Permissible Delay Research Articles

Credit financing in economic ordering policies for deteriorating items with stochastic demand and promotional efforts in two-warehouse environment

Retailers are nowadays focusing on promotional activities in order to attract customers because of increasing competition. Promotional efforts have significant impact on the replenishment policy and the sale price of goods. In this paper, a two warehouse inventory model is developed for deteriorating items subject to promotional efforts under permissible delay in payments. Here, a price dependent stochastic demand function is considered with partially backlogged shortages. Several realistic cases, sub cases and scenarios have been taken into account and the corresponding problems have been formulated as nonlinear constrained optimisation problems. To illustrate the proposed model two numerical examples have been solved. Further, a numerical example has been extended to perform sensitivity analysis of the model and discuss specific managerial insights.

Credit financing in economic ordering policies for deteriorating items with stochastic demand and promotional efforts in two-warehouse environment

Retailers are nowadays focusing on promotional activities in order to attract customers because of increasing competition. Promotional efforts have significant impact on the replenishment policy and the sale price of goods. In this paper, a two warehouse inventory model is developed for deteriorating items subject to promotional efforts under permissible delay in payments. Here, a price dependent stochastic demand function is considered with partially backlogged shortages. Several realistic cases, sub cases and scenarios have been taken into account and the corresponding problems have been formulated as nonlinear constrained optimisation problems. To illustrate the proposed model two numerical examples have been solved. Further, a numerical example has been extended to perform sensitivity analysis of the model and discuss specific managerial insights.

Green Inventory Supply Chain Model with Inflation under Permissible Delay in Finite Planning Horizon

Green Inventory Supply Chain Model with Inflation under Permissible Delay in Finite Planning Horizon

Optimal Ordering Policy for Deteriorating Items with Limited Storage Capacity under Two-Level Trade Credit Linked to Order Quantity by a Discounted Cash-Flow Analysis

Nowadays, the supplier often provides cash discount or permissible delay in payments to its retailers, if the order quantity attains a certain amount. Likewise, the retailer also provides a downstream trade credit period to his customers. In practice, as the supplier provides price discounts for bulk purchases, the retailer may purchase more goods than can be stored in its owned warehouse and store the excess quantities in a rented warehouse. Thus, a two-warehouse inventory model is needed to be considered. Further, the cost is usually affected by the present value of time and products deteriorate as time increases. Therefore, this paper develops a supplier-retailer-customer chain inventory model in which 1) two-level trade credit linked to order quantity is considered; 2) storage capacity is limited; 3) the effect of inflation and time value of money by a discounted cash-flow analysis is taken into account. The demand rate is linearly increasing with time and the deterioration rate is constant. Based on the viewpoint of cost minimization, the objective is to find the optimal replenishment cycle and order quantity to keep the present value of the total relevant cost per unit time as minimum as possible. The research shows that in each case discussed, the optimal solution for each case exists uniquely. Finally, numerical examples are provided for illustration and some managerial insights based on the numerical results are also presented.

An EOQ model for deteriorating item with promotional effort and credit linked demand

In the traditional supply chain models, it is observed that usually suppliers offer to the retailers a credit period and also the retailer to the customers to stimulate sales and reduce inventory. This practice of retailers increases the default risk of the percentage of customers not willing to pay back. In this paper, an inventory model has been developed under two levels of trade credit policy with customers' default risk consideration for a deteriorating item having a maximum lifetime. The supplier offers a partially permissible delay in payment per order and the retailer, in turn, provides a part of it to customers. Here, both demand and default risk are functions of the customer's trade credit period, whereas demand is also promotional effort sensitive. To mimic the changing market, the inventory costs are assumed to be imprecise. The models are illustrated numerically and some sensitivity analyses are presented. [Received: 13 January 2017; Revised: 14 September 2017; Revised: 10 June 2018; Accepted: 10 December 2018]

An Inventory Model for Ramp-Type Demand with Two-Level Trade Credit Financing Linked to Order Quantity

