Permissible Delay In Payments Research Articles

An EOQ Model Under the Condition of Permissible Delay in Payments with Allowed Stock-Out Cost and Lead Time

From this present study, derive the two consecutive demands between the time intervals: economic order quantity and total annual variable cost. The solution for this inventory model is optimizing the total annual variable cost. Here, given an arithmetical example and sensitivity analysis for the provision of the inventory model, assume the planning horizon and replenishment rate are infinite. To the best of our knowledge, this is the first study to find out the total annual variable cost using various costs under the condition of a permissible delay in payments with an allowed stock-out cost and lead time.

A Note on an EOQ Inventory Model with Varying Time-Proportional Deterioration, Time-Dependent Demand and Shortages under the Conditions of Permissible Delay in Payment

A Note on an EOQ Inventory Model with Varying Time-Proportional Deterioration, Time-Dependent Demand and Shortages under the Conditions of Permissible Delay in Payment

Optimal strategy on inventory model under permissible delay in payments and return policy for deteriorating items with shortages

In this model, the manufacturer offers a trade credit policy to the retailer. Demand depends upon selling price and time for non-instantaneous deterioration items. The retailer offers the customer a returns policy. Customers can return the product to the retailer if the product is unsatisfactory for the customer. The retailer does not ultimately return the amount to its customer for the returned product. The manufacturer offers the retailer a trade credit policy. The retailer resale the returned products at the same selling price. A partially backlogged shortage is permitted and its rate is thought to depend on how long it takes for the following lot to arrive after a lot has been replenished. The main objective is to increase the retailers' overall profit by determining the optimal order quantity, optimal selling price, and optimal replenishment cycle. An EOQ is framed for analyzing the sample, which can obtain the optimal solution.

Optimal procurement policy for growing items under permissible delay in payment

Optimal procurement policy for growing items under permissible delay in payment

A note on an EOQ inventory model with varying time-proportional deterioration, time-dependent demand and shortages under the conditions of permissible delay in payment

A note on an EOQ inventory model with varying time-proportional deterioration, time-dependent demand and shortages under the conditions of permissible delay in payment

The Inventory Model for Deteriorating Items with Permissible Delay in Payment and Investment in Preservative Technology: A Pragmatic Approach

The Inventory Model for Deteriorating Items with Permissible Delay in Payment and Investment in Preservative Technology: A Pragmatic Approach

Optimal inventory policies for finite horizon deterministic inventory models for non-instantaneous deteriorating items and permissible-delay in payment

This paper is concerned with the search for the optimal inventory policy for a finite horizon inventory model with time-varying demand, non-instantaneous deteriorating items, and permissible delay in payment. The optimal inventory policy consists of the determination of the number and timing of replenishment schedules that minimise some total inventory costs. The search for such policy is formulated as a mixed integer nonlinear programming problem (MINLP). It turns out that the non-instantaneous deterioration phenomenon coupled with permissible delay in payment introduce non-smoothness in the objective function of the MINLP. This leads to failure of direct applications of known solution methods to the MINLP. To circumvent this problem, a methodology is proposed for solving fully the MINLP problem. It is shown, through careful mathematical analysis, that earlier results on similar problems can be adapted to solve this problem. Conditions under which the solution of the MINLP is unique are identified. Moreover, convexity with respect to the number of replenishment orders is established. This makes the search for the optimal inventory policy handy. Numerical experiments are also conducted to test the applicability, to identify the key elements and to provide managerial insights to the model.

Sustainable Supply Chain Model for Defective Growing Items (Fishery) with Trade Credit Policy and Fuzzy Learning Effect

Fundamentally, newborn items that are used commercially, such as chicken, fish, and small camel, grow day by day in size and also increase their weight. The seller offers a credit policy to the buyer to increase sales for a particular growing item (fish), and in this paper, it is assumed that the buyer accepts the policy of the trade credit. In this paper, the buyer acquires the newborn items (fish) from the seller and then sells them when the newborn items have increased their size and weight. From this point of view, the present paper reveals a fuzzy-based supply chain model that includes carbon emissions and a permissible delay in payment for defective growing items (fish) under the effect of learning where the demand rate is imprecise in nature and is treated as a triangular fuzzy number. Finally, the buyer’s total profit is optimized with respect to the number of newborn items. A numerical example has been presented for the justification of the model. The findings clearly suggest that the presence of trade credit, learning, and a fuzzy environment have an affirmative effect on the ordering policy. The buyer should order more to avoid higher interest charges after the grace period, which eventually increases their profit, while at the same time, it is also beneficial for the buyer to order less to gain the benefit of the trade credit period. The fuzziness theory controls the uncertainty situation of inventory parameters with the help of a de-fuzzified method. The lower and upper deviation of demand affects the total fuzzy profit. The effect of learning gives a positive response concerning the size of the order and the buyer’s total fuzzy profit. This means that the decision-maker should be aware of the size of the newborn items, rate of learning, and trade credit period during the supply chain because these directly affect the buyer’s total fuzzy profit. The impact of the inventory parameter of this model is presented with the help of sensitivity analysis.

