Optimal payment time and replenishment decisions for retailer’s inventory system under trade credit and carbon emission constraints

This study presents a multi-item inventory and pricing model by considering marketing, service activities, trade credit, carbon emissions, and the restrictions of production cost and storage space. In the proposed model, shortages are allowed and demand rate is a power function of service and marketing costs, and selling price. The main objective of this study is to optimize retailer’s payments time, service and marketing expenditure, and replenishment decisions in order to maximize retailer’s total profit and minimize carbon emissions, simultaneously. Model is developed in a fuzzy environment under carbon tax regulation when the length of credit period provided by supplier is less than or equal to the length of time in which no shortage happens. To solve the proposed model, we first transform the original problem into a multi-objective Signomial Geometric Programming (SGP) problem using fuzzy and hybrid parameters, which minimizes both the mean value and the total dispersion value of the objective function. Then a global optimization problem method has been used to solve the SGP problem. Efficiency of this algorithm is tested and compared with multi-objective genetic algorithm, multi-objective genetic algorithm with varying population, and hybrid heuristic algorithm. At the end, several numerical examples and sensitivity analysis are performed to demonstrate the application of the proposed model and solution procedure to obtain managerial insights.

[1]  V. Hovelaque,et al.  The carbon-constrained EOQ model with carbon emission dependent demand , 2015 .

[2]  Bhaba R. Sarker,et al.  Optimal payment time under permissible delay in payment for products with deterioration , 2000 .

[3]  Biswajit Sarkar,et al.  Multi-item sustainable green production system under trade-credit and partial backordering , 2018, Journal of Cleaner Production.

[4]  Sunhee Suk,et al.  An analysis of company choice preference to carbon tax policy in China , 2015 .

[5]  P. He,et al.  Production lot-sizing and carbon emissions under cap-and-trade and carbon tax regulations , 2015 .

[6]  Gongxian Xu,et al.  Global optimization of signomial geometric programming problems , 2014, Eur. J. Oper. Res..

[7]  Salwa Hanim Abdul-Rashid,et al.  Economic order quantity models for items with imperfect quality and emission considerations , 2018 .

[8]  A. Azadeh,et al.  Optimum Integrated Design of Crude Oil Supply Chain by a Unique Mixed Integer Nonlinear Programming Model , 2017 .

[9]  Chung-Yuan Dye,et al.  A finite horizon deteriorating inventory model with two-phase pricing and time-varying demand and cost under trade credit financing using particle swarm optimization , 2012, Swarm Evol. Comput..

[10]  Ali Azadeh,et al.  Evolutionary multi-objective optimization of environmental indicators of integrated crude oil supply chain under uncertainty , 2017 .

[11]  R. Hammami,et al.  Carbon emissions in a multi-echelon production-inventory model with lead time constraints , 2015 .

[12]  Gerhard-Wilhelm Weber,et al.  An inventory model for non-instantaneous deteriorating items with partial backlogging, permissible delay in payments, inflation- and selling price-dependent demand and customer returns , 2015, Ann. Oper. Res..

[13]  Erbao Cao,et al.  Trade credit financing and coordination for an emission-dependent supply chain , 2018, Comput. Ind. Eng..

[14]  L. Cárdenas-Barrón,et al.  Retailer’s economic order quantity when the supplier offers conditionally permissible delay in payments link to order quantity , 2014 .

[15]  Vandana,et al.  An EOQ model for retailers partial permissible delay in payment linked to order quantity with shortages , 2016, Math. Comput. Simul..

[16]  Mir Mohsen Pedram,et al.  Fuzzy pricing, marketing and service planning in a fuzzy inventory model: A geometric programming approach , 2013 .

[17]  Oshmita Dey,et al.  A fuzzy random integrated inventory model with imperfect production under optimal vendor investment , 2019, Oper. Res..

[18]  P. He,et al.  Joint production and pricing decisions for multiple products with cap-and-trade and carbon tax regulations , 2016 .

