A note on: Optimal ordering policy for stock-dependent demand under progressive payment scheme

In a recent paper, Soni and Shah [Soni, H., Shah, N. H. (2008). Optimal ordering policy for stock-dependent demand under progressive payment scheme. European Journal of Operational Research 184(1), 91–100] developed a model to find the optimal ordering policy for a retailer with stock-dependent demand and a supplier offering a progressive payment scheme to the retailer. This note corrects some errors in the formulation of the model of Soni and Shah. It also extends their work by assuming that the credit interest rate of the retailer may exceed the interest rate charged by the supplier. Numerical examples illustrate the benefits of these modifications

A comprehensive extension of optimal ordering policy for stock-dependent demand under progressive payment scheme

[[abstract]]In a recent paper, Soni and Shah (2008) presented an inventory model with a stock-dependent demand under progressive payment scheme, assuming zero ending-inventory and adopting a cost-minimization objective. However, with a stock-dependent demand a non-zero ending stock may increase profits resulting from the increased demand. This work is motivated by Soni and Shah’s (2008) paper extending their model to allow for: (1) a non-zero ending-inventory, (2) a profit-maximization objective, (3) a limited inventory capacity and (4) deteriorating items with a constant deterioration rate. For the resulted model sufficient conditions for the existence and uniqueness of the optimal solution are provided. Finally, several economic interpretations of the theoretical results are also given.[[incitationindex]]SCI[[booktype]]紙

Economic ordering and payment policies under progressive payment schemes and time-value of money

Trade credits have received considerable attention in recent years and have become one of the most important sources of short-term funding for many companies. The paper at hand studies the optimal ordering and payment policies of a buyer assuming that the supplier offers a progressive interest scheme. The contribution to the literature is twofold. First, the different financial conditions of the companies involved are taken into account by assuming that the credit interest rate of the buyer may, but not necessarily has to, exceed the interest rate charged by the supplier. In addition, the time-value of money is considered in this scenario which is relevant when trade credit terms are valid for a long period of time and payment flows need to be evaluated by their net present value to ensure long-term profitability. The models proposed enable decision makers to improve ordering and payment decisions and the results reveal that taking into account the temporal allocation of payments, the prevailing interest relation influences replenishment policies significantly

The influence of financial conditions on optimal ordering and payment policies under progressive interest schemes

In many business-to-business transactions, the buyer is not required to pay immediately after the receipt of an order, but is instead allowed to postpone the payment to its suppliers for a certain period. In such a situation, the buyer can either settle the account at the end of the credit period or authorize the payment later, usually at the expense of interest that is charged by the supplier on the outstanding balance. Some payment terms, which are often referred to as trade credit contracts, contain progressive interest charges. In such cases, the supplier offers a sequence of credit periods, where the interest rate that is charged on the outstanding balance usually increases from period to period. If a buyer faces a progressive trade credit scheme, various options for settling the unpaid balance exist, where the financial impact of each option depends on the current credit interest structure and the alternative investment conditions. This paper studies the influence of different financial conditions in terms of alternative investment opportunities and credit interest structure on the optimal ordering and payment policies of a buyer on the condition that the supplier provides a progressive interest scheme. For this purpose, mathematical models are developed and analyzed

Stackcelberg Game Inventory Model With Progressive Permissible Delay of Payment Scheme

Supplier has many schemes to motivate retailer to buy more and of them one is a progressive permissible delay of payment. Instead of analyst from the retailer side alone, in this chapter, we develop the inventory model of supplier and retailer. In reality, some suppliers and retailers cannot have collaboration and they try to optimize their own decision so we develop a Stackelberg Game model. Two models are developed wherein the first model supplier acts as the leader and in the second model, the retailer acts a leader. Since the models are complex, a hybrid Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) is developed to solve the model. A numerical analysis and sensitivity analysis are conducted to get management insights of the model. The results show that a Stackelberg Game model for progressive permissible delay of payment is sensitive in varies values of the first and second delay interest rate if supplier acts as a leader. The retailer gets less inventory cost when he acts as a leader compared to when vendor acts a leader at high interest rate of the first and second delay period

Impact of economic inventory and payment policies on working capital optimization in purchase-to-pay processes

