An inventory model for deteriorating items with inflation induced variable demand under two level partial trade credit : A hybrid ABC-GA approach

Abstract In this research work an inventory model of a deteriorating item is considered under two level partial trade credit policy incorporating inflation and time value of money in a finite planning horizon. Here it is assumed that a wholesaler offers a partial trade credit to a retailer i.e., trade credit period is offered on an portion of the total purchase amount. In turn the retailer also offers a partial trade credit to its customers. Demand of the item linearly decreases with time and influenced by unit selling price of the item. As selling price is influenced by the inflation and time value of money, so the base demand depends on inflation and bank interest rate also. The retailer also introduces some promotional cost to boost the demand of the item. Under this circumstances, marketing decisions are made to maximize the present value of the total profit. On the other hand combining the features of artificial bee colony (ABC) and genetic algorithm (GA), a hybrid algorithm, artificial bee genetic algorithm (ABGA) has been developed to find the most appropriate business strategies for the proposed model. Efficiency of this algorithm is tested and compared with some ABC variants using a set of benchmark test functions. The model has been illustrated with several numerical examples and some managerial insights are outlined.

[1]  R. Bénabou Inflation and markups : Theories and evidence from the retail trade sector , 1992 .

[2]  Lakdere Benkherouf,et al.  Optimal replenishment policies for deteriorating items and permissible delay in payments , 2015 .

[3]  Gour Chandra Mahata Retailer’s optimal credit period and cycle time in a supply chain for deteriorating items with up-stream and down-stream trade credits , 2015 .

[4]  Shaojun Wang,et al.  Supply chain models for perishable products under inflation and permissible delay in payment , 2000, Comput. Oper. Res..

[5]  S. Sana,et al.  Coordination contracts for competitive two-echelon supply chain with price and promotional effort sensitive non-linear demand , 2015 .

[6]  Xiao-Yan Sun,et al.  A discrete artificial bee colony algorithm incorporating differential evolution for the flow-shop scheduling problem with blocking , 2015 .

[7]  Yung-Fu Huang,et al.  Economic order quantity under conditionally permissible delay in payments , 2007, Eur. J. Oper. Res..

[8]  B. Sarkar,et al.  An inventory model with variable demand, component cost and selling price for deteriorating items , 2013 .

[9]  Kun-Jen Chung,et al.  The optimal retailer's ordering policies for deteriorating items with limited storage capacity under trade credit financing , 2007 .

[10]  Manoranjan Maiti,et al.  Two-storage inventory model with lot-size dependent fuzzy lead-time under possibility constraints via genetic algorithm , 2007, Eur. J. Oper. Res..

[11]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[12]  Ata Allah Taleizadeh,et al.  A lot sizing model with advance payment and planned backordering , 2018, Ann. Oper. Res..

[13]  S. Aggarwal,et al.  Credit financing in economic ordering policies of deteriorating items , 1994 .

[14]  Kun-Jen Chung,et al.  Lot-sizing decisions under trade credit depending on the ordering quantity , 2004, Comput. Oper. Res..

[15]  Maw-Sheng Chern,et al.  AN INVENTORY MODEL FOR INCREASING DEMAND UNDER TWO LEVELS OF TRADE CREDIT LINKED TO ORDER QUANTITY , 2013 .

[16]  Manoranjan Maiti,et al.  A production inventory model with price discounted fuzzy demand using an interval compared hybrid algorithm , 2017, Swarm Evol. Comput..

[17]  Roman Kapuscinski,et al.  Coordinating Contracts for Decentralized Supply Chains with Retailer Promotional Effort , 2004, Manag. Sci..

[18]  S. Singh,et al.  Multi Item Inventory Model for Deteriorating Items with Expiration Date and Allowable Shortages , 2014 .

[19]  Weifeng Gao,et al.  A modified artificial bee colony algorithm , 2012, Comput. Oper. Res..

