Considering the literature analysis described in the Section 3.5, we identify in this section some research gaps. Moreover, research opportunities and aLiterature Mapare also provided.
Figure34illustrates the Literature Map resulted from thisSLR, providing an overview of distinct pro-posed formulations of the safety stock problem in the literature. TheLiterature Mapconsists of four levels of iterations. The first level shows the literature gaps identified in the literature. The second level describes the safety stock problems, namely Safety stock dimensioning, Safety stock management and Safety stock placement (allocation or positioning). The third level describes several uncertainties factors and risks as-sociated with the procurement process and therefore considered as input to address safety stock related problems, namely Demand uncertainty, Lead-time Uncertainty, Yield uncertainty and Multiple uncertain-ties and risks. The last level represents different approaches followed, as well as scientific contributions that use these same approaches to solve safety stock related problems.
Analysing Figure34we highlight that:
• In general, the Optimization approach is the most used to address safety stock problem and tech-niques such as heuristics, dynamic programming and mixed-integer nonlinear programming are the most used techniques related to the Optimization approach (as described in Table7).
• Demand uncertainty is the most common uncertainty factor in the proposed inventory models. On the other hand, there is a lack of studies that considered the lead time uncertainty, as well as the yield uncertainty.
• Recent data-driven approaches, such asBAandBig Data Analytics (BDA), are producing a strong impact in diverse research fields, including supply chain management. However,BAandBDAhas not yet been explored to solve safety stock related problems.
After conducting a critical literature analyses, described in section3.5, some research gaps are iden-tified and discussed herein, as well as the research opportunities:
• Several studies in the literature and leading supply chain books, as well as inventory management software tools, assume that the demand during the lead time follows a normal distribution. Yet, several authors have already warned that such assumption may be flawed because lead time de-mand is often skewed (see, Janssens and Ramaekers (2011), Lee and Rim (2019), and Ruiz-Torres and Mahmoodi (2010)). This statistical assumption can lead to higher service level than desired, resulting an overestimation of safety stock and consequently higher inventory costs (Ruiz-Torres
& Mahmoodi, 2010). Hence, in practice, future demands must be forecasted based on historical observations.
• The majority of peer-reviewed articles focus on determining safety stock/inventory based on statisti-cal parameters (e.g., standard deviation or mean of demand) and simplifications (e.g., distribution
of statistical parameters, parameters are known) (Schmidt et al.,2012). There is a lack of articles that focus on providing dynamic models that consider the knowledge of future volatility of param-eters for determining safety stock. More research is needed to explore not only the application of more realistic safety stock closed-form stochastic approaches considering the variation of forecast-ing errors rather than the variation of demand, especially in multi-product multi-echelon inventory management settings, but also to study the benefits of such safety stock methods in case studies with practical interest. Moreover, empirical non-parametric approaches for estimating the variabil-ity of forecast errors (see, Trapero et al. (2019a), Gonçalves et al. (2021) and Trapero et al. (2019b)) could be further exploited using for example business analytics techniques. Note thatBAandBDA techniques allow the use of predictive analytics for applying machine learning techniques on real data in order to learn or obtain knowledge from data and predict future supply chain demand based on historical and current data. In this context, the prediction capabilities could be also optimized using metaheuristics.
• Several methods for calculating safety stock can be found in the literature based on two main service level measures, namely cycle service level and fill rate. Although the cycle service level has been criticized for not being relevant from a customer perspective and also not recommended for inventory control practice (Axsäter, 2015; Jonsson & Mattsson, 2019), it remains the most used in the literature, as illustrated in Figure 33. Several studies and supply chain books considered theCSLmeasure because, unlike theFRmeasure, it is of easy computation. Chopra and Meindl (2016), Tyworth (1992), and Vandeput (2020) argued the necessity of transition fromCSLtoFR because fill rate is a more relevant measure.