In the traditional economic order quantity (EOQ) model, it is assumed that the demand rate is constant. Thereafter, many researchers developed inventory model with time-varying demand to reflect sales in different phases of product life cycle in the market. However, in practice, especially for fashionable and high-tech product, the demand rate during the growth stages of its life cycle increases significantly with linear or exponential in the growth stage and then gradually stabilizes, and remains near constant in the maturity stage. It can be taken a ramp-type demand rate into account. Furthermore, in today’s supply chain, a supplier usually offers a permissible delay in payment to retailers to encourage them to buy more products, and a retailer in turn provides a downstream trade-credit period to its customers. Therefore, this paper focus on 1) ramp-type demand rate and 2) the upstream and downstream trade credit financing linked to order quantity for retailer is considered. The objective is to find the optimal replenishment cycle and order quantity to keep the total relevant cost per unit time as minimum as possible. The study shows that in each case discussed, the optimal solution not only exists but also is unique. Numerical examples are provided to illustrate the proposed model. Finally, some relevant managerial insights based on the results are characterized.

Application of Quick Switching System-1 with Single sampling Plan as reference plan through Minimum Sum of Risks in Determining Economic Ordering Policies under Permissible Delay in Payments

Conventionally, all Economic Ordering model tacitly assumes that the immediate payment with the shipment of the products. But, in practice, the vendor may allow permissible delay in payments to the buyer. Quality management with minimized cost is the crucial factor for organization’s growth. Inspecting 100% of the products are time-consuming and costly especially when it involves destructive testing or inspection cost is huge. Acceptance sampling plan by attributes provides an effective solution to minimize the cost and consumes less time. Quick Switching System-1with two intensity of inspection is ease to apply as it enables instantaneous switch between normal and tightened inspection depends on the quality of the product. With more reliable products normal inspection is employed and vice versa.QSS-1 plan with minimum sum of risks carries another advantage of reducing the consumer and producer’s risk. With the application of the QSS-1 through minimum sum of risks on the EOQ model with permissible delay in payments buyer and vendor gets minimized cost, minimized risk and less time consuming process.

Time factor in critical modes of radio electronic system functioning

Introduction. At the present stage of the development of technical systems, it is important to predict their development, quality, and process characteristics. This also applies to radio electronic systems. Sufficiently unfavorable situations for the functioning of radio electronic systems arise in the context of information conflicts, when it becomes necessary to predict the consequences of information loss or the effect of deliberate interference on the capabilities of radio electronic systems. In critical situations the time factor plays a significant role. On the one hand, information that comes with a delay and loses its relevance. From another point of view, it is necessary to carry out the assigned task within the prescribed time. Thus, the task of determining time indicators of the functioning of radio electronic systems in critical regimes remains urgent and requires further research. Problem statement. Take into account that the effectiveness of the radio electronic systems functioning can be estimated by the performing the task probability. In the process of information flow this probability increases and asymptotically come close to one. In critical modes of operation due to the uncertainty and unpredictability of emerging situations the processing time of information increases. Thus the available information which is perceived by the system is different from the information that is provided by the regular mode. It is necessary to find out the influence of time on processing information on the regularity of the change in the probability of accomplishing the task. It is necessary to estimate the radio electronic operation time, which is necessary to perform the task. It is necessary to set restrictions on the processing time of information and to clarify the requirements for the main parameters that characterize the operation of radio electronic systems in critical modes. From a practical point of view it is necessary to compare real and potential indicators of radio electronic systems and to provide for the possibility of predicting the consequences of their functioning critical modes. Results. On the basis of the informational approach to the analysis of processes in radio electronic systems, the main relations regarding the necessary time of their work and the restrictions on the information delay time are established. Typical situations of critical operating modes of radio electronic systems and the effect of false or lost information on their qualitative characteristics are analyzed. Indicators of a systems operation stable mode are defined. System information analysis of processes using typical forecasting models and the method of analogies is carried out. The effectiveness of the radio electronic systems depends on the amount and value of information that comes to them in the process of functioning. Taking into account the peculiarities of the work of the radio electronic systems In critical operating modes, we will consider useful information and misleading or lost information. Analysis of the work of systems with feedback in the conditions of information delay, allowed to set limits on the permissible delay time, determine the efficiency and the required operating time of the systems. For systems with information losses in the information conflict context in conditions of information capacities increasing and delaying the reaction of one of the parties to the conflict the following indicators are established: real and potential systems efficiency; limitations on the possible efficiency of systems; admissible delay time of reaction by one of the parties to the conflict; necessary time for the performance of the assigned functional task. Conclusions. The obtained results show that in critical modes of the functioning of radio electronic systems, the factor influences both the radio electronic systems performance indicators and their potential capabilities. For information systems that extract information, it became possible to take into account the time that is necessary for processing information, use a typical predictive model for the regularity of increasing the information amount and determine the efficiency and necessary time of the system operating. These results can be used in the process of the radio electronic systems modernization and at the initial stage of radio electronic systems designing.

