optimization model using GAMS software. Their method can handle the vagueness and uncertainty considering qualitative and quantitative criteria. Ahmadi and Amin (2019) introduced the supplier selection and order allocation in closed-loop network of cellular phone industry in Toronto Canada. They developed a fuzzy based solution approach using IBM ILOG CPLEX 12.7.1.0 software. developed a bi-objective mixed-integer programming model (stochastic) for the SSOA problem. They illustrated the application of the model in the automotive industry. introduced F-AHP and F-PROMETHEE to study uncertainty in the decision-making environment. Govindan et al. (2020) described sustainability through incorporating circular supplier selection and order allocation. They combined all activities such as waste reduction in transportation. Hasan et al. (2020) developed a Decision Support System (DSS) for companies operating under logistics industry 4.0. Jia et al. (2020) developed a robust optimization goal programming model for a steel company. They solved the problem by CPLEX, and optimized it considering the total cost, CO 2 emission, and environmental objectives. Kaur and Singh (2020) proposed a model with consideration of risks and disruption (both natural and man made), suitable for industry 4.0 environment. The uncertain optimization models are categorized in Table 3 according to the multiple elements. In addition, the uncertainty sources are shown in Table 4 ; Fig. 1 . Demand, capacity, and cost are the major sources of uncertainty in the reviewed papers. We divide the references according to the operations research (optimization) techniques in Table 5 . Several authors have utilized hybrid techniques in this field. Table 6 includes the types of the objective functions in different papers. In addition, single objective and multi-objective functions are illustrated in Fig. 2 . In this part, observations and recommendations according to the reviewed papers are provided. In this paper, we discussed three domains of supplier selection and order allocation including literature reviews, deterministic optimization models, and uncertain optimization models. The most popular domain is the uncertain optimization models (73 % of the papers). Deterministic optimization models (17 % of the papers), and Literature reviews (10 % of the papers) domains have the next ranks. According to Table 4 ; Fig. 1 , the most popular sources of uncertainty are demand, capacity, and cost, respectively. Among them, demand has been considered more than the other factors (29 % of the papers). This parameter usually affects the order allocation significantly, and it is considered as one of the constraints of the optimization models. Based on the information in Table 5 , Fuzzy TOPSIS, Fuzzymulti objective programming, Stochastic programming, and Mixed-integer linear programming are the most popular techniques in the literature of SSOA. Fuzzy TOPSIS is a useful technique to determine the weights (importance) of the suppliers. Fuzzy sets theory enables researchers to consider uncertainty in the parameters. Fuzzy multi-objective programming considers uncertainty and the effects of some objectives on the problem. There are several stochastic programing models in the literature which are based on the probabilities in the SSOA problem. Mixed-integer linear programming also have been utilized in the literature because it can handle both non-negative and 0-1 variables. There are several techniques for solving multi-objective problems. Based on our observation, weighted-sums method is the most popular one. Several authors also have utilized goal programming and ɛ-constraints method to solve multiobjective SSOA problems. The applications of the models have been categorized in Table 7 . Several authors have considered case studies. "Automotive industry" is a popular application in the supplier selection and order allocation field. Table 8 includes the information related to the names of the journals. These journals have published papers related to SSOA. "Journal of Cleaner Production", "Computers & Industrial Engineering", "International Journal of Production Research", "International Journal of Production Economics", and "Expert Systems with Applications" have published several papers in this field. Table 9 includes the classification of the papers based on year and the mentioned three domains. The journal papers from 2015 to 2020 have been examined in this research. It is noticeable that Arabzad et al. (2015) Max total stake-holder satisfaction score Scott et al. (2015) Min total cost Bohner and Minner (2017) Max total profit Cui et al. (2015) Min outsourcing cost Fu et al. (2016) Max total score Beauchamp et al. (2015) Max over all performance of the system Hu et al. (2018) Min deviation (cost, CO 2, emission, society and supplier's value) Jia et al. (2020) Min cost Esmaeili-Najafabadi et al. (2019), Jain et al. (2015) , Kuo et al. (2015) , Meena and Sarmah (2016) , Mohammaditabar and Ghodsypour (2016) , Pazhani et al. (2016) , Torabi et al. (2015) , Wang et al. (2020) Max conditional service at risk Sawik ( (4) Min cost, late delivery, rate of defects, Max total utility of the system Çebi and Otay (2016) (2) Min cost, Max total score Cheraghalipour and Farsad (2018) (2) Max efficiency of supplier, Max order quantity Dotoli et al. (2015) (2) Min total cost, Max green value Duan et al. (2019) (3) Min total cost, carbon emission, Max total purchasing value Feng and Gong (2020) (2) Min cost, Max supplier's performance Ghadimi et al. (2018) (3) Max positive score of supplied material, Min negative score of supplied material and cost Ghorabaee et al. (2017) (2) Min total cost, Max total value purchasing Bektur (2020), (5) Min total cost, total quality rejection, late delivery, waste, total carbon emission Govindan and Sivakumar (2016) (4) Min cost, defective items, delay in delivery, Max vendor performance Gupta et al. (2016) (4) Min price, delay, Max coverage of customer's suppliers, supplier evaluation more realistic Hajikhani et al. (2018) (2) Max total preference, Min total cost (2) Max total performance, Min total cost Kaur and Singh (2020) ; Hamdan and Cheaitou (2017a, b) (3) Max green purchasing, Min cost, Min defects Hamdan and Jarndal (2017) (2) Max profit, Min loss Hamdi et al. (2016) our paper has been written in 2020. Therefore, the number of the published journal papers in 2020 are limited in Table 9 . In this research, three problem domains including literature reviews, deterministic optimization models, and uncertain optimization models have been considered, and the related papers have Tirkolaee et al. (2020) (2) Min rejects, late delivery Tsai (2015) (2) Max total sustainability, Min total cost Vahidi et al. (2018) (2) Min total cost, and Min total purchase value Prasanna Venkatesan and Goh (2016) (7) Max trend value, average value, green consensus, market bonus, Min risk, cost, market penalty Wong (2020) (2) Min total cost and shortages Govindan et al. (2020) Fig . 2 Mono-objective and multi-objective models been gathered and analyzed. In addition, these papers (92 publications between 2015 and 2020) have been classified according to the operations research methods. Furthermore, observations have been provided and discussed. We have observed that most of the mathematical models in SSOA belong to the uncertain optimization models category. Supplier selection and order allocation methods may create competitive advantages for companies, and at the same time, poor selection of the suppliers may result in the failure of the companies. The basic criteria for supplier selection include cost, quality, and time. Recently, more green and environmental factors such as minimization of carbon emissions have been considered in the SSOA process. There are numerous directions for future research in the SSOA problem. Some of them are as follow: (i) Usually a few sources of uncertainty have been considered in the optimization models of order It is useful to consider several sources of uncertainty simultaneously using advanced methods such as robust optimization. (ii) Most of the SSOA papers have focused on manufacturing systems such as automobile It is valuable to consider SSOA in service industry such as healthcare systems (e.g., hospitals). (iii) Fuzzy sets theory and fuzzy logic have been combined with other techniques to handle However, there are some practical challenges in applying these methods in More case studies can be considered in this area to show and discuss the applications of these methods. (iv) Under special circumstances such as COVID-19, the normal supplier selection and order allocation may not lead to excellent Developing new methods for these situations can be an avenue of future research. (v) There are several parameters such as cost, capacity, and demand in the optimization models of the order These parameters can be estimated using advanced forecasting techniques such as machine learning, deep learning, and neural To our knowledge, this area of research is new, and has not been explored in the SSOA papers. Cheraghalipour and Farsad Bohner and Minner Nourmohamadi Shalke et Kilici and Yalcin (2020) Moghaddam (2015a, b) Kaur and Singh (2020) Moheb-Alizadeh and Handfield Shadkam and Bijari Bektur (2020) Moheb-Alizadeh and Handfield Kaur and Singh (2020) Shadkam and Bijari Sawik (2016) References Demand Ahmadi and Amin Hosseini and Nezhad Meena and Sarmah Shadkam and Bijari Moheb-Alizadeh and Handfield Prasanna Venkatesan and Goh Integrated dynamic vendor selection and order allocation problem for the time dependent and stochastic data An integrated chance-constrained stochastic model for a mobile phone closed-loop supply chain network with supplier selection Supplier selection and order allocation decisions under quantity discount and fast service options Supplier selection in supply chain management: a review study Sustainable supplier selection and order allocation under risk and inflation condition A systematic review on supplier selection and order allocation problems An integrated fuzzy MOORA method and FMEA technique for sustainable supplier selection considering quantity discounts and supplier's risk Employing fuzzy TOPSIS and SWOT for supplier selection and order allocation problem A multi-objective mathematical model for sustainable supplier selection and order lot-sizing under inflation An integrated