Optimal ordering policy in a two-echelon supply chain model with variable backorder and demand uncertainty (original) (raw)
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Development of a Consignment Inventory Model in a Two-echelon Supply Chain with Backorder
International Journal of Emerging Technology and Advanced Engineering, 2013
This paper considers a two-level supply chain consisting of a manufacturer and two buyers. The manufacturer produces one type of products at a finite rate and replenishes them to the buyers. Each buyer's demand is sensitive to his selling price and the backorder is allowed at the buyers. Moreover, it is assumed that the buyers delay paying for goods to the manufacturer and two types of delay in payment are considered; delay paying for the purchased items till they are used or sold to the end customers, and delay paying till the next replenishment order. The main aim of this research is formulating the manufacturer and the buyers' problems in terms of integer-ratio policy and discounted cash flow under these two types of delay in payment.
Journal of the Operational Research Society, 2020
As supply chains span across one or more continents, an intermediate firm becomes an inevitable supply chain component. While seller-financing options (e.g. delay in payment), are well studied, researchers have rarely investigated them from the perspective of an intermediate firm in a supply chain. We construct a three-echelon supply chain that consists of a supplier, distributor, and retailer. In our model, the supplier and distributor may offer seller financing to their buyer, but only the distributor is subject to the buyer's default risk. We consider a seller-financing supply chain wherein either all or none of the sellers premise delay in payment and a special case where the distributor may coordinate with the supplier or retailer. An algorithm solves optimal replenishment and delay-in-payment decisions. Numerical analyses illustrate managerial insights, which show that when the retailer's default risk is high, the distributor's best strategy is not to offer any delay-in-payment. When the distributor-retailer coordination can subsidise the retailer's default risk, the distributor's best strategy is coordination with the retailer and bargaining for more financial support from the supplier. In contrast, as the retailer's default risk is inevitable, the distributor-supplier integration is the optimal supply chain financing strategy.
Journal of Industrial Engineering International, 2017
Traditional supply chain inventory modes with trade credit usually only assumed that the upstream suppliers offered the downstream retailers a fixed credit period. However, in practice the retailers will also provide a credit period to customers to promote the market competition. In this paper, we formulate an optimal supply chain inventory model under two levels of trade credit policy with default risk consideration. Here, the demand is assumed to be credit-sensitive and increasing function of time. The major objective is to determine the retailer's optimal credit period and cycle time such that the total profit per unit time is maximized. The existence and uniqueness of the optimal solution to the presented model are examined, and an easy method is also shown to find the optimal inventory policies of the considered problem. Finally, numerical examples and sensitive analysis are presented to illustrate the developed model and to provide some managerial insights.
Computers & Industrial Engineering, 2014
This paper develops a model of an integrated vendor-buyer supply chain with imperfect production and shortages. We assume that market demand is sensitive to the buyer's selling price and thus study combined operations and pricing decisions in the supply chain. We first derive the expected profit per unit of time using the well-known renewal-reward theorem, and then maximize profit for the cases of independent and joint optimization. Numerical examples and a sensitivity analysis are provided to illustrate the proposed models. The results indicate that coordination and backordering improve the total expected profit of the system, and that both measures become more important for the supply chain as the price sensitivity of demand increases. Furthermore, the coordinated supply chain often prefers to perform inspection at the vendor, who is more familiar with the product and its deficiencies than the buyer in many cases.
Optimal Pricing and Ordering Policy for Two Echelon Varying Production Inventory System
Journal of Industrial Engineering, 2014
The paper proposes a two-stage supply chain model for price sensitive demand in imperfect production system while manufacturer and supplier are the members of the chain. The supplier screens the raw materials first and supplies good materials to the manufacturer at a constant rate. The production rate varies randomly within a finite interval. The inventory cycle of the manufacturer starts with shortages and production and it finishes with shortages again, in which shortages are partially backlogged. We consider a mixture of LIFO (last in, first out) and FIFO (first in, first out) dispatching policies to fill the backlogged demand. Thus, the objective of the proposed paper is to determine the optimal ordering lot-size and selling price of the manufacturer such that the per unit average integrated expected profit of the supply chain model is maximized. A numerical example is provided to analyze and illustrate the behavior and application of the model. Finally, sensitivity analysis of ...
