A Lagrangian Relaxation for a Fuzzy Random EPQ Problem with Shortages and Redundancy Allocation: Two Tuned Meta-heuristics

This paper develops an economic production quantity model for a multi-product multi-objective inventory control problem with fuzzy-stochastic demand and backorders. In this model, the annual demand is represented by trapezoidal fuzzy random numbers. The centroid defuzzification and the expected value methods are applied to defuzzify and make decisions in a random environment. In the case where the warehouse space is limited, the Lagrangian relaxation procedure is first employed to determine the optimal order and the maximum backorder quantities of the products such that the total inventory cost is minimized. The optimal solution obtained by the proposed approach is compared with that obtained by the traditional deterministic method. Moreover, a sensitivity analysis presents the rationality of the solution. Then, the model is extended to a multi-objective integer programming problem in which the optimal numbers of redundant production machines are determined to maximize the production system reliability. In the second proposed model, several constraints are considered to fit real-world situations. As the second model is developed for an NP-hard problem and hence cannot be solved using exact methods in a reasonable computational time, a multi-objective evolutionary algorithm called non-dominated sorting genetic algorithm-II (NSGA-II) is employed to provide Pareto front solutions. Due to non-availability of benchmark in the literature, another multi-objective evolutionary algorithm called non-dominated ranking genetic algorithm is implemented as well to validate the obtained results and evaluate the performance of NSGA-II. In addition, the Taguchi method is used to calibrate the parameters of both algorithms for better performance.

[1]  Ching-Lai Hwang,et al.  Multiple attribute decision making : an introduction , 1995 .

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

[3]  Debjani Chakraborty,et al.  A single-period inventory model with fuzzy random variable demand , 2005, Math. Comput. Model..

[4]  Jinsong Hu,et al.  Random Fuzzy Demand Newsboy Problem , 2012 .

[5]  R. Roy.  A Primer on the Taguchi Method , 1990 .

[6]  Liang-Yuh Ouyang,et al.  Fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand , 2006, Eur. J. Oper. Res..

[7]  Huey-Ming Lee,et al.  Economic production quantity for fuzzy demand quantity, and fuzzy production quantity , 1998, Eur. J. Oper. Res..

[8]  Huibert Kwakernaak,et al.  Fuzzy random variables - I. definitions and theorems , 1978, Inf. Sci..

[9]  Debjani Chakraborty,et al.  A production inventory model with fuzzy random demand and with flexibility and reliability considerations , 2009, Comput. Ind. Eng..

[10]  Manoranjan Maiti,et al.  Multi-item stochastic and fuzzy-stochastic inventory models under two restrictions , 2004, Comput. Oper. Res..

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

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

[13]  Arnold F. Shapiro,et al.  Fuzzy random variables , 2009 .

[14]  G. M. Komaki,et al.  An Enhanced Intelligent Water Drops Algorithm for Scheduling of an Agile Manufacturing System , 2016, Int. J. Inf. Technol. Decis. Mak..

[15]  R. J. Tersine.  Principles of inventory and materials management , 1982 .

[16]  Hossein Faraji,et al.  A genetic algorithm-based computed torque control for slider–crank mechanism in the ship’s propeller , 2014 .

[17]  Shine-Der Lee,et al.  An economic production quantity model with a positive resetup point under random demand , 2013 .

[18]  S. Mondal,et al.  Multi-item fuzzy EOQ models using genetic algorithm , 2003 .

[19]  Ching-Lai Hwang,et al.  Multiple Attribute Decision Making: Methods and Applications - A State-of-the-Art Survey , 1981, Lecture Notes in Economics and Mathematical Systems.

[20]  Harvey H. Millar,et al.  Lagrangian heuristics for the capacitated multi-item lot-sizing problem with backordering , 1994 .

[21]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[22]  M. Darwish.  EPQ models with varying setup cost , 2008 .

[23]  Dipankar Chakraborty,et al.  Multi-item integrated supply chain model for deteriorating items with stock dependent demand under fuzzy random and bifuzzy environments , 2015, Comput. Ind. Eng..

[24]  Tapan Kumar Roy,et al.  Fuzzy multi-item economic production quantity model under space constraint: A geometric programming approach , 2007, Appl. Math. Comput..

