A Single-Manufacturer Multi-Retailer Integrated Inventory Model with Price Dependent Demand and Stochastic Lead Time

Document Type: FORBS 2019

Authors

Department of Mathematics Jadavpur University Kolkata, India

Abstract

This paper deals with a two-level supply chain composed of a single manufacturer and multiple retailers. Ordered quantities of the retailers are dispatched in some equal batches from the manufacturer. Customer demand linearly depends on the selling price of the item. Lead time is random and it follows a normal distribution. The proposed model is developed for both the centralized and the decentralized scenarios. In the decentralized scenario, a Stackelberg gaming approach is used to derive the optimal decisions. The developed models are illustrated by a numerical example. It is found that integration of the supply chain players gives an impressive increment in the profit of the whole supply chain. Sensitivity analysis is also performed to explore the impacts of key-model parameters on the expected average profit of the supply chain.

Keywords


Alfares H. K. and Ghaithan A. M. (2016). Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts. Computers & Industrial Engineering, Vol. 94, pp. 170-177.

Banerjee A. (1986). A joint economic-lot-size model for purchaser and vendor. Decision sciences, Vol. 17(3), pp. 292-311.

Banerjee A. (2005). Concurrent pricing and lot sizing for make-to-order contract production. International Journal of Production Economics, Vol. 93, pp. 189-195.

Ben-Daya M. and Hariga M. (2004). Integrated single vendor single buyer model with stochastic demand and variable lead time. International Journal of Production Economics, Vol. 92(1), pp. 75-80.

Biswas S. and Giri B. C. (2019). A Single-vendor Single-buyer Integrated Model for Deteriorating Items with Partial Backlogging and Price-dependent Market Demand. International Journal of Applied Engineering Research, Vol. 14(1), pp. 254-261.

Das S. C., Zidan A. M., Manna A. K., Shaikh A. A. and Bhunia A. K. (2020). An application of preservation technology in inventory control system with price dependent demand and partial backlogging. Alexandria Engineering Journal, Vol. 59(3), pp. 1359-1369.

Giri B.C. and Roy B. (2015). A single-manufacturer multi-buyer supply chain inventory model with controllable lead time and price-sensitive demand. Journal of Industrial and Production Engineering, Vol. 32(8), pp. 516-527.

 Giri B. C., Bhattacharjee R. and Maiti T. (2018). Optimal payment time in a two-echelon supply chain with price-dependent demand under trade credit financing. International Journal of Systems Science: Operations & Logistics, Vol. 5(4), pp. 374-392.

Giri B. C. and Masanta M. (2018). Developing a closed-loop supply chain model with price and quality dependent demand and learning in production in a stochastic environment. International Journal of Systems Science: Operations & Logistics, pp. 1-17.

Giri B. C. and Masanta M. (2019). Optimal production policy for a closed-loop supply chain with stochastic lead time and learning in production. Scientia Iranica, Vol. 26(5), pp. 2936-2951.

Glock C. H. (2012). The joint economic lot size problem: A review. International Journal of Production Economics, Vol. 135(2), pp. 671-686.

Glock C. H. (2012). Lead time reduction strategies in a single-vendor-single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand. International Journal of Production Economics, Vol. 136(1), pp. 37-44.

Goyal S. K. (1976). An integrated inventory model for a single supplier-single customer problem. The International Journal of Production Research, Vol. 15(1), pp. 107-111.

Goyal S. K., and Nebebe F. (2000). Determination of economic production-shipment policy for a single-vendor-single-buyer system. European Journal of Operational Research, Vol. 121(1), pp. 175-178.

Ho C. H. (2009). A minimax distribution free procedure for an integrated inventory model with defective goods and stochastic lead time demand. International Journal of Information and Management Sciences, Vol. 20(1), pp. 161-171.

Hoque M. A. (2013). A manufacturer-buyer integrated inventory model with stochastic lead times for delivering equal-and/or unequal-sized batches of a lot. Computers & Operations Research, Vol. 40(11), pp. 2740-2751.

Khalilpourazari S., Pasandideh S. H. R. and Niaki S. T. A. (2019a). Optimizing a multi-item economic order quantity problem with imperfect items, inspection errors, and backorders. Soft Computing, Vol.23(22), pp. 11671-11698.

Khalilpourazari S., Mirzazadeh A., Weber G. W. and Pasandideh S. H. R. (2019b). A robust fuzzy approach for constrained multi-product economic production quantity with imperfect items and rework process. Optimization. https://doi.org/10.1080/02331934.2019.1630625

Khalilpourazari S., Teimoori S., Mirzazadeh A., Pasandideh S. H. R. and Ghanbar Tehrani N. (2019c). Robust Fuzzy chance constraint programming for multi-item EOQ model with random disruption and partial backordering under uncertainty. Journal of Industrial and Production Engineering, Vol.36(5), pp. 276-285.

Khalilpourazari S., Soltanzadeh S., Weber G. W. and Roy, S. K. (2020). Designing an efficient blood supply chain network in crisis: neural learning, optimization and case study. Annals of Operations Research, Vol.289(1), pp. 123-152.

Khanra S., Sana S. S. and Chaudhuri K. (2010). An EOQ model for perishable item with stock and price dependent demand rate. International Journal of Mathematics in Operational Research, Vol. 2(3), pp. 320-335.

Jha J. K. and Shanker K. (2013). Single-vendor multi-buyer integrated production-inventory model with controllable lead time and service level constraints. Applied Mathematical Modelling, Vol. 37(4), pp. 1753-1767.

Lee W. C., Wu J. W. and Lei C. L. (2007). Computational algorithmic procedure for optimal inventory policy involving ordering cost reduction and back-order discounts when lead time demand is controllable. Applied mathematics and computation, Vol. 189(1), pp. 186-200.

Li Y., Xu X. and Ye F. (2011). Supply chain coordination model with controllable lead time and service level constraint. Computers & Industrial Engineering, Vol. 61(3), pp. 858-864.

 Lin H. J. (2016). Investing in lead-time variability reduction in a collaborative vendor-buyer supply chain model with stochastic lead time. Computers & Operations Research, Vol. 72, pp. 43-49.

Mandal P. and Giri B. C. (2015). A single-vendor multi-buyer integrated model with controllable lead time and quality improvement through reduction in defective items. International Journal of Systems Science: Operations & Logistics, Vol. 2(1), pp. 1-14.

Maragatham M. and Lakshmidevi P. K. (2014). A fuzzy inventory model for deteriorating items with price dependent demand. Intern. J. Fuzzy Mathematical Archive, Vol. 5(1), pp. 39-47.

Maragatham M. and Palani R. (2017). An Inventory Model for Deteriorating Items with Lead Time price Dependent Demand and Shortages. Advances in Computational Sciences and Technology, Vol. 10(6), pp. 1839-1847.

Mashud A. H. M., Wee H. M. and Huang C. V. (2019). Preservation technology investment, trade credit and partial backordering model for a non-instantaneous deteriorating inventory. RAIRO-Operations Research. https://doi.org/10.1051/ro/2019095

Mashud A. H. M., Wee H. M., Sarkar B. and Li Y. H. C. (2020). A sustainable inventory system with the advanced payment policy and trade-credit strategy for a two-warehouse inventory system. Kybernetes. https://doi.org/10.1108/K-01-2020-0052

Ouyang L. Y., Chuang B. R. and Lin Y. J. (2007). The inter-dependent reductions of lead time and ordering cost in periodic review inventory model with backorder price discount. International Journal of Information and Management Sciences, Vol. 18(3), pp. 195-208.

 

Pandey A., Masin M. and Prabhu V. (2007). Adaptive logistic controller for integrated design of distributed supply chains. Journal of Manufacturing Systems, Vol. 26(2), pp. 108-115.