Supply chain is not limited to delivering products to the end-costumers since the defective products that are returned back to the producers by the consumers. The producers should be superior knowledge to utilize the return products effectively so as to maintain our natural resources and to provide better service to customers. In this paper, a distributor and a warehouse consisting of a serviceable part and a recoverable part supply chain problem is considered in which there are several products, the distributor has limited space capacity and budget to purchase all products. In this supply chain, the defective products are returned back to the warehouse by the distributor and the warehouse recovered those defective products into perfect products having the same value as the procured products. The lead-time of receiving products from a warehouse to a distributor is a variable which is controllable by adding extra crashing cost. For each product, a fraction of the shortage is backordered and the rest are lost. A mathematical model is employed in this study for optimizing the order quantity, lead time and total number of deliveries with the objective of minimizing system total cost. We show that the model of this problem is a constrained non-linear programme and present a simple Lagrangian multiplier technique to solve it. Numerical and sensitivity analysis are given to show the applicability of the proposed model in real-world product returns inventory problems.
A multi-retailer supply chain model with backorder and variable production cost
RAIRO - Operations Research, 2017
The modern marketing environment involves variability and randomness within the numerous parties of any supply chain network. Thus, formation of a supply chain model including multiple buyers and variable production rate is more acceptable than assuming a single-buyer with constant production rate model. This paper considers a supply chain network, where a single-vendor manufactures products in a batch production process and supplies them to a set of buyers over multiple times. Instead of assuming a fixed production rate, as commonly used in the literature, a variable production rate is introduced by the vendor and the production cost of the vendor is treated as a function of production rate. The continuous review inventory model is applied for multiple buyers to inspect inventory levels and a crashing cost is incurred by all buyers to reduce their lead times. The lead time demand follows a normal distribution. The unsatisfied demands at the buyers end are partially backordered. A m...
Journal of Uncertainty Analysis and Applications, 2013
In this paper, an integrated production-inventory model is presented for a supplier, manufacturer, and retailer supply chain under conditionally permissible delay in payments in uncertain environments. The supplier produces the item at a certain rate, which is a decision variable, and purchases the item to the manufacturer. The manufacturer has also purchased and produced the item in a finite rate. The manufacturer sells the product to the retailer and also gives the delay in payment to the retailer. The retailer purchases the item from the manufacture to sell it to the customers. Ideal costs of supplier, manufacturer, and retailer have been taken into account. An integrated model has been developed and solved analytically in crisp and uncertain environments, and finally, corresponding individual profits are calculated numerically and graphically.
Applied Mathematics and Computation, 2013
Recently, Kreng and Tan [Expert Systems with Applications 37 (2010) 5514-5522] developed an economic order quantity (EOQ) model under two levels of trade credit policy in which the supplier offers to the wholesaler a permissible delay period M, and the wholesaler also provides its retailers a permissible delay period N (with M > N). In this paper, we point out some inappropriate mathematical expressions in both interest charged and interest earned in Kreng and Tan. For generality, we then extend their model to allow the following facts: (1) the interest rate I c charged by the supplier is not necessarily higher than the interest rate I e earned by the wholesaler, and (2) the permissible delay period M offered by the supplier is independent of the permissible delay period N offered by the wholesaler. Furthermore, we study the necessary and sufficient conditions for finding the optimal solution, and thus establish several theoretical results to characterize the solution that provides the minimum annual total relevant cost. Finally, numerical examples are given to illustrate the theoretical results and obtain some managerial insights. j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a m c the down-stream trade credit period N is less than the up-stream trade credit period M.
International Journal of Strategic Decision Sciences, 2011
This paper investigates the economic order quantity inventory model for a retailer under two levels of trade credit to reflect the supply chain management situation. It is assumed that the retailer maintains a powerful position and can obtain full trade credit offered by supplier, yet the retailer just offers the partial trade credit to customers. Under these conditions, the retailer can obtain the most benefits. This study also investigates the retailer’s inventory policy for deteriorating items in a supply chain management situation as a cost minimization problem. The present study shows that the annual total variable cost for the retailer is convex, that is, a unique solution exists. Mathematical theorems and algorithms are developed to efficiently determine the optimal inventory policy for the retailer. The results in this paper generalize some already published results. Finally, numerical examples are given to illustrate the theorems and obtain managerial phenomena.