Trade Credit Policies for Supplier, Manufacturer, and Retailer: An Imperfect Production-Inventory System with Rework
Keywords:holding cost, imperfect production, net profit, rework, supply chain, trade credit policy
In this study, we developed a trade credit policy for a three-layer supply chain consisting of a supplier, a manufacturer and a retailer. We propose an optimal production rate and selling price for the manufacturer and the retailer under an imperfect production system. The suggested coordination policy optimizes the profit of each supply chain member. Two models were formulated for two real-life strategies respectively. The first one is a collaborative (integrated) system and the second one is a Stackelberg leadership system. Both strategies were analyzed for various credit periods, respectively offered by the supplier to the manufacturer, by the manufacturer to the retailer, and by the retailer to the customers, by considering price-sensitive demand and a certain replenishment rate. Finally, we concluded which strategy will be better for inventory management under the given restrictions in the form of propositions. The concavity property for the net profit function was established with respect to the selling price and the production rate, which was also described graphically and analyzed by numerical examples.
Aggarwal, S. P. & Jaggi C. K., Ordering Policies of Deteriorating Items Under Permissible Delay in Payments, Journal of the Operational Research Society, 46(5), pp. 658-662, 1995.
Anand A., Das S., Agarwal M. & Yadavalli, V.S.S., Optimal Scheduling Policy for a Multi-Upgraded Software System under Fuzzy Environment, Journal of Mathematical and Fundamental Sciences 51(3), pp. 278-293, 2019.
Arcelus F. J., Shah N. H. & Srinivasan G., Retailer?s Response to Special Sales: Price Discount Vs Trade Credit, Omega, the International Journal of Management Science, 29, pp. 417-428, 2001.
Cardenas-Barron, L.E., On Optimal Manufacturing Batch Size with Rework Process at Single-Stage Production System, Computers & Industrial Engineering, 53 pp. 196-198, 2008.
Cardenas-Barron L. E. & Trevino-Garza G., An Optimal Solution to A Three Echelon Supply Chain Network with Multi-Product and Multi-period, Applied Mathematical Modelling, 34(5), pp. 1911-1918, 2014.
Cardenas-Barr L.E., Trevi-Garza G., Taleizadeh A. A. & Vasant P., Determining Replenishment Lot Size and Shipment Policy for an EPQ Inventory Model with Delivery and Rework, Mathematical Problems in Engineering, Article ID 595498,8 pageshttp://dx.doi.org/10.1155/2015/595498,2015.
Cheng Z. Xiao J. Xie K. & Huang X., Optimal Product Quality of Supply Chain Based On Information Traceability in Fashion and Textiles Industry, An Adverse Logistics Perspective, 2013, doi.org/10.1155/2013/629363.
Chung K. J. & Huang Y. F., The Optimal Cycle Time for EPQ Inventory Model Under Permissible Delay in Payments, International Journal of Production Economics, 84(3), pp. 307-318, 2003.
Chung K. J. Goyal S. K. & Huang Y. F., The Optimal Inventory Policies Under Permissible Delay in Payments Depending On the Order Quantity, the International Journal of Production Economics, 95(2), pp. 203-213, 2005.
Chung K. J., Ting P. Sh. & Cardenas-Barr L.E., A Simple Solution Procedure for Solving the Multi-Delivery Policy into Economic Production Lot Size Problem with Partial Rework, Scientia Iranica Transactions E, 24(5), pp. 2640-2644, 2017.
Chung K. J., Cdenas-Barr L. E., Liao J. J., & Ting P.S., The Simplified Solution Procedures for Solving Replenishment Lot Size Problem with Discontinuous Issuing Policy and Rework, Journal of Information and Optimization Sciences, DOI: 10.1080/02522667.2017.1395148, 2017.
Gautam P. & Khanna A., An Imperfect Production Inventory Model with Setup Cost Reduction and Carbon Emission for an Integrated Supply Chain, Uncertain Supply Chain Management 6, pp. 271-286, 2018.
Gautam P., Kishore A., Khanna A. & Jaggi C. K., Strategic Defect Management for A Sustainable Green Supply Chain, Journal of Cleaner Production, Accepted, DOI: 10.1016/j.jclepro.2019.06.005.
Goyal S. K., Economic Order Quantity Under Conditions of Permissible Delay in Payments, Journal of Research Society, 36(4), pp. 335-338, 1985.
Haji R., Haji, A., Sajadifar, M., & Zolfaghari, S., Lot Sizing with Non-Zero Setup Times for Rework, Journal of Systems Science and Systems Engineering, 17(2), pp. 230-240, 2008.
Huang Y. F., Optimal Retailers Ordering Policies in EOQ model under
Trade Credit Financing, Journal of the Operational Research Society, 54(9), pp. 1011-1015, 2003.
Huang Y.F., Economic Order Quantity Under Conditionally Permissible Delay in Payments, European Journal of Operational Research, 176(2), pp. 911-924, 2007.
Inderfurth K., Janiak A., Kovalyov M. Y. & Werner F., Batching Work and Rework Processes with Limited Deterioration of Reworkables, Computers & Operations Research 336), pp. 1595-1605, 2003.
Jamal A. M. M., Sarker B. R. & Wang S., Optimal Payment Time for A Retailer Under Permitted Delay of Payment by The Wholesaler, International Journal of Production Economics, 66(1), pp 59-66, 2000.
Jamal A. M. M., Sarker B. R. Mondal S, Optimal Manufacturing Batch Size with Rework Process at A Single-Stage Production System, Computers & Industrial Engineering, 47(1), pp. 77-89, 2004.
Jaggi C. K., Gautam P., and Khanna A., Inventory Decisions for Imperfect Quality Deteriorating Items with Exponential Declining Demand Under Trade Credit and Partially Backlogged Shortages, In Quality, IT and Business Operations (pp. 213-229) is Springer, Singapore 2018.