Pervin, M., Roy S. K. and Weber G. W. (2019). Multi-item deteriorating two-echelon inventory model with price-and stock-dependent demand: A trade-credit policy. Journal of Industrial and Management Optimization, Vol.15(3), pp. 1345-1373.

Pervin M., Roy S. K. and Weber G. W. (2020). Deteriorating inventory with preservation technology under price-and stock-sensitive demand. Journal of Industrial and Management Optimization, Vol. 16(4), pp. 1585-1612.

Poorbagheri T. and Niaki S. T. A. (2014). Vendor Managed inventory of a single-vendor multiple-retailer single-warehouse Supply Chain under stochastic Demands. International Journal of Supply and Operations Management, Vol. 1(3), pp. 297-313.

Rastogi M., Singh S. R. and Kushwah P. (2018). An inventory model for non-instantaneous deteriorating products having price sensitive demand and partial backlogging of occurring shortages. Int. J. Oper. Quant. Manag, Vol. 24(1), pp. 59-73.

Ray S. and Jewkes E. M. (2004). Customer lead time management when both demand and price are lead time sensitive. European Journal of operational research, Vol. 153(3), pp. 769-781.

Roy S. K., Pervin M. and Weber G. W. (2018). A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy. Journal of Industrial and Management Optimization, Vol. 16(2), pp. 553-578.

 Sajadieh M. S., Jokar M. R. A. and Modarres M. (2009). Developing a coordinated vendor-buyer model in two-stage supply chains with stochastic lead-times. Computers & Operations Research, Vol. 36(8), pp. 2484-2489.

Sarkar S., Tiwari S., Wee H. M. and Giri B. C. Channel coordination with price discount mechanism under price-sensitive market demand. International Transactions in Operational Research, DOI: 10.1111/itor.12678.

Sohrabi M. S., Fattahi P., Kheirkhah A. S. and Esmaeilian G. (2016). Supplier Selection in Three Echelon Supply Chain & Vendor Managed Inventory Model Under Price Dependent Demand Condition. International Journal of Supply and Operations Management, Vol. 2(4), pp. 1079-1101.

Taleizadeh A. A., Niaki S. T. A. and Makui A. (2012). Multiproduct multiple-buyer single-vendor supply chain problem with stochastic demand, variable lead-time, and multi-chance constraint. Expert Systems with Applications, Vol. 39(5), pp. 5338-5348.

Uthayakumar R. and Kumar M. G. (2019). Single-vendor multi-buyer integrated inventory system for multi-item. International Journal of Mathematics in Operational Research, Vol. 14(3), pp. 359-376.

Vijayashree M. and Uthayakumar R. (2015). Integrated inventory model with controllable lead time involving investment for quality improvement in supply chain system. International Journal of Supply and Operations Management, Vol. 2(1), pp. 617-639.

Vijayashree M. and Uthayakumar R. (2017). Lead time reduction in an integrated inventory model for non-defective items under a supply chain system. Computer Game Development and Education: An International Journal, Vol. 1, pp. 39-58.

Wangsa I. D. and Wee H. M. (2019). A vendor-buyer inventory model for defective items with errors in inspection, stochastic lead time and freight cost. INFOR: Information Systems and Operational Research, pp. 1-26.

Whitin T. M. (1955). Inventory control and price theory. Management science, Vol. 2(1), pp. 61-68.

Yang C. T., Ouyang L. Y. and Wu H. H. (2009). Retailer’s optimal pricing and ordering policies for non-instantaneous deteriorating items with price-dependent demand and partial backlogging. Mathematical Problems in Engineering, https://doi.org/10.1155/2009/198305

Yang P. C., Chung S. L., Wee H. M., Zahara E. and Peng C. Y. (2013). Collaboration for a closed-loop deteriorating inventory supply chain with multi-retailer and price-sensitive demand. International Journal of Production Economics, Vol. 143(2), pp. 557-566.