[25]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[26]  Kaj-Mikael Björk,et al.  An Economic Production Quantity Problem with Fuzzy Backorder and Fuzzy Demand , 2013, WorldCIST.

[27]  Madhumangal Pal,et al.  Intuitionistic fuzzy optimization technique for Pareto optimal solution of manufacturing inventory models with shortages , 2013, Eur. J. Oper. Res..

[28]  Dilay elebi,et al.  Inventory control in a centralized distribution network using genetic algorithms , 2015 .

[29]  Genichi Taguchi,et al.  Taguchi's Quality Engineering Handbook , 2004 .

[30]  T. Ross.  Fuzzy Logic with Engineering Applications , 1994 .

[31]  Kaj-Mikael Björk,et al.  A multi-item fuzzy economic production quantity problem with a finite production rate , 2011 .

[32]  David W. Pentico,et al.  A survey of deterministic models for the EOQ and EPQ with partial backordering , 2011, Eur. J. Oper. Res..

[33]  Seyed Taghi Akhavan Niaki,et al.  A parameter-tuned genetic algorithm for multi-product economic production quantity model with space constraint, discrete delivery orders and shortages , 2010, Adv. Eng. Softw..

[34]  Philip M. Kaminsky,et al.  Designing and managing the supply chain : concepts, strategies, and case studies , 2007 .

[35]  Rasaratnam Logendran,et al.  Hybrid flow shop batching and scheduling with a bi-criteria objective , 2016 .

[36]  Baoding Liu.  Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[37]  Mitsuo Gen,et al.  Genetic algorithms and engineering design , 1997 .

[38]  Madjid Tavana,et al.  Multi-objective control chart design optimization using NSGA-III and MOPSO enhanced with DEA and TOPSIS , 2016, Expert Syst. Appl..

[39]  Rasaratnam Logendran,et al.  An Enhanced tabu search algorithm to minimize a bi-criteria objective in batching and scheduling problems on unrelated-parallel machines with desired lower bounds on batch sizes , 2017, Comput. Oper. Res..

[40]  Vahid Kayvanfar,et al.  Enhanced intelligent water drops and cuckoo search algorithms for solving the capacitated vehicle routing problem , 2016, Inf. Sci..

[41]  S. Chopra,et al.  Supply Chain Management: Strategy, Planning & Operation , 2007 .

[42]  Lakshmi Rajamani,et al.  NON-DOMINATED RANKED GENETIC ALGORITHM FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS: NRGA , 2008 .

[43]  Mostafa Zandieh,et al.  Scheduling hybrid flowshops with sequence dependent setup times to minimize makespan and maximum tardiness , 2009 .

[44]  Debjani Chakraborty,et al.  Continuous review inventory model in mixed fuzzy and stochastic environment , 2007, Appl. Math. Comput..

[45]  Tapan Kumar Roy,et al.  A fuzzy EPQ model with flexibility and reliability consideration and demand dependent unit production cost under a space constraint: A fuzzy geometric programming approach , 2006, Appl. Math. Comput..

[46]  Mohammadali Pirayesh,et al.  GPSO-LS algorithm for a multi-item EPQ model with production capacity restriction , 2015 .

[47]  Seyed Taghi Akhavan Niaki,et al.  A genetic algorithm approach to optimize a multi-products EPQ model with discrete delivery orders and constrained space , 2008, Appl. Math. Comput..

[48]  Michael Hanss,et al.  Applied Fuzzy Arithmetic: An Introduction with Engineering Applications , 2004 .

[49]  C. Hwang.  Multiple Objective Decision Making - Methods and Applications: A State-of-the-Art Survey , 1979 .

[50]  Seyed Taghi Akhavan Niaki,et al.  Optimising multi-item economic production quantity model with trapezoidal fuzzy demand and backordering: two tuned meta-heuristics , 2016 .

[51]  Adel Hatami-Marbini,et al.  Author's Personal Copy Applied Soft Computing an Extended Compromise Ratio Method for Fuzzy Group Multi-attribute Decision Making with Swot Analysis , 2022 .

[52]  Jaan Kiusalaas,et al.  Numerical Methods in Engineering , 2010 .

[53]  Babak Abbasi,et al.  An efficient tabu search algorithm for flexible flow shop sequence-dependent group scheduling problems , 2012 .