Multi-objective optimization of hybrid backorder inventory model

An intelligent hybrid backorder inventory system is developed with MOPSO.Pareto curves are generated between cost and service levels for the practitioners.Sensitivity of optimal parameters with respect to holding cost is studied.Applications of proposed expert and intelligent system in real world are discussed. This paper addresses inventory problem for the products that are sold in monopolistic and captive markets experiencing hybrid backorder (i.e., fixed backorder and time-weighted backorder). The problem with stochastic demand is studied first by developing single objective (cost) inventory model. Computational results of a numerical problem show the effectiveness of hybrid backorder inventory model over fixed backorder inventory model. The model is later extended to multi-objective inventory model. Three objectives of multi-objective inventory model are the minimization of total cost, minimization of stockout units and minimization of the frequency of stockout. A multi-objective particle swarm optimization (MOPSO) algorithm is used to solve the inventory model and generate Pareto curves. The Pareto curves obtained for hybrid backorder inventory model are compared with the existing Pareto curves that are based on fixed backorder. The results show a substantial reduction in stockout units and frequency of stockout with a marginal rise in cost with proposed hybrid backorder inventory system in comparison to existing fixed backorder inventory system. Sensitivity analysis is done to study the robustness of total cost, order quantity, and safety stock factor with the change in holding cost. In the end, the performance of the MOPSO algorithm is compared with the multi-objective genetic algorithm (MOGA). The metrics that are used for the performance measurement of the algorithms are error ratio, spacing and maximum spread.

[1]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithms: classifications, analyses, and new innovations , 1999 .

[2]  Justo Puerto,et al.  The multiscenario lot size problem with concave costs , 2004, Eur. J. Oper. Res..

[3]  Steven Nahmias,et al.  Production and operations analysis , 1992 .

[4]  Seyed Taghi Akhavan Niaki,et al.  Optimizing a bi-objective multi-product multi-period three echelon supply chain network with warehouse reliability , 2015, Expert Syst. Appl..

[5]  D. Montgomery,et al.  INVENTORY MODELS WITH A MIXTURE OF BACKORDERS AND LOST SALES. , 1973 .

[6]  Bernhard Sendhoff,et al.  A critical survey of performance indices for multi-objective optimisation , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[7]  Sunil Agrawal,et al.  Multi Objective Cuckoo Search Optimization for Fast Moving Inventory Items , 2014, ISI.

[8]  Steven Nahmias,et al.  Production and Operations Analysis, 6th Edition , 2014 .

[9]  Bernd Noche,et al.  Simulation-based optimization for a capacitated multi-echelon production-inventory system , 2015, J. Simulation.

[10]  Ching-Shih Tsou,et al.  Multi-objective inventory planning using MOPSO and TOPSIS , 2008, Expert Syst. Appl..

[11]  Luis A. San-José,et al.  A general model for EOQ inventory systems with partial backlogging and linear shortage costs , 2009, Int. J. Syst. Sci..

[12]  Per Joakim Agrell.  A multicriteria framework for inventory control , 1995 .

[13]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[14]  Vahid Hajipour,et al.  A bi-objective continuous review inventory control model: Pareto-based meta-heuristic algorithms , 2015, Appl. Soft Comput..

[15]  Adrijit Goswami,et al.  An interpolating by pass to Pareto optimality in intuitionistic fuzzy technique for a EOQ model with time sensitive backlogging , 2014, Appl. Math. Comput..

[16]  Teruko Takano-Yamamoto,et al.  Effect of Cytokines on Osteoclast Formation and Bone Resorption during Mechanical Force Loading of the Periodontal Membrane , 2014, TheScientificWorldJournal.

[17]  Steven Nahmias.  On the equivalence of three approximate continuous review inventory models , 1976 .

[18]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[19]  Justo Puerto,et al.  Pareto-optimality in classical inventory problems , 1998 .

[20]  Seyed Taghi Akhavan Niaki,et al.  Bi-objective optimization of a multi-product multi-period three-echelon supply chain problem under uncertain environments: NSGA-II and NRGA , 2015, Inf. Sci..

[21]  Mostafa Zandieh,et al.  Comparisons of some improving strategies on MOPSO for multi-objective (r, Q) inventory system , 2011, Expert Syst. Appl..

[22]  Ching-Shih Tsou,et al.  Evolutionary Pareto optimizers for continuous review stochastic inventory systems , 2009, Eur. J. Oper. Res..

[23]  Haim Shore.  General Approximate Solutions for some Common Inventory Models , 1986 .

[24]  Ardeshir Bahreininejad,et al.  Multi-Item Multiperiodic Inventory Control Problem with Variable Demand and Discounts: A Particle Swarm Optimization Algorithm , 2014, TheScientificWorldJournal.

[25]  Terry P. Harrison,et al.  A mirror-image lead time inventory model , 2010 .

[26]  KyoungJong Park,et al.  Optimization of total inventory cost and order fill rate in a supply chain using PSO , 2014 .

[27]  Susmita Bandyopadhyay,et al.  Solving a tri-objective supply chain problem with modified NSGA-II algorithm , 2014 .

[28]  James H. Bookbinder,et al.  Multicriteria Trade-Offs in a Warehouse/Retailer System , 1992 .

[29]  Yaochu Jin,et al.  A Critical Survey of Performance Indices for Multi-Objective Optimisation , 2003 .

[30]  Haim Shore.  Simple Approximations for the Inverse Cumulative Function, the Density Function and the Loss Integral of the Normal Distribution , 1982 .

[31]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[32]  Seyed Taghi Akhavan Niaki,et al.  Optimizing a bi-objective multi-product EPQ model with defective items, rework and limited orders: NSGA-II and MOPSO algorithms , 2013 .

[33]  S. Agrawal,et al.  On single item time weighted mixture inventory models with independent stochastic lead times , 2015 .

[34]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[35]  L. Zurich,et al.  Operations Research in Production Planning, Scheduling, and Inventory Control , 1974 .

[36]  Seyed Taghi Akhavan Niaki,et al.  A hybrid genetic and imperialist competitive algorithm for green vendor managed inventory of multi-item multi-constraint EOQ model under shortage , 2015, Appl. Soft Comput..

[37]  Eckart Zitzler,et al.  Evolutionary algorithms for multiobjective optimization: methods and applications , 1999 .

[38]  Marko Pfeifer,et al.  Inventory Management And Production Planning And Scheduling , 2016 .

[39]  Chandrasekhar Das.  Q,r Inventory Models with Time-Weighted Backorders , 1983 .