[19]  Manoranjan Maiti,et al.  Multi-item EOQ model with hybrid cost parameters under fuzzy/fuzzy-stochastic resource constraints: A geometric programming approach , 2008, Comput. Math. Appl..

[20]  Manoranjan Maiti,et al.  Inventory model of deteriorated items with a constraint: A geometric programming approach , 2006, Eur. J. Oper. Res..

[21]  Hua Zhou,et al.  MM algorithms for geometric and signomial programming , 2014, Math. Program..

[22]  U. Passy,et al.  Generalized Polynomial Optimization , 1967 .

[23]  Y. Tsao,et al.  Sustainable newsvendor models under trade credit , 2017 .

[24]  Chih-te Yang,et al.  Sustainable trade credit and replenishment decisions with credit-linked demand under carbon emission constraints , 2015, Eur. J. Oper. Res..

[25]  Shuo-Jye Wu,et al.  Optimal payment time with deteriorating items under inflation and permissible delay in payments , 2009, Int. J. Syst. Sci..

[26]  Fan Ting,et al.  Optimal ordering policies for perishable multi-item under stock-dependent demand and two-level trade credit , 2014 .

[27]  Yu-Chung Tsao,et al.  A MULTI-ITEM SUPPLY CHAIN WITH CREDIT PERIODS AND WEIGHT FREIGHT COST DISCOUNTS , 2012 .

[28]  Manoranjan Maiti,et al.  Multi-item inventory models with price dependent demand under flexibility and reliability consideration and imprecise space constraint: A geometric programming approach , 2009, Math. Comput. Model..

[29]  H. Wee,et al.  Sustainable inventory management with deteriorating and imperfect quality items considering carbon emission , 2018, Journal of Cleaner Production.

[30]  Manoranjan Maiti,et al.  Fuzzy Optimization for Multi-item Supply Chain with Trade Credit and Two-Level Price Discount Under Promotional Cost Sharing , 2018, Int. J. Fuzzy Syst..

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

[32]  Christodoulos A. Floudas,et al.  Deterministic global optimization - theory, methods and applications , 2010, Nonconvex optimization and its applications.

[33]  Jung-Fa Tsai,et al.  Range reduction techniques for improving computational efficiency in global optimization of signomial geometric programming problems , 2012, Eur. J. Oper. Res..

[34]  Manoranjan Maiti,et al.  Uncertain multi-item supply chain with two level trade credit under promotional cost sharing , 2018, Comput. Ind. Eng..

[35]  Jennifer A. Pazour,et al.  A new inventory model for cold items that considers costs and emissions , 2014 .

[36]  Hardik N. Soni.  Optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment , 2013 .

[37]  Nima Kazemi,et al.  Fuzzy inventory models: A comprehensive review , 2017, Appl. Soft Comput..

[38]  B. Sarker,et al.  Optimal payment time for a retailer under permitted delay of payment by the wholesaler , 2000 .

[39]  Eleonora Bottani,et al.  A Fuzzy Reverse Logistics Inventory System Integrating Economic Order/Production Quantity Models , 2016, International Journal of Fuzzy Systems.

[40]  R. Uthayakumar,et al.  Analysis and optimization of an EOQ inventory model with promotional efforts and back ordering under delay in payments , 2017 .

[41]  Xiping Song,et al.  On optimal payment time for a retailer under permitted delay of payment by the wholesaler , 2006 .

[42]  Barun Das,et al.  A two-storage multi-item inventory model with hybrid number and nested price discount via hybrid heuristic algorithm , 2017, Ann. Oper. Res..

[43]  Ralf W. Seifert,et al.  A review of trade credit literature: Opportunities for research in operations , 2013, Eur. J. Oper. Res..

[44]  Ezutah Udoncy Olugu,et al.  An economic order quantity model considering different holding costs for imperfect quality items subject to fuzziness and learning , 2016, J. Intell. Fuzzy Syst..