A bi-objective non-linear approach for determining the ordering strategy for group B in ABC analysis inventory

Document Type : Original Manuscript

Authors

Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

10.22094/joie.2021.1864151.1634

Abstract

The main aim of this research is to find the best inventory review policy for different types of items in group B in ABC analysis through minimizing the total cost of the system and maximizing the service level. Moreover, this study has considered several operational constraints such as limitations on storage space, number of orders, and allowable shortage. To solve this problem, first, an individual optimization method is utilized to obtain optimal solutions. Then, two classic and novel multi-objective optimization methods have been used to convert the bi-objective problem to a single-objective and reach the near-optimal solutions for both objectives simultaneously. Finally, the proposed methods are compared in terms of objective function values and computational time to find the better method.

Graphical Abstract

A bi-objective non-linear approach for determining the ordering strategy for group B in ABC analysis inventory

Highlights

  • Presenting a mathematical approach to find the best ordering strategy for group B
  • Considering two important objectives consisting of costs and service level
  • Considering different constraints in stochastic forms
  • Study the efficiency of two MODM methods

Keywords


Abdolazimi, O., Esfandarani, M. S., & Shishebori, D. (2021). Design of a supply chain network for determining the optimal number of items at the inventory groups based on ABC analysis: a comparison of exact and meta-heuristic methods. Neural Computing and Applications, 33(12), 6641-6656, doi:https://doi.org/10.1007/s00521-020-05428-y.
Ahmadi, A., Mohabbatdar, S., & Sajadieh, M. S. (2016). Optimal manufacturer-retailer policies in a supply chain with defective product and price dependent demand. Journal of Optimization in Industrial Engineering, 9(19), 37-46.
Ahmadzadeh, E., & Vahdani, B. (2017). A location-inventory-pricing model in a closed loop supply chain network with correlated demands and shortages under a periodic review system. Computers & Chemical Engineering, 101, 148-166, doi:https://doi.org/10.1016/j.compchemeng.2017.02.027.
Axsäter, S. (2007). A heuristic for triggering emergency orders in an inventory system. European Journal of Operational Research, 176(2), 880-891, doi:https://doi.org/10.1016/j.ejor.2005.09.002.
Berk, E., & Gürler, Ü. (2008). Analysis of the (Q, r) Inventory Model for Perishables with Positive Lead Times and Lost Sales. Operations Research, 56(5), 1238-1246, doi:10.1287/opre.1080.0582.
Betts, J. M., & Johnston, R. B. (2005). Determining the optimal constrained multi-item (Q, r) inventory policy by maximising risk-adjusted profit. IMA Journal of Management Mathematics, 16(4), 317-338, doi:10.1093/imaman/dpi006.
Bonami, P., Cornuéjols, G., Lodi, A., & Margot, F. (2009). A feasibility pump for mixed integer nonlinear programs. Mathematical Programming, 119(2), 331-352, doi:https://doi.org/10.1007/s10107-008-0212-2.
Chand, S., Li, J., & Xu, Y. (2016). A periodic review inventory model with two delivery modes, fractional lead-times, and age-and-period-dependent backlogging costs. International Journal of Production Economics, 173, 199-206, doi:https://doi.org/10.1016/j.ijpe.2015.12.002.
Chang, C.-T. (2007). Multi-choice goal programming. Omega, 35(4), 389-396, doi:https://doi.org/10.1016/j.omega.2005.07.009.
Chang, C.-T. (2011). Multi-choice goal programming with utility functions. European Journal of Operational Research, 215(2), 439-445, doi:https://doi.org/10.1016/j.ejor.2011.06.041.
Charnes, A., Cooper, W. W., & Ferguson, R. O. (1955). Optimal estimation of executive compensation by linear programming. Management Science, 1(2), 138-151.
Cobb, B. R., Johnson, A. W., Rumí, R., & Salmerón, A. (2015). Accurate lead time demand modeling and optimal inventory policies in continuous review systems. International Journal of Production Economics, 163, 124-136, doi:http://dx.doi.org/10.1016/j.ijpe.2015.02.017.
Dillon, M., Oliveira, F., & Abbasi, B. (2017). A two-stage stochastic programming model for inventory management in the blood supply chain. International Journal of Production Economics, 187, 27-41, doi:https://doi.org/10.1016/j.ijpe.2017.02.006.
Fatehi Kivi, A., Atashi Abkenar, A. A., & Alipour, H. (2018). Fuzzy mathematical model for a lot-sizing problem in closed-loop supply chain. Journal of Optimization in Industrial Engineering, 11(1), 133-141.