Supply Chain with Customer-Based Two-Level Credit Policies under an Imperfect Quality Environment

The present model develops a three-echelon supply chain, in which the manufacturer offers full permissible delay to the whole seller, while the latter, in turn, adopts distinct trade credit policies for his subsequent downstream retailers. The type of credit policy being offered to the retailers is decided on the basis of their past profiles. Hence, the whole seller puts forth full and partial permissible delays to his old and new retailers respectively. This study considers bad debts from the portion of new retailers who fail to make up for the delayed part of the partial payment. The analysis shows that it is beneficial for the whole seller to make shorter contracts, particularly with new retailers, along with the fetching of a higher fraction of initial purchase cost from them. In addition to the above-described scenario, the lot received by the whole seller from the manufacturer is not perfect, and it contains some defects for which he employs an inspection process before selling the items to the retailers. In order to make the study more realistic, Type-I, as well as Type-II misclassification errors, and the case of out-of-stock are considered. The impact of Type-I error has been found to be crucial in the study. The present paper determines the optimal policy for the whole seller by maximizing the expected total profit per unit time. For the optimality of the solution, theoretical results are provided. Finally, a numerical example and a sensitivity analysis are done to validate the model.

Mixture inventory model of lost sale and back-order with stochastic lead time demand on permissible delay in payments

It is seen that the trade credit period has an important role in real business world. In this article, an inventory model has been developed by considering stochastic lead time demand with lead time crashing cost. Here, also to get the impact between credit period and lead time, a lead time dependent credit period has been considered. In this model, considering partial back-order, the effect of lost sale has been included. Under the above considerations, an inventory model has been optimized in the parlance of infinite time horizon. Here, three objective functions have been developed on the basis of the position of credit period and business period. Finally, to study the feasibility of the model, three different numerical examples have been illustrated with sensitivity analysis with respect to a parameter.

Retailer's optimal ordering policy in the EOQ model with imperfect‐quality items under limited storage capacity and permissible delay

With a view to reducing inventory and increase sales, a supplier frequently offers its buyers a permissible delay in payment to attract new retailers for bulk purchase, and so extra storage spaces are needed for the buyers. Moreover, in a real environment, some defective items are produced because not only the production processes but also the inspection processes are not perfect, thereby generating defects then resulting in extra costs. Keeping these facts in mind, this article proposes a profit‐maximizing economic order quantity model that incorporates both imperfect production quality and permissible delay in payments in the case when the own warehouse with limited capacity is not sufficient to store the ordered quantity and, therefore, a rented warehouse is needed to store the excess units over the capacity of the owned warehouse. Mathematical model and solution procedures are developed with major insight into its functional characteristics. Numerical examples and sensitivity analysis are provided to illustrate and analyze the model performances. It is observed that our model has significant impacts on the optimal lot size and the optimal profit of the mathematical model, which is considered in this article.

Endorsement of Optimal ordering cycle implementing Quick Switching System with Single Sampling Plan with Permissible delay in Payments involving non-destructive testing

Endorsement of Optimal ordering cycle implementing Quick Switching System with Single Sampling Plan with Permissible delay in Payments involving non-destructive testing

Two-warehouse partial backlogging inventory model with ramp type demand rate, three-parameter Weibull distribution deterioration under inflation and permissible delay in payments

Abstract Decay or deterioration of physical goods while in stock is a natural phenomenon in many inventory systems. The three-parameter Weibull distribution is an excellent generalization of exponential decay, which can be used for items with any initial value of the rate of deterioration and for items which starts deteriorating only after a certain period of time. To reduce the amount of deterioration and the limited storage facility in own warehouse (OW) the retailer’s is moving their excess items to store in a rented warehouse (RW). Generally it is seen that for any new brand of consumer goods coming to the market, the demand rate increases with time up to a certain period and then ultimately stabilize and becomes constant. This kind of stabilization has been termed as ’ramp-type’ demand rate. So, in this paper, we have developed two warehouse inventory models with ramp type demand rate and three-parameter Weibull distribution deterioration (ThPWD) under inflationary conditions, where permissible delay in payment is available for retailer if outstanding amount is compensated within the given credit period. Since, not all customers are willing to wait for backlogged during the shortage period, in this investigation shortages are also allowed and partially backlogged. The purpose of this study is not only to find retailer’s optimal replenishment policies but also to minimize the total average cost. Finally, a numerical example is presented to illustrate the proposed model and sensitivity analysis of the optimal solutions with respect to major parameters is carried out using the Mathematica-8.0 software.

Optimal ordering policies for a single deteriorating item with ramp-type demand rate under permissible delay in payments

In this paper, we assume that the supplier offers the retailer a credit period (i.e., M) and the retailer purchases a single deteriorating item from the supplier to satisfy the market demand, and shortages are not allowed. With the consideration of trade credit, we develop an inventory model for a single deteriorating item with ramp-type demand rate. Unlike the previous research, on the one hand, we consider both cases of and thoroughly (where is the changing point from linear demand to the constant demand and T is the replenishment cycle time). On the other hand, our objective is to optimal the replenishment cycle time T to minimise the average total cost, while the previous study is to determine the optimal shortage time point. Then, we obtain some theoretical results and employ an alternative approach to find the optimal replenishment policy efficiently. In order to verify whether the credit period offered by the supplier is significant to affect retailer’s ordering behaviour, we make a comparison between models without and with the strategy of delay in payments. Through numerical examples, we show that when the delay period is longer than the changing point , the advantage of the delay in payments is more obvious, and thus it can entice more potential retailers to order more quantities. Therefore, our study can offer a reference for suppliers to set trade credit period reasonably and retailers to order rationally when they deal with a deteriorating item facing ramp-type demand rate.

Inventory and credit decisions for deteriorating items with displayed stock dependent demand in two-echelon supply chain using Stackelberg and Nash equilibrium solution

With the prevalence of network technologies, the world is shrinking and it is observed that the decision policies of the players of the supply chain go hand in hand. Thus the optimal replenishment decisions of retailers cannot be taken in isolation and need to be integrated with that of the supplier. This research work establishes a supplier-retailer supply chain in which demand for the products is displayed stock dependent. Nowadays, trade credit is also seen as prime source of short term financing, thus the retailer takes the benefit of permissible delay in payments from the supplier. The objective of the proposed model is to obtain the optimal decisions of the supply chain under three different policies- centralized, Supplier-led Stackelberg policy and Nash equilibrium solution. In this study, the influence of trade credit offered by the supplier, replenishment decisions and integration among the players of supply chain through different centralized and decentralized policies is analyzed for deteriorating items where retailer faces displayed stock dependent demand with two storage facilities. The model is best suitable for the emerging retail markets or supermarkets with limited shelf space displaying consumable items such as grocery, consumer goods, etc. The results have been validated with the help of a numerical example. Sensitivity analysis has also been performed to study the effect of various parameters on the optimal solution.

An economic order quantity model under two-level partial trade credit for time varying deteriorating items

ABSTRACTIn general, supplier/retailer frequently offers trade credit to its credit-risk downstream member in order to stimulate their respective sales. This trade credit may either be full or partial, depending upon the past profile of downstream members. Partial trade credit may be offered by supplier/retailer to their credit-risk downstream member who must pay a portion of the purchase amount at the time of placing an order and then receives a permissible delay on the rest of the outstanding amount to avoid non-payment risks. In addition, many products deteriorate continuously and cannot be sold after their expiration dates. In this paper, a supplier–retailer–customer chain system is developed in which supplier, as well as retailer, offers partial trade credit to the subsequent credit-risk downstream member; deterioration rate is non-decreasing over time and near 100% particularly close to its expiration date, and demand rate is a credit period-dependent and default risk is incorporated. This paper demonstrates that the retailer's optimal credit period and replenishment time not only exist, but also are unique. We commit that our proposed model is a general theoretical model of the many previous models. Lastly, via numerical examples, sensitivity analysis illustrates the influence of key model parameters.

Integration of three echelon supply chain (supplier-manufacturer-distributor-drop shipper) with permissible delay in payment and penalty contract

Supply Chain Management (SCM) has to be considered in the company in order to improve the sustainability and competitiveness. SCM executed to integrating any companies on the supply chain in a way of coordinating the flow of goods, information, and financial. Permissible delay in payment is one of the coordination ways with allowing the costumers delay the payments to a vendor in some certain periods without any interest charges. In the supply chain system, drop-shipping player already familiar in this era. In drop-shipping internet retailing, the supplier will hold supplies and also carry out physical distribution service on behalf of drop-shipper. Drop-shipper will just focus on selling, on the other hand, their supplier will be responsible for the physical process. Generally, drop-shipper have information of the customer demands better than the distributor. But, it is also unrare when the drop-shipper send the estimation of demands which bigger than their own estimation in order to maximize their own interest, so they hope supplies of the distributor will always enough to accommodate their demands. Contributions in this research will be focused on integration of three echelons supply chain, which are the supplier, manufacturer, distributor, and drop-shipper. With considering delay in payment on first and second echelons, and also the contract penalty on third echelon. The problem on this research will be modeled in some kind of cases which can represent the problem of real supply chain system. Sensitivity analysis will be done on certain significant variables toward the changes of total supply chain cost. Coordination with delay in payment success to integrate supply chain. Contract penalty plan success to maintain the profit of distributor and drop-shipper.

Optimal production model with quality sensitive market demand, partial backlogging and permissible delay in payment

In this study, we consider an imperfect production inventory system with quality of the products dependent market’s demand structures and allowable delay in payments. Two alternative approaches of trade credit policies have been discussed when the manufacturer could not pay the due amount to the supplier within the credit period offered. Here, a new cycle is begun with new production when the manufacturer’s inventory touches to a certain level of shortages. The cycle also ends when backlogged inventory level is reached a certain level. The backlogging rate for the player is dependent on waiting time. The production cost of the manufacturer varies with ordering lot size and quality of product. The behavior of the model under integrated system is analyzed. The sensitivity of the key parameters is examined to test feasibility of the model. Finally, a numerical example is provided to investigate the proposed model.

Closed-Form Solutions for the EPQ-Based Inventory Model for Exponentially Deteriorating Items Under Retailer Partial Trade Credit Policy in Supply Chain

Mahata (Expert Syst Appl 39(3):3537–3550, 2012) developed an economic production quantity (EPQ) inventory model for exponentially deteriorating items under permissible delay in payments considering that both demand and production are constant and known. This paper, applying well-known approximation mathematical expressions, derives closed-form formulas for the time at which the production ends, the cycle length and the total cost of inventory system. Moreover, this work presents a comparison of the solutions to the numerical examples by approximation closed-form formulas and Mahata (2012)’s method. The approximated method works properly because the percent of penalty is negligible less than 0.09%.

A Fuzzy Inventory Model for a Deteriorating Item with Variable Demand, Permissible Delay in Payments and Partial Backlogging with Shortage Follows Inventory (SFI) Policy

This research studies a fuzzy inventory model for a deteriorating item with permissible delay in payments. For this paper, the demand depends on selling price and the frequency of the advertisement. In order to make a more realistic inventory model, it is considered the case of stock-out which is partial backlogged. In this work, it is taken account the shortage follows inventory (SFI) policy. Several scenarios and sub-scenarios have been provided, and each corresponding problem has been defined as a constrained optimization problem in the fuzzy environment. Further, these problems have converted into a new problem using the nearest interval approximation technique of fuzzy numbers. Quantum-behaved particle swarm optimization (QPSO) algorithm with the help of interval mathematics has been used to solve the optimization problems. Numerical examples have been solved in order to illustrate the proposed inventory model. Finally, with the aim to analyse the significant influence of different factors on the optimal policies, a sensitivity analysis is done.