• The inventory control problem under lead-time uncertainty is not sufficiently studied, particularly in assembly networks (M. A. Louly et al., 2008). Demand uncertainty is the most considered factor in the literature (see Figure 26 and 34). Several studies considered constant lead time, which is not realistic for major of supply chain environments due to the unexpected events that can occur causing random delays. These delays may require to incurring the special/premium freight so that to avoid stockouts and consequently an extra cost for organizations. Moreover, there are few studies that address the safety stock problems onMRPenvironment considering the lead time uncertainty. Herein, empirical non-parametric approaches could also be exploited to address lead-time uncertainty.
• The impact of order crossover in determining safety stock is under-researched. Recent studies in the literature demonstrated not considering order crossover can be translated to larger inventory costs (Chatfield & Pritchard,2018). Riezebos (2006) argued that the modern supply chain needs to address the issues concerning expected order crossovers, generally neglected in inventory control literature. Modern supply chains facing the growing occurrence of order crossover, as well as with the increasing importance of service performance (Chatfield & Pritchard, 2018). Chatfield and
Pritchard (2018) stated that ”classical inventory modelling methods should be re-examined and perhaps reformulated in order to accommodate the possibility of order crossover”.
• There is a lack of research studies that address the safety stock problem by considering the variation of demand over the PLCand seasonality (Strohhecker & Größler, 2019). In this review, the only works addressing this issue are Hsueh (2011) and L. Yue et al. (2016). The PLC is becoming smaller due to technological advances as happens for instance in the mobile phone and electronics components industries. During thePLC, the product demand may increase rapidly at the ramp-up stage, then it stabilizes and starts decreasing at the decline stage. Several traditional inventory models considered that this increase of product demand as stationary, instead of a change in demand in a certain stage of the product life cycle. An accurate demand forecasting is crucial for real-world application (directly effects the safety stock level, as well as the total inventory costs) and sometimes is very difficult to be estimated under short product life cycle (for instance, fashion products such as shoes and clothing). Techniques such asBA andBDAcould be helpful to cope with this issue. For instance, Huang et al. (2016) highlight that companies can take advantage of big data for coping with demand surges. In effect, BDAis producing a great impact in various research fields includingSCM, providing tools for supporting and enabling strategic and operational decision-making.
67%
33%
CSL FR
Figure 33: Distribution of Service level measure adopted
LEGEND Safety stock
dimensioning Safety stock
management Safety stock
placement
Mathematical Modeling
Optimization Simulation
Simulation-based optimization Demand
uncertainty Lead-time
uncertainty Multiple uncertainties
& risks Yield
uncertainty
is part of uses is related to Ohno et al. (1995)
Adenso-Diaz (1996) Krupp, 1997 Grubbström et al. (1999)
Buzacott (1999) Grubbström (1999)
Urban (2005) Wang et al. (2010)
Hsueh (2011) Jodlbauer & Reitner (2012)
Moeeni et al. (2012) Braglia et al. (2013) Van Donselaar &
Broekmeulen (2013) Lukinskiy & Lukinskiy (2017)
Lee & Rim (2019) Dey (2019) Zhang et al. (2019)
Martinelli & Valigi (2004) Sana & Chaudhuri (2010) Cobb (2016)
Campbell (1995) Talluri et al. (2004) Vernimmen et al. (2008)