Fattahi, P., Hajipour, V., & Nobari, A. (2015). A bi-objective continuous review inventory control model. Appl. Soft Comput., 32(C), 211-223, doi:10.1016/j.asoc.2015.02.044.
Ghalebsaz-Jeddi, B., Shultes, B. C., & Haji, R. (2004). A multi-product continuous review inventory system with stochastic demand, backorders, and a budget constraint. European Journal of Operational Research, 158(2), 456-469, doi:https://doi.org/10.1016/S0377-2217(03)00363-1.
Hafezalkotob, A., Khalili-Damghani, K., & Ghashami, S. S. (2016). A three-echelon multi-objective multi-period multi-product supply chain network design problem: A goal programming approach. Journal of Optimization in Industrial Engineering, 10(21), 67-78.
Hajiagha, S. H. R., Daneshvar, M., & Antucheviciene, J. (2021). A hybrid fuzzy-stochastic multi-criteria ABC inventory classification using possibilistic chance-constrained programming. Soft Computing, 25(2), 1065-1083, doi:https://doi.org/10.1007/s00500-020-05204-z.
Hajiaghaei-Keshteli, M., Sajadifar, S. M., & Haji, R. (2011). Determination of the economical policy of a three-echelon inventory system with (R, Q) ordering policy and information sharing. The International Journal of Advanced Manufacturing Technology, 55(5-8), 831-841, doi:https://doi.org/10.1007/s00170-010-3112-6.
Hemmati, M., & Pasandideh, S. H. R. (2020). A bi-objective supplier location, supplier selection and order allocation problem with green constraints: scenario-based approach. Journal of Ambient Intelligence and Humanized Computing, 1-24, doi:https://doi.org/10.1007/s12652-020-02555-1.
Horng, S.-C., & Lin, S.-S. (2017). Ordinal optimization based metaheuristic algorithm for optimal inventory policy of assemble-to-order systems. Applied Mathematical Modelling, 42, 43-57, doi:https://doi.org/10.1016/j.apm.2016.10.002.
Johansen, S. G. (2013). Modified base-stock policies for continuous-review, lost-sales inventory models with Poisson demand and a fixed lead time. International Journal of Production Economics, 143(2), 379-384, doi:https://doi.org/10.1016/j.ijpe.2012.02.021.
Keshavarz-Ghorbani, F., & Pasandideh, S. H. R. (2021). Optimizing a two-level closed-loop supply chain under the vendor managed inventory contract and learning: Fibonacci, GA, IWO, MFO algorithms. Neural Computing and Applications, 1-26, doi:https://doi.org/10.1007/s00521-021-05703-6.
Kettani, O., Aouni, B. d., & Martel, J.-M. (2004). The double role of the weight factor in the goal programming model. Computers & Operations Research, 31(11), 1833-1845, doi:https://doi.org/10.1016/S0305-0548(03)00142-4.
Kong, X., Wang, H., Chen, X., & Feng, G. (2020). Optimal policy for inventory systems with capacity commitment and fixed ordering costs. Operations Research Letters, 48(1), 9-17, doi:https://doi.org/10.1016/j.orl.2019.10.006.
Kundu, A., & Chakrabarti, T. (2012). A multi-product continuous review inventory system in stochastic environment with budget constraint. Optimization letters, 6(2), 299-313, doi:https://doi.org/10.1007/s11590-010-0245-3.
Lau, A. H. L., & Lau, H.-S. (2008). An improved (Q,R) formulation when the stockout cost is incurred on a per-stockout basis. International Journal of Production Economics, 111(2), 421-434, doi:http://dx.doi.org/10.1016/j.ijpe.2006.04.022.
M’Hallah, R., Benkherouf, L., & Al-Kandari, A. (2020). Optimal inventory policies for a two-dimensional stochastic inventory model: A numerical investigation. Computers & Operations Research, 119, 104939, doi:https://doi.org/10.1016/j.cor.2020.104939.
Maleki, L., Pasandideh, S. H. R., Niaki, S. T. A., & Cárdenas-Barrón, L. E. (2017). Determining the prices of remanufactured products, capacity of internal workstations and the contracting strategy within queuing framework. Applied Soft Computing, 54, 313-321.
Mardan, E., Govindan, K., Mina, H., & Gholami-Zanjani, S. M. (2019). An accelerated benders decomposition algorithm for a bi-objective green closed loop supply chain network design problem. Journal of Cleaner Production, 235, 1499-1514, doi:https://doi.org/10.1016/j.jclepro.2019.06.187.
Massonnet, G., Gayon, J. P., & Rapine, C. (2014). Approximation algorithms for deterministic continuous-review inventory lot-sizing problems with time-varying demand. European Journal of Operational Research, 234(3), 641-649, doi:http://dx.doi.org/10.1016/j.ejor.2013.09.037.
Mattsson, S.-A. (2010). Inventory control in environments with seasonal demand. Operations Management Research, 3(3-4), 138-145, doi:https://doi.org/10.1007/s12063-010-0035-1.
Mirkhorsandi, S. S., & Pasandideh, S. H. R. (2020). A Bi-objective Multi-Product Multi-Constraint EPQ Model in a Stochastic Environment and Partial Shortage. Journal of Advanced Manufacturing Systems, 19(03), 567-587.
Mohammaditabar, D., Hassan Ghodsypour, S., & O'Brien, C. (2012). Inventory control system design by integrating inventory classification and policy selection. International Journal of Production Economics, 140(2), 655-659, doi:https://doi.org/10.1016/j.ijpe.2011.03.012.
Nemati-Lafmejani, R., & Davari-Ardakani, H. (2020). Multi-mode resource constrained project scheduling problem along with contractor selection. INFOR: Information Systems and Operational Research, 1-20, doi:https://doi.org/10.1080/03155986.2020.1803720
Niknamfar, A. H., & Pasandideh, S. H. R. (2014). A bi-objective optimization for vendor managed inventory model. Journal of Optimization in Industrial Engineering, 7(15), 37-45.
Pasandideh, S. H. R., Niaki, S. T. A., & Asadi, K. (2015). Optimizing a bi-objective multi-product multi-period three echelon supply chain network with warehouse reliability. Expert Systems with Applications, 42(5), 2615-2623.
Pasandideh, S. H. R., Niaki, S. T. A., & Tokhmehchi, N. (2011). A parameter-tuned genetic algorithm to optimize two-echelon continuous review inventory systems. Expert Systems with Applications, 38(9), 11708-11714, doi:https://doi.org/10.1016/j.eswa.2011.03.056.
Poorbagheri, T., & Akhavan Niaki, S. T. (2015). Vendor Managed Inventory of a Supply Chain under Stochastic Demands. Journal of Optimization in Industrial Engineering, 8(18), 47-60.
Poormoaied, S., & Atan, Z. (2020). A continuous review policy for two complementary products with interrelated demand. Computers & Industrial Engineering, 150, 106980, doi:https://doi.org/10.1016/j.cie.2020.106980.
Priyan, S., & Uthayakumar, R. (2015). Continuous review inventory model with controllable lead time, lost sales rate and order processing cost when the received quantity is uncertain. Journal of Manufacturing Systems, 34, 23-33, doi:http://dx.doi.org/10.1016/j.jmsy.2014.09.002.
Qi, L. (2013). A continuous-review inventory model with random disruptions at the primary supplier. European Journal of Operational Research, 225(1), 59-74, doi:https://doi.org/10.1016/j.ejor.2012.09.035.
Rao, U. S. (2003). Properties of the periodic review (R, T) inventory control policy for stationary, stochastic demand. Manufacturing & Service Operations Management, 5(1), 37-53.
Saracoglu, I., Topaloglu, S., & Keskinturk, T. (2014). A genetic algorithm approach for multi-product multi-period continuous review inventory models. Expert Systems with Applications, 41(18), 8189-8202, doi:https://doi.org/10.1016/j.eswa.2014.07.003.
Soylu, B., & Akyol, B. (2014). Multi-criteria inventory classification with reference items. Computers & Industrial Engineering, 69(Supplement C), 12-20, doi:https://doi.org/10.1016/j.cie.2013.12.011.
Taleizadeh, A. A., Shokr, I., Konstantaras, I., & VafaeiNejad, M. (2020). Stock replenishment policies for a vendor-managed inventory in a retailing system. Journal of Retailing and Consumer Services, 55, 102137, doi:https://doi.org/10.1016/j.jretconser.2020.102137.
Tamjidzad, S., & Mirmohammadi, S. H. (2015). An optimal (r, Q) policy in a stochastic inventory system with all-units quantity discount and limited sharable resource. European Journal of Operational Research, 247(1), 93-100, doi:http://dx.doi.org/10.1016/j.ejor.2015.05.073.
Tao, Y., Lee, L. H., Chew, E. P., Sun, G., & Charles, V. (2017). Inventory control policy for a periodic review system with expediting. Applied Mathematical Modelling, 49, 375-393, doi:https://doi.org/10.1016/j.apm.2017.04.036.
Xu, Y., Bisi, A., & Dada, M. (2017). A finite-horizon inventory system with partial backorders and inventory holdback. Operations Research Letters, 45(4), 315-322, doi:https://doi.org/10.1016/j.orl.2017.04.007.
Yang, L., Li, H., Campbell, J. F., & Sweeney, D. C. (2017). Integrated multi-period dynamic inventory classification and control. International Journal of Production Economics, 189(Supplement C), 86-96, doi:https://doi.org/10.1016/j.ijpe.2017.04.010.
Yousefi-Babadi, A., Tavakkoli-Moghaddam, R., Bozorgi-Amiri, A., & Seifi, S. (2017). Designing a Reliable Multi-Objective Queuing Model of a Petrochemical Supply Chain Network under Uncertainty: A Case Study. Computers & Chemical Engineering, 100, 177-197, doi:https://doi.org/10.1016/j.compchemeng.2016.12.012.
Zhao, X., Qiu, M., Xie, J., & He, Q. (2012). Computing (r, Q) policy for an inventory system with limited sharable resource. Computers & Operations Research, 39(10), 2368-2379, doi:https://doi.org/10.1016/j.cor.2011.12.012.