Technical Note Incorporating human learning into a fuzzy EOQ inventory model with backorders q Nima Kazemi a,⇑ , Ehsan Shekarian a , Leopoldo Eduardo Cárdenas-Barrón b , Ezutah Udoncy Olugu a a Center for Product Design and Manufacturing (CPDM), Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Wilayah Persekutuan, Malaysia b School of Engineering and Sciences, Tecnológico de Monterrey, E. Garza Sada 2501 Sur, C.P. 64849, Monterrey, N.L., Mexico article info Article history: Received 14 September 2014 Received in revised form 2 February 2015 Accepted 8 May 2015 Available online 16 May 2015 Keywords: EOQ Backorders Human learning Fuzzy inventory management Learning in fuzziness abstract Even though publications on fuzzy inventory problems are constantly increasing, modelling the decision maker’s characteristics and their effect on his/her decisions and consequently on the planning outcome has not attracted much attention in the literature. In order to fill this research gap and model reality more accurately, this paper develops a new fuzzy EOQ inventory model with backorders that considers human learning over the planning horizon. The paper is an extension of an existing EOQ inventory model with backorders in which both demand and lead times are fuzzified. Here, the assumption of constant fuzzi- ness is relaxed by incorporating the concept of learning in fuzziness into the model considering that the degree of fuzziness reduces over the planning horizon. The proposed fuzzy EOQ inventory model with backorders and learning in fuzziness has a good performance in efficiency. Finally, it is worth mentioning that learning in fuzziness decreases the total inventory cost. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Lot-sizing inventory models (i.e. economic order/production quantity (EOQ/EPQ)) have extensively been studied in the inven- tory management literature since the EOQ inventory model was introduced in 1913. It is important to note that a variety of inven- tory models have appeared with the aim to model reality more precisely. Readers are referred to Glock, Grosse, and Ries (2014) for a comprehensive review of the lot-sizing problem. Investigating uncertainty in inventory replenishment decisions, and in particular modeling it using stochastic or fuzzy set theory, has been one of the extensions that has received wide attention by several researchers such as Kazemi, Ehsani, and Jaber (2010), Alinovi, Bottani, and Montanari (2012), Shekarian, Glock, Pourmousavi Amiri, and Schwindl (2014a), Shekarian, Jaber, Kazemi, and Ehsani (2014b), Soni and Patel (2015), and Kazemi, Olugu, Abdul-Rashid, and Bin Raja Ghazilla (in press), just to name a few recent works. Björk (2009) developed an EOQ inventory model with backorders considering fuzzy demand and lead times, where the well-known triangular fuzzy numbers are used. The author were used an analytical approach to derive an optimal policy for the fuzzy case. A very restrictive assumption in Björk (2009) is that the values of fuzzy demand and lead times are con- stant during the planning horizon. However, this is not a valid assumption in some cases. Glock, Schwindl, and Jaber (2012) stated that as time goes by during the planning period, more updated and reliable information could be collected and analyzed. This means that learning occurs and consequently decision makers can acquire more actual information about demand and lead times. In addition, humans play an important role and have a great influence on the inventory planning process doing activities such as collecting, pro- cessing and revising inventory system’s information. Actually, the inventory model of Björk (2009) provides an inadequate picture of real-world’s inventory planning problems. Since human learning has not been modeled in a fuzzy EOQ inventory model with back- orders, the model of Björk (2009) is modified to incorporate human learning. 2. Formulation of the EOQ model with backorders and learning in fuzziness In order to incorporate learning of the decision maker into the fuzzy model, the concept of learning in fuzziness proposed by Glock et al. (2012) is applied. In fact, the decision maker learns with every order and gains more reliable information with regard to the demand and lead times. Therefore, the decision maker is http://dx.doi.org/10.1016/j.cie.2015.05.014 0360-8352/Ó 2015 Elsevier Ltd. All rights reserved. q This manuscript was processed by Area Editor Christoph H. Glock. ⇑ Corresponding author. E-mail addresses: nimakzm@gmail.com, nimakzm@siswa.um.edu.my (N. Kazemi). Computers & Industrial Engineering 87 (2015) 540–542 Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie