A vendor–buyer inventory model with lot-size and production rate dependent lead time under time value of money

Abstract

The paper studies an integrated vendor-buyer model with shortages under stochastic lead time which is assumed to be variable but depends on the buyer's order size and the vendor's production rate. The replenishment lead time and the market demand uncertainty are assumed to be reduced by changing the regular production rate of the vendor at the risk of paying additional cost. Shortages are partially backlogged and the backlogging rate depends on the length of the buyer's replenishment lead time. The proposed model is formulated to obtain the net present value (NPV) of the expected total cost of the integrated system through optimization of (i) the buyer's order quantity, (2) the buyer's safety factor, and (3) the vendor's production rate. Theoretical results are derived to demonstrate the existence and uniqueness of the optimal solution. Through extensive numerical study, some valuable managerial insights are obtained.Mathematics Subject Classification. 90B05, 90B06.

A multi-retailer sustainable supply chain model with information sharing and quality deterioration

“…Sarkar and Majumder [39] and developed integrated supply chain models in which methods were discussed to reduce setup cost which has remarkable impact on minimizing the overall expected supply chain cost. An inventory model was discussed by Sarkar and Giri [44] in uncertain demand environment.…”

“…The integrated models with imperfect quality have always been the interest area of many. Like, Sarkar et al [44] worked on imperfect production manufacturing system and provided its safety stock, optimal batch size and reliability. Sana [37] offered an inventory model for manufacturer and retailer.…”

The beneficial effect of information sharing in the integrated production–distribution planning of textile and apparel supply chain

“…More recently, Sarkar and Giri [35] formulated an integrated supply chain model with backorder price discount by assuming the replenishment lead time as a linear function of order size, setup time and transportation time. Sarkar et al [36] investigate how replenishment lead time affects the backorder quantity and possible way to increase the backorder rate during shortage.…”

“…The literature on integrated production-distribution planning problem is abundant as shown by Mula et al [28], Chen [7], Fahimnia et al [12] and Moons et al [25]. Different variants of this problem have been investigated: some works involve a single manufacturer and/or a single retailer [3,8,30] with multiple products, while others take into account a single product [6,24,35,36]. Some other papers study the case of multiple manufacturers with multiple products [18,19,43], though the latter are limited to a single period.…”

“…Noticeably, many integrated production-distribution planning models are sector specific and have been especially devoted to time-sensitive [36] and/or perishable products such as medicine [15], food [8,13,22], dairy products [16], newspapers [33] and fashion apparel [2,11,14,34].…”