The thesis at hand includes eight chapter and is structured as follows: Following a brief introduction of the topic in Chapter 1, Chapter 2 provides a survey of literature reviews in the area of lot sizing. Its intention is to show which streams of research emerged from Harris' seminal lot size model, and which major achievements have been accomplished in the respective areas. It first develops the methodology and then descriptively analyzes the sample. Subsequently, a content-related classification scheme for lot sizing models is developed, and the reviews contained in the sample are discussed in light of this classification scheme. The analysis reveals that various extensions of Harris' lot size model have been developed over the years, such as lot sizing models that include multi-stage inventory systems, incentives, or productivity issues. The aims of such a tertiary study are the following: firstly, it helps primary researchers to position their own work in the literature, to reproduce the development of different types of lot sizing problems, and to find starting points if they intend to work in a new research direction. Secondly, the study identifies several topics that offer opportunities for future secondary research apart from the ones covered in this thesis. In the presence of a progressive payment scheme, the supplier offers a sequence of credit periods, where the interest rate that is charged on the outstanding balance usually increases from period to period. If a buyer faces a progressive trade credit scheme, various options for settling the unpaid balance exist, where the financial impact of each option depends on the current credit interest structure and the alternative investment conditions. Chapter 3 takes up this issue by generalizing the trade credit inventory model with progressive interest scheme by considering a) the case where the credit interest rate of the buyer may (but not necessarily has to) exceed the interest rate charged by the supplier, b) where the buyer has the option to settle the outstanding balance continuously within the credit periods, c) where compound interest accrues at the retailer, and d) bank loans are available as a substitute for the trade credit. In addition, some inaccuracies in earlier formulations of the effective interest cost are corrected. Subsequently, Chapter 4 studies and extends solution algorithms for deriving the optimal ordering and payment policies of a retailer on the condition that the supplier provides a progressive interest scheme. Based on the finding that the piecewise total cost functions are convex but not necessarily continuous, a modified solution algorithm is developed and collated with existing ones in the course of a simulation experiment. The results indicate that the modified algorithm can locate all optimal solutions and outperforms existing approaches. Chapters 5 and 6 further extend the scope of the analysis by considering models aimed at finding ordering and payment policies for a buyer with stock-dependent demand and a supplier that offers a progressive payment scheme. Such a setting can frequently be observed in retail stores where the demand rate is usually influenced by the amount of inventories displayed on the shelves. These chapters correct some errors in the formulation of previously published approaches and extend those works by assuming that the credit interest rate of the retailer may exceed the interest rate charged by the supplier. Several numerical examples illustrate the benefits of the suggested modifications. The results also illustrate the close linkage between operational and financial aspects in supply chain management, which should be considered by employing more integrated planning approaches. As decisions on the working capital structure of the company defined by an appropriate inventory and payment policy significantly influence future cash-flows and thus the temporal allocation of payments, they should also be evaluated in terms of long-term profitability by considering their net present value or equivalent measures. Especially in situations where trade credit agreements are used over a long period of time and where discount rates are varying, explicitly considering the time-value of money in inventory models helps to make them more realistic. This aspect is considered in Chapter 7 that studies the optimal ordering and payment policies of a buyer assuming that the supplier offers a progressive interest scheme. The models proposed enable decision makers to improve decision making and the results reveal that taking into account the temporal allocation of payments, the prevailing interest relation influences replenishment policies significantly. Finally, Chapter 8 studies a buyer sourcing a product from multiple suppliers under stochastic demand. The buyer uses a (Q,s) continuous review, reorder point, order quantity inventory control system to determine the size and timing of orders. Lead time is assumed to be deterministic and to vary linearly with the lot size, wherefore lead time and the associated stock-out risk may be influenced both by varying the lot size and the number of contracted suppliers. After presenting several mathematical models for a multiple supplier single buyer integrated inventory problem with stochastic demand and variable lead time, the impact of different delivery structures on the risk of incurring a stock-out during lead time and the required inventories is analyzed

The Optimal Replenishment Policy under Trade Credit Financing with Ramp Type Demand and Demand Dependent Production Rate

This paper investigates the optimal replenishment policy for the retailer with the ramp type demand and demand dependent production rate involving the trade credit financing, which is not reported in the literatures. First, the two inventory models are developed under the above situation. Second, the algorithms are given to optimize the replenishment cycle time and the order quantity for the retailer. Finally, the numerical examples are carried out to illustrate the optimal solutions and the sensitivity analysis is performed. The results show that if the value of production rate is small, the retailer will lower the frequency of putting the orders to cut down the order cost; if the production rate is high, the demand dependent production rate has no effect on the optimal decisions. When the trade credit is less than the growth stage time, the retailer will shorten the replenishment cycle; when it is larger than the breakpoint of the demand, within the maturity stage of the products, the trade credit has no effect on the optimal order cycle and the optimal order quantity

Deterministic EOQ models for non linear time induced demand and different holding cost functions

This paper presents an Economic order quantity (EOQ) model for deteriorating items. The demand rate is non-linear function of time. In this paper two models have been derived for different holding costs (i) The holding cost is linear function of the on hand inventory level. (ii). A non-linear function of time for which the item is kept in the stock. Optimization is done for both the models and numerical examples are presented to check the feasibility of the optimal solutions. Sensitivity analysis is also presented with respect to the various parameters used in the numerical example