Optimal pricing and ordering policy for an integrated inventory model with quadratic demand when trade credit linked to order quantity

Abstract

Purpose -The purpose of this paper is to study integrated inventory system and pricing and ordering strategy for vendor-buyer supply chain system. Here, the vendor offers a trade credit to the buyer when the buyer's order quantity exceeds a given pre-specified quantity. Therefore, to incorporate the concept of vendor-buyer integration and trade credit linked, the authors analyze the model to determine the optimal strategy for an integrated vendor-buyer inventory system under the condition of credit linked to the order quantity when demand is quadratic. Design/methodology/approach -A mathematical model for integrated inventory system is developed when demand rate is increasing function of the time and decreasing function of the retail price. By analyzing the total channel profit function, the authors developed some useful results to characterize the optimal solution and provide an iterative algorithm to find the retail price, buyer's order quantity and the number of shipments per production run from the vendor to the buyer. Findings -By developing a solution algorithm, the optimal retail price, order quantity and number of shipments from the vendor to the buyer are provided. Numerical examples and sensitivity analyses are presented to validate the proposed model. Through extensive numerical analyses, it is observed that a longer credit term increases profits of the player for the entire supply chain. The vendor should establish the threshold for allowing trade credit comprehensively to ensure the greatest benefit for both players. Originality/value -Most of the research articles available in the literature considered the constant demand or linearly changing demand. In this paper, a mathematical model is developed considering time dependent quadratic demand. Very few researchers have investigated joint optimal policy in vendor-buyer supply chain system, considering trade credit is linked to order quantity, and still there are not many findings on the benefit of integrated policy and trade credit.

Determining bucket structures in pricing plans for private user cloud computing storage services

“…More specifically, we simulate the CC storage demand of customers for each observed period and to determine user bucket choices, which are driven by their individual utility function. Based on this approach and similar to Shah et al (2012), different types of demand distributions and bucket ceiling setups are examined to determine the optimal structure for distinct scenarios. The two general types of the bucket ceiling allocations applied in the simulation are depicted in Section 4.1.…”

Reviewing the Literature of Inventory Models under Trade Credit Contact

“…EOQ Constant ------Teng and Lou [118] EOQ Credit dependent --✓ ---Dye [119] EOQ Price and time dependent ✓ ✓ ✓ ---Chung [120] Integrated Credit dependent --✓ ---Su [121] i n t e g r a t e d C o n s t a n t ✓ -----Thangam [122] E O Q C o n s t a n t -✓ ✓ ---Soni and Patel [123] Integrated Price dependent --✓ ---Zhong and Zhou [124] Noncooperative Constant ------Shah et al [125] Integrated Time and price dependent ---✓ --Guchhait et al [126] EOQ Stock and price dependent - [128] I n t e g r a t e d C o n s t a n t -✓ ----Liao et al [129] E O Q C o n s t a n t -✓ ----Yang and Chang [130] E O Q C o n s t a n t ✓ ✓ --✓ ✓ Feng et al [131] EPQ Constant --✓ ---Giri and Maiti [132] Integrated Price and credit dependent - [134] E O Q C o n s t a n t ✓ -----Yu [ [143] I n t e g r a t e d C o n s t a n t ✓ ✓ --✓ -Chiu et al [144] Integrated Price dependent ---✓ --Huang et al [145] EPQ Constant ------Ouyang et al [146] E O Q C o n s t a n t --✓ ✓ --Soni [147] EOQ Price and stock dependent -✓ --✓ -Shah et al [148] integrated Pricedependent ------Liao et al [149] E O Q C o n s t a n t -✓ --✓ -He and Huang [150] E O Q C r e d i t d e p e n d e n t -✓ ✓ ---Chuang et al [151] Integrated Constant ---✓ -- [153] E O Q C o n s t a n t ---✓ --Janková et al [154] EOQ Timedependent ------Singh and Sharma [155] EPQ Stock dependent -✓ ----Chung et al [156] E O Q C o n s t a n t -✓ -✓ -✓ Pal and Chandra [157] EOQ Stock dependent ✓ -----Tung et al [158] E O Q C o n s t a n t -✓ ----Wang et al [159] E O Q C r e d i t d e p e n d e n t -✓ ----Molamohamadi et al [160] EPQ Price dependent ✓ ✓ ----Bhunia et al [161] E...…”

“…Teng et al [108] modelled a vendorbuyer inventory system with order quantity-dependent trade credit contract and determined the optimal solution under two different scenarios: a noncooperative Nash equilibrium with no dominating firm and an integrated model, in which both vendor and buyer are considered as a single firm. Shah et al [125] studied order quantity-dependent trade credit to formulate an integrated supply chain model with time and price-sensitive quadratic demand. Chung [127] formulated an EOQ inventory model of a retailer who is offered partial order-quantity-dependent credit period by the supplier and may receive defective items.…”

Pricing model for instantaneous deteriorating items with partial backlogging and different demand rates

“…Teng et al (2007) extended Abad's (2003) model by calculating backlogging cost and lost sale cost in profit function. Shah et al (2012) formulated integrated ordering and pricing policy with quadratic demand function of time and power function of price without allowing shortages and deterioration. Mukhopadhyay et al (2004) computed demand rate as general function of price and deterioration rate as time dependent linear function without provision of shortages.…”