An inventory model with permissible delay in payment and different interest rate charges

Adopting the permissible delay method by suppliers offers ample opportunity to overcome the burden of holding costs from retailers. This compensates retailers against the competitive situation as an alternative to price discounts. We present an inventory model for a finite time horizon for deteriorating items. The model focuses on an optimal replenishment policy to maximize profit through inventory control by considering two different interest rate charges. The implementation is possible by the proposed mathematical model for a ramp-type demand with a permissible delay of payment approach. We compare two scenarios: with and without permissible delay in payment. The computational algorithm, numerical examples, theorems, Hessian matrix, and graphs confirm the effectiveness of the inventory model proposed in this study. Sensitivity analysis is used to find risk-compensate opportunities in a peculiar situation.

Effect of Future Price Increase for Products with Expiry Dates and Price-Sensitive Demand under Different Payment Policies

The current study works with an inventory management strategy under the discount cash flow approach for perishable commodities with expiry dates, price-sensitive demand, and investment in preservation technology. In addition, this study examines the probable influence of price-increase on the replenishment strategy of the retailer where specific delivery units can be purchased. Furthermore, in this model, two circumstances are deliberated: (I) when the time of the specific delivery matches with the reordering time of the retailer or (II) when the time of the specific delivery emerges within the duration of the sale. Before the price increase, the supplier provides two payment policies to the retailer from which they can choose one. The policies are either: (1) a permissible delay in payment on regular orders or (2) a discount in payment for the specific delivery. The key goal is to optimize the overall profit for the retailer with respect to the sales price, investment in preservation technology, and cycle time during the depletion time of the specific delivery. In addition, an algorithm is created to optimize the results and seven numerical illustrations are discussed to explain the results along with the special case. Finally, to display the pertinence of this model, a sensitivity analysis of the main parameters is performed with important managerial implications. The key findings of this research are (1) before the price increase, the retailer gets the maximum profit if the retailer chooses a discount in payment policy on the specific delivery; (2) how much to order from the supplier and when to place a specific delivery to generate a maximum profit; and (3) the price-sensitive demand and assumption of future price increase negatively affect the retailer’s overall profit, and the retailer gets maximum benefits if the retailer initially orders the maximum number of units from the supplier before the price increase.

A Healthcare Divisions Inventory Model for Deteriorating Items with a Variable Deterioration Rate Under Permissible Delay in Payments

A Healthcare Divisions Inventory Model for Deteriorating Items with a Variable Deterioration Rate Under Permissible Delay in Payments

Building a sustainability in a two-echelon closed loop supply chains: a mathematical approach for permissible delay in payment and backlogging

This paper develops a supply chain framework where payments take place with permissible delays. Unlike other studies, the supply chain is modelled as a closed-loop system, in which returning the products is incorporated into classical supply chain models and the full backorder is permitted. Among the most important research questions is the order amount of chain members to maximize Retailer delays and the profit chains. The study determines the portion of the time interval in which inventory system experiences shortage and determines the optimal replenishment time and the frequency. Ultimately, it was shown that, if the delay from the supplier to the retailer increases, the chain profit also increases. For all three proposed models, a closed-form solution is developed and a solution algorithm is presented. Applying the coordinated model considerably increases the total profit earned by the whole SC as well as all SC members. An example of our model is a bottle supplier for the drink producer. Another example is military oriented. Furthermore, the study elaborates the feasibility of the suggested models by means of some numerical examples and discusses the results using sensitivity analysis.

Inventory optimization model of deteriorating items with nonlinear ramped type demand function

Inventory models for deteriorating items of a supply chain is of critical essence to the maritime industry. This study proposes a real and economically efficient multicriteria inventory policy of inventory models for deteriorating items of a supply chain with nonlinear ramp functions and permissible delay in payment under inflation, two conditions Shortages Followed by Inventory (SFI) and Inventory Followed by Shortages (IFS) have been considered for the formulation of models. Both the models consist of ordering cost, unit cost, deterioration cost, shortage cost and holding cost with replenishment where delay in payments is allowed. The development of these models is to minimize the total average cost per unit time. In order to validate the models, numerical examples have been considered and the sensitivity of several major parameters of exponential and quadratic functions is analyzed. From the numerical result, it is clear that the cost per unit time of IFS model decreases with the increment of the values of parameters of the quadratic function and holding cost whereas, with the increment of the values of parameters of the exponential function as well as holding cost per unite time, the cost per unit time of SFI model decreases. However, if the values of the parameters of the exponential functions as well as ordering cost and shortage cost increase, the cost per unit time of IFS model increases. On the other hand, it will also increase considering SFI condition, if the values of parameters of the quadratic function as well as ordering cost and shortage cost increase. Finally, it is observed that the model considering IFS case works better than SFI model up to a certain level. 