[20]  Ata Allah Taleizadeh,et al.  A lot-sizing model with backordering under hybrid linked-to-order multiple advance payments and delayed payment , 2015 .

[21]  Manoranjan Maiti,et al.  Inventory model of a deteriorating item with price and credit linked fuzzy demand : A fuzzy differential equation approach , 2014 .

[22]  Dervis Karaboga,et al.  A comparative study of Artificial Bee Colony algorithm , 2009, Appl. Math. Comput..

[23]  Y.-F. Huang,et al.  Optimal retailer's ordering policies in the EOQ model under trade credit financing , 2003, J. Oper. Res. Soc..

[24]  Chun-Tao Chang An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity , 2004 .

[25]  A. Taleizadeh,et al.  Imperfect economic production quantity model with upstream trade credit periods linked to raw material order quantity and downstream trade credit periods , 2016 .

[26]  Kun-Jen Chung,et al.  THE OPTIMAL ORDERING POLICY IN A DCF ANALYSIS FOR DETERIORATING ITEMS WHEN TRADE CREDIT DEPENDS ON THE ORDER QUANTITY , 2006 .

[27]  Andries Petrus Engelbrecht,et al.  Fundamentals of Computational Swarm Intelligence , 2005 .

[28]  Manoranjan Maiti,et al.  An appropriate business strategy for a sale item , 2018 .

[29]  Asoke Kumar Bhunia,et al.  An inventory model of deteriorating items with lot-size dependent replenishment cost and a linear trend in demand , 1999 .

[30]  Nita H. Shah,et al.  Economic order quantity for deteriorating items under inflation with time and advertisement dependent demand , 2017 .

[31]  Manas Kumar Maiti,et al.  A fuzzy genetic algorithm with varying population size to solve an inventory model with credit-linked promotional demand in an imprecise planning horizon , 2011, Eur. J. Oper. Res..

[32]  Fu Qiang,et al.  Hybrid artificial bee colony algorithm with variable neighborhood search and memory mechanism , 2018 .

[33]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[34]  Ata Allah Taleizadeh,et al.  Partial up-stream advanced payment and partial down-stream delayed payment in a three-level supply chain , 2016, Ann. Oper. Res..

[35]  Xiaoyan Sun,et al.  Evolutionary algorithms for optimization problems with uncertainties and hybrid indices , 2011, Inf. Sci..

[36]  D. Karaboga,et al.  On the performance of artificial bee colony (ABC) algorithm , 2008, Appl. Soft Comput..

[37]  Dun-Wei Gong,et al.  Evolutionary algorithms with preference polyhedron for interval multi-objective optimization problems , 2013, Inf. Sci..

[38]  Yong-Wu Zhou,et al.  Coordination of cooperative advertising models in a one-manufacturer two-retailer supply chain system , 2011, Comput. Ind. Eng..

[39]  Ali H. Diabat,et al.  A lot sizing model with partial downstream delayed payment, partial upstream advance payment, and partial backordering for deteriorating items , 2017 .

[40]  Biswajit Sarkar,et al.  An EMQ model with price and time dependent demand under the effect of reliability and inflation , 2014, Appl. Math. Comput..

[41]  Cemal Köse,et al.  A modified firefly algorithm for global minimum optimization , 2018, Appl. Soft Comput..

[42]  Lindu Zhao,et al.  Coordinating a supply chain with effort and price dependent stochastic demand , 2009 .

[43]  Dervis Karaboga,et al.  AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION , 2005 .

[44]  Sam Kwong,et al.  Gbest-guided artificial bee colony algorithm for numerical function optimization , 2010, Appl. Math. Comput..

[45]  L. Ouyang,et al.  Optimal strategy for an integrated system with variable production rate when the freight rate and trade credit are both linked to the order quantity , 2008 .

[46]  Elsayed A. Elsayed,et al.  Analysis of inventory systems with deteriorating items , 1983 .

[47]  Jinn-Tsair Teng,et al.  An economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity , 2009, Eur. J. Oper. Res..