approach of fuzzy quality function deployment and fuzzy multi-objective programming tosustainable supplier selection and order allocation Sustainable supplier selection and order lot-sizing: an integrated multi-objective decisionmaking process A multi-objective mathematical model integrating environmental concerns for supplier selection and order allocation based on fuzzy QFD in beverages industry Supplier selection and order allocation based on integer programming An integrated methodology for the selection of sustainable suppliers and order allocation problem with quantity discounts, lost sales and varying supplier availabilities Supplier selection under failure risk, quantity and business volume discounts A two-stage fuzzy approach for supplier evaluation and order allocation problem with quantity discounts and lead time Decision-making techniques in supplier selection: Recent accomplishments and what lies ahead A bi-objective sustainable supplier selection and order allocation considering quantity discounts under disruption risks: A case study in plastic industry Optimal supplier selection and order allocation for multi-product manufacturing featuring customer flexibility September) Integrated supplier selection and order allocation under uncertainty in agile supply chains An extended alternative queuing method with linguistic Z-numbers and its application for green supplier selection and order allocation A joint supplier selection and order allocation model with disruption risks in centralized supply chain Integrated linguistic entropy weight method and multi-objective programming model for supplier selection and order allocation in a circular economy: A case study A robust optimisation approach to the problem of supplier selection and allocation in outsourcing A multi-agent systems approach for sustainable supplier selection and order allocation in a partnership supply chain A new multi-criteria model based on interval type-2 fuzzy sets and EDAS method for supplier evaluation and order allocation with environmental considerations A decision framework for sustainable supplier selection and order allocation with lost sales Green supplier selection and order allocation in a low-carbon paper industry: integrated multi-criteria heterogeneous decision-making and multi-objective linear programming approaches Multi criteria decision making approaches for green supplier evaluation and selection: a literature review An integrated hybrid approach for circular supplier selection and closed loop supply chain network design under uncertainty A weighted possibilistic programming approach for sustainable vendor selection and order allocation in fuzzy environment A fuzzy multi-objective multi-product supplier selection and order allocation problem in supply chain under coverage and price considerations: An urban agricultural case study Green supplier selection and order allocation using an integrated fuzzy TOPSIS, AHP and IP approach Dynamic green supplier selection and order allocation with quantity discounts and varying supplier availability Supplier selection and order allocation with green criteria: An MCDM and multi-objective optimization approach A two-stage green supplier selection and order allocation using AHP and multi-objective genetic algorithm optimization Supplier selection and order allocation under disruption risk Resilient supplier selection in logistics 4.0 with heterogeneous information Developing an optimal policy for green supplier selection and order allocation using dynamic programming Resilient supplier selection and optimal order allocation under disruption risks Joint decision model of supplier selection and order allocation for the mass customization of logistics services A mixed integer programming model for supplier selection and order allocation problem with fuzzy multiobjective An improved multi-choice goal programming approach for supplier selection problems A Chaotic Bee Colony approach for supplier selection-order allocation with different discounting policies in a coopetitive multi-echelon supply chain Sustainable supplier selection and order allocation: Distributionally robust goal programming model and tractable approximation Taxonomy and review of non-deterministic analytical methods for supplier selection Multi-stage hybrid model for supplier selection and order allocation considering disruption risks and disruptive technologies A mathematical programming model for a multi-objective supplier selection and order allocation problem with fuzzy objectives Sustainability in supplier selection and order allocation: combining integer variables with Markowitz portfolio theory Sustainable supplier selection and order allocation: a fuzzy approach Modified two-phase fuzzy goal programming integrated with IF-TOPSIS for green supplier selection A fuzzy AHP and fuzzy multiobjective linear programming model for order allocation in a sustainable supply chain: A case study The integration of association rule mining and artificial immune network for supplier selection and order quantity allocation Assessing business impacts of agility criterion and order allocation strategy in multi-criteria supplier selection An integrated model for solving problems in green supplier selection and order allocation Supplier selection and demand allocation under supply disruption risks Group multi-criteria supplier selection using combined grey systems theory and uncertainty theory A preemptive fuzzy goal programming model for generalized supplier selection and order allocation with incremental discount Fuzzy multi-objective model for supplier selection and order allocation in reverse logistics systems under supply and demand uncertainty Supplier selection and order allocation in closed-loop supply chain systems using hybrid Monte Carlo simulation and goal programming A supplier-selection model with classification and joint replenishment of inventory items An integrated methodology for a sustainable two-stage supplier selection and order allocation problem A hybrid MCDM-FMOO approach for sustainable supplier selection and order allocation An integrated chanceconstrained stochastic model for efficient and sustainable supplier selection and order allocation Sustainable supplier selection and order allocation: A novel multi-objective programming model with a hybrid solution approach Supplier selection and order allocation using a stochastic multi-objective programming model and genetic algorithm Supplier selection and evaluation in military supply chain and order allocation Analyzing pricing, promised delivery lead time, supplier-selection, and ordering decisions of a multi-national supply chain under uncertain environment Sustainable supplier selection and order allocation through quantity discounts Recent approaches to supplier selection: a review of literature within 2006-2016 A regional information-based multiattribute and multi-objective decision-making approach for sustainable supplier selection and order allocation A serial inventory system with supplier selection and order quantity allocation considering transportation costs Multi-objective supplier selection and order allocation under disruption risk Supplier selection and order allocation in supply chain Mokhatab Rafiei F (2020) Supplier Selection and Order Allocation with Lean Manufacturing Criteria: An Integrated MCDM and Bi-objective Modelling Approach A concurrent optimization model for supplier's selection, tolerance and component allocation with fuzzy quality loss On the risk-averse optimization of service level in a supply chain under disruption risks A decision support system for supplier selection and order allocation in stochastic, multistakeholder and multi-criteria environments Multi-objective simulation optimization for selection and determination of order quantity in supplier selection problem under uncertainty and quality criteria 50 years of fuzzy set theory and models for supplier assessment and selection: A literature review Modeling synergies in multi-criteria supplier selection and order allocation: An application to commodity trading A weight-consistent model for fuzzy supplier selection and order allocation problem Vendor selection and order allocation using an integrated fuzzy mathematical programming model A novel hybrid method using fuzzy decision making and multiobjective programming for sustainable-reliable supplier selection in two-echelon supply chain design Resilient supplier selection and order allocation under operational and disruption risks Order allocation for multi-item sourcing with supply disruptions in shipment quality and delivery Sustainable supplier selection and order allocation under operational and disruption risks Supplier selection and order allocation under a carbon emission trading scheme: a case study from China A systematic assessment of supplier selection literature-state-of-theart and future scope Dynamic procurement risk management with supplier portfolio selection and order allocation under green market segmentation Multi-criteria decision-making methods for supplier selection: A literature review Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Alegoz and Yapicioglu (2019) Acknowledgements This research has been supported by a NSERC Discovery grant. On behalf of all authors, the corresponding author states that there is no conflict of interest. (2) Max total value of purchase, total profit Hosseini and Nezhad (2019) (2) Max distance between all pairs of supplier locations, Min cost (3) Min rejection, late delivery, purchasing cost Hu et al. (2016) (3) Min cost, rejects, late deliveries Jadidi et al. (2015) (3) Min cost, Max quality, and delivery reliability Kazemi et al. (2015) (3) Min cost, supply risk, Max sustainability Kellner and Utz (2019) (6) Min cost, risk, inflation effect, Max economic score, environmental score, social score Khoshfetrat et al. (2019) (2) Max satisfaction degree of the goal, Max total weighted satisfaction degreeKilici and Yalcin (2020) (7) Min carbon emission, waste, order cost, percentage of rejection, percentage of late delivery, Max percentage of profit Kumar et al. (2017) (4) Min cost, delay, defect rate, Max organizational utility Lo et al. (2018) (2) Min cost, Min lead time Memon et al. (2015) (3) Min total cost, Max total value of purchase and total achievement degree (2015), Torabi et al. (2015) , Prasanna Venkatesan and Goh (2016)