Inventory Policy for Retail Stores: A Multi-Item EOQ Model Considering Permissible Delay in Payment and Limited Warehouse Capacity

The retail industry such as minimarkets has many products consisting of several types of products that have expiration dates. Their warehouses have limited capacity, making it difficult to make decision about optimum inventory. Most of the suppliers will give permissible delay in payment, that can be used to increase income potential through earned by considering the risk of fines imposed if payments are exceeded and help companies raise capital before generating sales. These three factors must be considered when developing the inventory model. The purpose of this study is to develop a multi-item inventory model by considering perishable or damaged products, permissible delay in payment in limited warehouse. Model development is carried out in 2 stages. The first stage was the development of a multi-item EOQ model by considering product defects and permissible delay in payment. The second stage model is by adding a capacity constraint factor to the model. The results obtained are getting the optimal order quantity by considering the number of product types, product damage factors, late payments in limited warehouses, the best ordering policy can be found, and it is known that the total inventory costs to changes in parameters are good and sensitive to changes in percentage, interest percentage, payment allowances, and warehouse capacity through sensitivity tests.

Inventory Replenishment Policies for Two Successive Generations of Technology Products Under Permissible Delay in Payments

In this age of digitalization, when every industry is undergoing technological disruption, there is a big role of digital gadgets and technology products. A key feature of these digital gadgets is the short length of the product life cycle, since the newer and more advanced generations of technologies are developed regularly to replace the earlier conventional technologies. The traditional EOQ models that assume a constant demand cannot be used here. This research paper formulates an inventory optimization model for the multi-generational products under the trade credits and the credit-linked and innovation diffusion dependent demand. The study also performs a numerical illustration of the proposed model, and establishes important dynamics among the key variables. It also performs the sensitivity analysis with the cost of credit and the trade credit period. The paper concludes with the managerial implications for the inventory practitioners and the possible areas of extension for this research in the future.

Fuzzy inventory model with multilevel permissible delay in payments

In the last few decades the study of deteriorating items has gained enormous importance. Most of the companies are facing cut throat competition due to the wastage of resources that drastically reduce their profit margins. So decision makers adopt various techniques for disposal of decaying items with minimum inventory cost. In the present paper a fuzzy inventory model for deteriorating items is considered with four levels of permissible delay in payments. Time and selling price induced quadratic demand is considered and fuzzy approach is introduced in certain parameters to count the uncertainty in the environment. The objective of the study is to optimize the total cost function to reduce economic losses. Empirical Investigation is demonstrated and sensitivity analysis is carried out to gain managerial insights.

An optimal inventory model for a deteriorating item with multivariate demand function

Managing the inventory of perishable items is a vital task in the supply chain. The demand for some deteriorating items is influenced by many factors that make their management a complicated task. Therefore, it is important to take multiple key factors into account to develop a more realistic model. In this paper, an inventory model for non-instantaneous deteriorating items is proposed, for the case where the quality and quantity of the item decrease over time. The demand is an additive, continuous, and differentiable function of price, stock level, and also age of the product. The deterioration starts after a fixed period with a constant rate and the shortage is not allowed. Permissible delay in payment and time value of money are also considered in the model. First, we formulate the problem in a piecewise mixed-integer nonlinear programming model. We then propose an algorithm to solve a number of examples.

Optimal procurement and pricing policy for deteriorating items with price and time dependent seasonal demand and permissible delay in payment

Optimal procurement and pricing policy for deteriorating items with price and time dependent seasonal demand and permissible delay in payment

Effect of Inflation and Time Varying Holding Cost on an Inventory Model with Permissible Delay in Payment under Ramp Type Demand

In the present market scenario, inflation has become a permanent feature of economy throughout the world. In this paper we have proposed an inventory system of deteriorating items with time varying holding cost under inflationary environment. Most of the inventory faces the problem of deterioration which decreases the total profit. To control the rate of deterioration preservation technology techniques is used. In the proposed inventory model demand is ramp type and shortages are allowed and partially backlogged with constant backlogging rate. Due to ramp type demand, this inventory system is divided into two inventory models. Both inventory models have been solved by using distinct numerical examples. Also the concavity of the objective function for each model has been shown. Finally, the sensitivity analysis is also performed for different parameters to find some useful observation.

A note on 'a two-warehouse partial backlogging inventory model for deteriorating items with permissible delay in payment under inflation'

A note on 'a two-warehouse partial backlogging inventory model for deteriorating items with permissible delay in payment under inflation'