[48]  Ata Allah Taleizadeh,et al.  Ordering policies for non-instantaneous deteriorating items under hybrid partial prepayment, partial trade credit and partial backordering , 2018, J. Oper. Res. Soc..

[49]  Yong-Wu Zhou,et al.  An inventory model for deteriorating items under stock-dependent demand and two-level trade credit , 2010 .

[50]  S. Aggarwal,et al.  Ordering Policies of Deteriorating Items under Permissible Delay in Payments , 1995 .

[51]  H. Wee Deteriorating inventory model with quantity discount, pricing and partial backordering , 1999 .

[52]  B. Sarkar,et al.  An inventory model with time dependent demand and shortages under trade credit policy , 2013 .

[53]  Kun-Jen Chung,et al.  The simplified solution procedures for the optimal replenishment decisions under two levels of trade credit policy depending on the order quantity in a supply chain system , 2011, Expert Syst. Appl..

[54]  Yung-Fu Huang An inventory model under two levels of trade credit and limited storage space derived without derivatives , 2006 .

[55]  Jianyong Sun,et al.  A novel hybrid multi-objective artificial bee colony algorithm for blocking lot-streaming flow shop scheduling problems , 2018, Knowl. Based Syst..

[56]  A. Goswami,et al.  An EOQ Model for Deteriorating Items with Linear Time-dependent Demand Rate and Shortages under Inflation and Time Discounting , 1995 .

[57]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[58]  A. Taleizadeh,et al.  An inventory control problem for deteriorating items with back-ordering and financial considerations under two levels of trade credit linked to order quantity , 2015 .

[59]  Prasenjit Pramanik,et al.  A supply chain with variable demand under three level trade credit policy , 2017, Comput. Ind. Eng..

[60]  Kun-Jen Chung,et al.  The EPQ model under conditions of two levels of trade credit and limited storage capacity in supply chain management , 2013, Int. J. Syst. Sci..

[61]  S. Goyal Economic Order Quantity under Conditions of Permissible Delay in Payments , 1985 .

[62]  Sanyang Liu,et al.  A Novel Artificial Bee Colony Algorithm Based on Modified Search Equation and Orthogonal Learning , 2013, IEEE Transactions on Cybernetics.

[63]  Manoranjan Maiti,et al.  Two storage inventory model of a deteriorating item with variable demand under partial credit period , 2013, Appl. Soft Comput..

[64]  G. C. Mahata,et al.  An EOQ inventory system of ameliorating items for price dependent demand rate under retailer partial trade credit policy , 2016 .

[65]  Manoranjan Maiti,et al.  Three level partial trade credit with promotional cost sharing , 2017, Appl. Soft Comput..

[66]  Behrooz Karimi,et al.  Optimizing the pricing and replenishment policy for non-instantaneous deteriorating items with stochastic demand and promotional efforts , 2014, Comput. Oper. Res..

[67]  Yu-Chung Tsao,et al.  Managing multi-echelon multi-item channels with trade allowances under credit period , 2010 .

[68]  Hung-Chang Liao,et al.  An inventory model with deteriorating items under inflation when a delay in payment is permissible , 2000 .

[69]  Yung-Fu Huang,et al.  AN EOQ MODEL UNDER RETAILER PARTIAL TRADE CREDIT POLICY IN SUPPLY CHAIN , 2008 .

[70]  Gour Chandra Mahata,et al.  An EPQ-based inventory model for exponentially deteriorating items under retailer partial trade credit policy in supply chain , 2012, Expert Syst. Appl..

[71]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[72]  Mesut Gündüz,et al.  Artificial bee colony algorithm with variable search strategy for continuous optimization , 2015, Inf. Sci..

[73]  Yung-Fu Huang,et al.  Optimal retailer's replenishment decisions in the EPQ model under two levels of trade credit policy , 2007, Eur. J. Oper. Res..

[74]  Shib Sankar Sana,et al.  An EOQ model with backlogging , 2016 .