Inderfurth (2009) Ozguven & Ozbay (2012)
Braglia et al. (2014) Disney et al. (2016) Lu et al. (2016) Caceres et al. (2018)
Zhao et al. (2001) Caridi & Cigolini (2002b) Brander & Forster (2006) Reichhart et al. (2008) Sitompul et al. (2008) Boulaksil et al. (2009) Zhou & Viswanathan (2011)
Boulaksil (2016) Trapero et al. (2019a) Bahroun & Belgacem (2019)
Abdel-Malek et al. (2005)
Guide V.D.R & Srivastava (1997) Hung & Chang (1999) Inderfurth & Vogelgesang (2013)
Kumar & Evers (2015) Kumar & Kumar (2018) Jonsson & Mattsson (2019) Strohhecker & Gröβler (2019)
Kim et al. (2005) Zhou & Viswanathan (2011)
Monthatipkul et al. (2010) Feng et al. (2011)
Glock (2012) Chen et al. (2013) Ganster et al. (2014) Tempelmeier & Bantel (2015)
Torkul et al. (2016) Woener et al. (2018b) Kumar & Aouam (2018a)
Benbitour et al. (2019) Brunaud et al. (2019)
Schneider (1995) Sellitto (2018)
de Armas & Laguna (2019) Molinder (1997) Bollapragada et al. (2004) Simchi-Levi & Zhao (2005) Jung et al. (2008) Hayya et al. (2009) Desmet et al. (2010) Kristianto et al. (2012) Avci & Selim (2017) Chatfield & Pritchard (2018)
Woener et al. (2018b)
Helber et al. (2013) Yue & You (2013)
Albrecht (2014) Klosterhalfen et al. (2014a) Klosterhalfen et al. (2014b) Moncayo-Martinez et al. (2014)
Rappold & Yoho (2014) Chen & Li (2015) Keskin et al. (2015)
McNair (2015) Petridis (2015) Chaturvedi &
Martínez-De-Albéniz (2016) Grace Hua & Willems (2016)
Grahl et al. (2016) Huang et al. (2016) Moncayo-Martínez et al. (2016)
Sricastav & Agrawal (2016) Li et al. (2017) Mou et al. (2017) Prak et al. (2017) Ross et al. (2017) Saad et al. (2017) Shuster Puga & Tancrez (2017)
van der Rhee et al. (2017) Hong et al. (2018a)
Negahban &
Dehghanimohammadabadi (2018) Kumar & Aouam (2018a)
Shahabi et al. (2018) Tookanlou & Wong (2019)
Zahraei & Teo (2018) Altendorfer (2019) Ben-Ammar et al. (2019)
Kumar et al. (2019) Prawira et al. (2019) Trapero et al. (2019b)
Chandra & Grabis (2008) Louly et al. (2008) Zadeh et al. (2016) Song (2017) Taleizadeh et al. (2017) Sarkar & Sarkar (2019) Louly & Dolgui (2009)
Digiesi et al. (2013) Sellitto (2018)
Swaminathan & Tayur (1998) Tyworth & O'Neill (1997)
Lin et al. (2000) Chung et al. (2005) Katircioglu et al. (2007) Vanteddu et al. (2007) Tang et al. (2008) Kanet et al. (2010) Teimoury et al. (2010) Taleizadeh et al. (2011) Uthayakumar & Parvathi (2011)
Epstein et al. (2012) Osman & Demirli (2012) Kristianto & Zhu (2013) Humair et al. (2013) Zhang et al. (2014) Zhou & Chao (2014) Iida (2015) Keskin et al. (2015)
McNair (2015) Xiao et al. (2015) Chaturvedi &
Martínez-De-Albéniz (2016) Hua & Willems (2016) Graves & Schoenmeyr (2016)
Xu et al. (2016) Saad et al. (2017) Sonntag & Kismüller (2017)
Ghafour (2018) Bem-Ammar et al. (2019)
De Smet et al. (2019) Schuster Puga et al. (2019) Inderfurth (1995)
Ohno et al. (1995) Grubbström & Molinder (1996)
Chan (1997) Li et al. (1997) Minner (1997) Grubbström (1998) Inderfurth & Minner (1998)
Hsu & Wang (2001) Shen et al. (2003) Cao & Silver (2005) Chung et al. (2005) Hoque & Goyal (2006) Bossert & Willems (2007) Katircioglu et al. (2007) Monthatipkul &
Yenradee (2007) Persona et al. (2007) Graves & Willems (2008) Kaminsky & Kaya (2008) Manary & Willems (2008) Ozsen et al. (2008) You & Grossmann (2008) Kanyalkar & Adil (2009) Manary et al. (2009) Neale & Willems (2009) Schoenmeyr & Graves (2009)
Kanet et al. (2010) Nasiri et al. (2010) Yao et al. (2010) You & Grossmann (2010) Janssens & Ramaekers (2011)
Liao et al. (2011) Tian et al. (2011) You & Grossmann (2011)
Funaki (2012) Jodbauer & Reitner (2012)
Beutel & Minner (2012) Shang (2012)
Dynamic models Empirical
non-parametric approaches
Demand over PLC not sufficiently
studied Order crossover
Lead time uncertainty
Figure 34: Literature Map