Jaroengeratikun U. & Lawson N., A Combined Family of Ratio Estimators for Population Mean using an Auxiliary Variable in Simple Random Sampling, Journal of Mathematical and Fundamental Sciences, 51(1), pp. 1-12, 2019.
John J. L. & Ping Y., Optimal Lot-Sizing in an Imperfect Production System with Homogeneous Reworkable Jobs, European Journal of Operational Research, 91(1), pp. 517-527, 1996.
Khanna A., Gautam P. & Jaggi C. K., Inventory Modeling for Deteriorating Imperfect Quality Items with Selling Price Dependent Demand and Shortage Backordering under Credit Financing, International Journal of Mathematical, Engineering and Management Sciences, 2(2), pp. 110?124, 2017.
Khanna A., Mittal M., Gautama P. & Jaggi C. K., Credit Financing for Deteriorating Imperfect Quality Items with Allowable Shortages, Decision Science Letters, 5, pp. 45?60, 2016.
Khanna A., Gautam P. & Jaggi C. K., Coordinating Vendor-Buyer Decisions for Imperfect Quality Items Considering Trade Credit and Fully Backlogged Shortages, In AIP Conference Proceeding, 1715(1), pp. 020065-11, AIP publishing LLC, 2016.
Khedlekar U. K., Nigwal A. R., Khedlekar N. K. & Patel H. K., Integrated Three Layer Supply Chain Inventory Model for Price Sensitive and Time Dependent Demand with Suggested Retail Price by Manufacturer, International Journal of Non Linear and Applications, 12(1), pp. 1135-1152, 2021.
Khedlekar U. K., Namdeo A. & Nigwal A. R., Production Inventory Model with Disruption Considering Shortages and Time Proportional Demand, Yugoslav Journal of Operations Research, 28(1), pp. 123-138, 2017.
Khedlekar U.K., Nigwal A.R., Khedlekar N.K., Reverse Supply Chain Coordinations for Multi-collectors, Multi-retailers and Single Remanufacturer with Symmetric Information, International Journal of Operations Research, 18(2), pp. 1-16, 2021.
Lee H. L. and Rosenblatt M. J., Simultaneous Determination of Production Cycle and Inspection Schedules in A Production System, Management Science, 33(9), pp. 1125-1136, 1987.
Mohammed B.D. & Mohammed Seliaman R.A., An Integrated Production Inventory Model with Raw Material Replenishment Coordinations in A Three-Layer Supply Chain, International Journal of Production Economics, 143(1), pp. 53-61, 2013.
Nobil A. H., Nobil E. & Cdenas-Barr L. E., Note On ?Lot Sizing with Non-Zero Setup Times for Rework?, International Journal of Applied and Computational Mathematics, DOI:10.1007/s40819-017-0340-6, 2017.
Nobil A.H, Afshar Sedigh A.H. & Cdenas-Barr L.E., Multi-Machine Economic Production Quantity of Scrapped and Reworked Items Considering Shortages and Allocation Decisions, Scientia Iranica Transactions E, 25(4), pp. 2331-2346, 2018.
Pal, B., Sana S.S. & Chaudhuri, K., Three Stage Trade Credit Policy in A Three-Layer Supply Chain-A Production Inventory Model, International Journal of Systems Science, 45(9), pp. 1844-1868, 2013.
Pal, B., Sana S.S. & Chaudhuri K., Three-Layer Supply Chain ? A Production-Inventory Model for Reworkable Items, Applied Mathematics and Computation, 219(2), pp. 530-543, 2012.
Rachokarn T. & Lawson N., An Efficient General Family of Estimators for Population Mean in The Presence of Non-Response, Journal of mathematical and fundamental sciences, 49(3), pp. 283-293, 2017.
Sarker B. R., Jamal A. M. M. & Mondal S., Optimal Batch Sizing in A Multi-Stage Production System with Rework Consideration, European Journal of Operational Research, 184(3), pp. 915-929, 2008.
Sarkar B., Sana S. S. & Chaudhuri K., Optimal Reliability, Production Lot Size and Safety Stock in an Imperfect Production System, International Journal of Mathematics in Operational Research, 2(4), pp. 467-490, 2010.
Shinn S. W. & Hwang H., Optimal Pricing and Ordering Policies for Retailers Under Order Size-Dependent Delay in Payment, Computer and Operational Research, 30(1), pp. 30-35, 2003.
Svajone B. & Sarka H. M., Decision Tree-based Classification Model for Identification of Effective Leadership Indicators, Journal of Mathematical and Fundamental Sciences, 50(2), pp. 121-141, 2018.
Taleizadeh1 A. A., Kalantari S.S. & Cdenas-Barr L. E., Determining Optimal Price, Replenishment Lot Size and Number of Shipments for an EPQ Model with Rework and Multiple Shipments, Journal of Industrial and management Optimization, 11(4) pp. 1059-1071, 2016.
Taleizadeh A. A., Kalantari S. S. & Cdenas-Barr L. E., Pricing and lot Sizing for an EPQ Inventory Model with Rework and Multiple Shipments, TOP, 24 pp. 143-155, 2016.
Taleizadeh A. A., Sari-Khanbaglo. M. P., Cardenas-Barr L. E., (In Press), Outsourcing Rework of Imperfect Items in the Economic Production Quantity (EPQ) Inventory Model with Backordered Demand, IEEE Transactions on Systems, Man, And Cybernetics: Systems, DOI:10.1109/TSMC.2107.2778943, 2017.
Tai, A.H., Economic Production Quantity Models for Deteriorating/Imperfect Products and Service with Rework, Computer & Industrial Engineering, 66(4), pp. 879-888, 2013.