How to make the replenishment and payment strategy under flexible two-part trade credit

In the existing inventory models concerning the two-part trade credit, a common assumption is that the retailer either pays for all the ordered items within a short permissible delay period and receives a cash discount or pays for all the ordered items within a long permissible delay period at the regular price. In this paper, this unrealistic assumption is relaxed. We assume that the retailer may pay any fraction of the purchase cost within the short permissible delay period and receives a cash discount and then the rest is paid within the long permissible delay period. A decision model is proposed for a retailer to determine the optimal ordering policy and payment plan. The closed-form optimal solution to the model is developed and analyzed. Numerical studies show that a retailer can obtain more benefits from the proposed payment plan than from the extreme payment plan in the existing literature.     

A fuzzy framework for coordinating pricing and inventory policies for deteriorating items under retailer partial trade credit financing

In this paper, we proposed a generalized economic order quantity (EOQ) – based inventory model using a trade credit policy in a fuzzy sense. The trade credit policy adopted here is a two-level trade credit policy in which the supplier offers the retailer a permissible delay period M, and the retailer, in turn, partially provides customers a permissible delay period N. This study considers fuzzy EOQ model to allow for: (1) selling price dependent demand rate which is imprecise in nature, (2) a profit maximization objective and (3) an imprecise holding cost, ordering cost, purchasing cost, interest earned and interest charged rate. Besides, the cases N ? M and N ? M are explored thoroughly. The objective function for the retailer in fuzzy sense is defuzzified using Modified Graded Mean Integration Representation Method. For the defuzzified objective function sufficient conditions for the existence and uniqueness of the optimal solution are provided. An efficient algorithm is designed to determine the optimal pricing and inventory policies for the retailer. Finally, numerical examples are presented to illustrate the proposed model and the effect of key parameters on optimal solution is examined.     

Two-echelon trade credit financing for perishable items in a supply chain when demand depends on both selling price and credit period

A profitable decision policy between a supplier and the retailers can be characterized by an agreement on the trade credit scenario such as permissible delay in payments. In real life business, we observe that the demand is a function of both the selling price and credit period rather than the constant demand. Incorporating this demand function to the retailer of a supply chain, we develop an EPQ – based model for perishable items under two-echelon trade financing. The purpose of this paper is to maximize the profit by determining the optimal selling price, credit period and replenishment time. It is shown that the model developed by Jaggi et al. [Jaggi, J. K., Goyal, S. K., & Goel, S. K., 2008. Retailer’s optimal replenishment decisions with creditlinked demand under permissible delay in payments. European Journal of Operational Research, 190, 130–135] can be treated as a special case of this paper. Finally, through numerical examples, sensitivity analysis shows the influence of key model parameters.     

An alternative approach to analyze economic ordering quantity and economic production quantity inventory problems using the completing the square method

In most papers and textbooks, the economic order quantity (EOQ) models and their variants, and the economic production quantity (EPQ) models and their variants are commonly solved using differential calculus. This study proposes an alternative approach that transform the problem into a suitable form and a procedure using the completing the squares method is employed to obtain the optimal solution. The applicability of the method is demonstrated for some selected single and multi-variable problems given in the literature.     

Economic production quantity (EPQ) models under an imperfect production process with shortages backordered

In this paper, we develop economic production quantity (EPQ) models to determine the optimal production lot size and backorder quantity for a manufacturer under an imperfect production process. The imperfect production process is characterised by the fraction of defective items at the time of production γ. The paper considers different cases of the EPQ model depending on (1) whether γ is known with certainty or is a random variable, and (2) whether imperfect items are drawn from inventory (a) as they are detected, (b) at the end of each production period or (c) at the end of each production cycle. Straightforward convexity results are shown and closed-form solutions are provided for the optimal order and backorder quantities for each of the cases we considered. We provide two numerical examples: one in which the defective probability follows a uniform distribution and the second which we assume follows a beta distribution, to illustrate the effects of yield variability and timing of the withdrawal of defectives on the optimal solutions. We obtain similar results for both numerical examples, which show that both the yield variability and the withdrawal timing are not critical factors.     

The effect of inflation‐induced demand and trade credit on ordering policy of exponentially deteriorating and imperfect quality items

This paper develops an inventory model for exponentially deteriorating and imperfect quality items when a trade credit is offered by the supplier. As it has been seen that the changing rates of inflation do not just have an effect on the ordered quantity but they also stimulate the demand for products, so this paper considers the combined effect of inflation, deterioration, imperfect quality and ‘’ trade credit policy on the economic ordering policy using a discounted cash flow (DCF) approach. In the study, mathematical models are derived under two different circumstances, i.e., Case I: When the discount offered by the supplier with a condition of making the payment by a specified period, M₁ is accepted; and Case II: Discount is not taken and instead the payment is made by the end of the full credit period M (M > M₁). Finally, a numerical example demonstrating the applicability of the proposed model has been included.     

Developing economic order quantity model for non-instantaneous deteriorating items in vendor-managed inventory (VMI) system

This paper develops an economic order quantity model for non-instantaneous deteriorating items with and without shortages to investigate the performance of the vendor-managed inventory (VMI) system. This model is developed for a two-level supply chain consisting of a single supplier and single retailer with a single non-instantaneous deteriorating item. A numerical example and sensitivity analysis are provided to illustrate how increasing or reducing the related parameters change the optimal values of the decision variables of the two proposed models. The results show that VMI works better and charges lower cost in all conditions.     

Comment on ‘Optimal inventory replenishment policy for the EPQ model under trade credit derived without derivatives’

In this article, we complement the shortcoming of the inventory economic production quantity (EPQ) model developed by Huang and Huang (2008 Huang, YF and Huang, HF. 2008. Optimal Inventory Replenishment Policy for the EPQ Model Under Trade Credit Derived Without Derivatives. International Journal of Systems Science, 39: 539–546. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), ‘Optimal Inventory Replenishment Policy for the EPQ Model Under Trade Credit Derived Without Derivatives’, International Journal of Systems Science, 39, 539–546), and propose an arithmetic–geometric inequality method to obtain the global optimal solution without taking complex differential calculus or using tedious algebraic manipulations. Finally, we provide an economical interpretation of the theoretical result so that the reader can understand the insight of the result.     

Three stage trade credit policy in a three-layer supply chain–a production-inventory model

The main purpose of this paper is to investigate the optimal replenishment lot size of supplier and optimal production rate of manufacturer under three levels of trade credit policy for supplier–manufacturer–retailer supply chain. The supplier provides a fixed credit period to settle the accounts to the manufacturer, while the manufacturer gives a fixed credit period to settle the account to the retailer and the retailer, in turn, also offers a credit period to each of its customers to settle the accounts. We assume that the supplier supplies the raw material to the manufacturer and sends back the defective raw materials to the outside supplier after completion of inspection at one lot with a sales price. The system always produces good items in the model. Also, we consider the idle times of supplier and manufacturer. Finally, numerical examples are provided to illustrate the behaviour and application of the model with graphical simulation.     

A general model for EOQ inventory systems with partial backlogging and linear shortage costs

We present a mathematical model which generalises several known deterministic Economic Order Quantity (EOQ) inventory systems with partial backlogging. This inventory model considers purchasing cost, holding cost, shortage costs and replenishment cost. Shortage costs (backorder cost and lost sales cost) are both made up of a fixed cost and a variable cost which depends on the length of the waiting time for the next replenishment. The optimal policy is characterised through a sequential optimisation procedure. To illustrate the model, numerical examples and sensitivity results are given.