Credit Period Research Articles

Joint pricing and lot-sizing for a perishable item under two-level trade credit with multiple demand classes

Abstract This paper addresses the differential pricing and lot-sizing problem for a perishable item with multiple demand classes under a two-level trade credit. The distributer sells a single perishable product at different prices to various markets and offers a varied credit period to customers. In the proposed model: (1) the demand rate at each market depends on the selling price, credit period and the price of other complementary and substitute products and (2) the time and temperature parameters affect the deterioration rate. A bi-objective model is developed, which aims to jointly maximize the total profit and minimize the total inventory to assess the supply chain’s inventory performance with multiple demand classes under switching cost constraints. Since most of the parameters are imprecise in nature, a tailored possibilistic programming method based upon the fuzzy measure Me is devised to construct the deterministic counterpart. Several theoretical results are derived which demonstrate the existence and uniqueness of the solution. An efficient search procedure based on the model’s properties is developed to find the pricing and lot-sizing decisions. Then, an efficient multi-objective programming method is used to find efficient compromise solutions. Finally, illustrative examples along with a number of sensitivity analyses are provided to show applicability of the proposed approach and study the influence of key parameters on the model’s performance.

An integrated inventory model with warranty dependent credit period under two policies of a manufacturer

This article considers an integrated inventory model that deals with one manufacturer and one retailer. The manufacturer provides warranty period for the finished product to ensure product reliability. Also, the manufacturer gives the opportunity to take the facility of delay payment to the retailer. The main objective of this article is to analyze the effect of the credit period offered by the manufacturer which is functionally depended on warranty period of the product. Again, the retailer also provides trade credit to the end customers. Thus, because of presence of product warranty and customers’ credit, demand rate of customers has been assumed depending on warranty period and customers’ credit period. In this paper, two policies have been discussed according to the manufacturer’s policy on warranty period such as (1) free repairing for the defective products within the warranty period and (2) no warranty period to be offered. The purpose of this article is to maximize the integrated model optimizing product warranty, customers’ credit period and cycle length. Also, solution algorithms have been developed to solve the derived model. Finally, numerical examples have been carried out to illustrate the feasibility of the model.

Optimal Replenishment for Perishable Products with Inventory-Dependent Demand and Backlogging under Continuous and Discrete Progressive Payments

Managing material and cash flows attracts concerns of physical and financial departments in most companies. We, therefore, focus on optimizing the replenishment policy for a channel with stock-dependent demand considering item deterioration and order backlogging under two financial schemes of progressive trade credit periods. We take both the continuous payment regime (CPR) and discrete payment regime (DPR) into account in the progressive trading process, which generates ten distinct scenarios. We show that the profit functions may not necessarily be concave and accordingly give a corresponding computing algorithm, which relaxes the convexity assumptions of objective functions in the existing literature and consequently enrich the research. We address the formulation characterization and the logic of pursuing global optimization from models arising in all settings. Computational studies and simulations are conducted to illustrate the effect of various parameters on the optimal replenishing policy and profit. Numerical experiments show that the CPR scheme is dominantly prior to DPR for long replenishment time intervals, whereas it is exactly the opposite for short time intervals. We also examine the impact of the shortage cost and deteriorating rate on optimum ordering policy and channel performance. Finally, future research directions are addressed in the end.

Optimal replenishment and credit policy in an inventory model for deteriorating items under two-levels of trade credit policy when demand depends on both time and credit period involving default risk

In this paper, we examine an optimal dynamic decision-making problem for a retailer’s inventory system of deteriorating items under two-level trade credit financing where the supplier, as well as the retailer, offers trade credit to the subsequent downstream member, the demand rate of which varies simultaneously with time and the length of credit period that is offered to the customers. The deterioration rate is non-decreasing over time. In addition, the risk of default increases with the credit period length. A generalized model is presented to determine the optimal trade credit and replenishment strategies that maximize the retailer’s annual total profit. We then demonstrate that the retailer’s optimal credit period and replenishment cycle time not only exist but also are unique. Thus, the search of the global optimal solution reduces to finding a local solution. Finally, we run several numerical examples to illustrate the problem and gain managerial insights.

Vendor-buyer integrated production-inventory system for imperfect quality item under trade credit finance and variable setup cost

This paper model a vendor-buyer integrated production-inventory system by considering issues of imperfect quality of the item, trade credit finance, setup cost reduction and shortages including partial backlogging and lost sale. The vendor produces a lot in one production setup and sends to the buyer in multiple shipments to fulfill customers’ demand. Due to imperfect production and/or unsafe transportation, the received lot of the buyer contains the imperfect quality of the item, which is detected through the screening process, and is sold at a discounted price in a single batch at the end of the process. To accelerate bulk purchasing, the vendor offers a trade credit period to the buyer to settle the amount. In this regard, we develop a methodology to account the opportunity cost and opportunity gain. Depending upon the screening period μ, trade credit period M, shortage beginning time t and the buyer’s scheduling period T, we consider four cases: (1) M < μ < t < T, (2) μ < M < t < T, (3) μ < t < M < T and (4) μ < t < T < M. The proposed integrated model is testified with numerical experiment and sensitivity analysis by changing the value of key parameters.

Optimal credit period and green consumption policies with cash-credit payments under asymmetric information

To encourage green consumption, companies that produce renewable energy products often offer customers cash-credit payments, which allow the customers to pay cash payments when signing a contract and grant the customers a credit payment after a certain period. However, granting credit also inevitably negatively impacts the capital opportunity cost and default risk, especially when customers are privileged with private information concerning their own credit status. Hence, the design of cash-credit payments is increasingly recognized as important in increasing the profitability of companies. Additionally, the supplier has three common mechanisms to address credit default problems: the screening, checking and insurance mechanisms. Under these three mechanisms, we develop a supplier-customer chain in which the customer's credit level, which is either high or low, is the customer's private information. We find that compared with symmetric information, the high-credit customer's credit period and green consumption are restricted and limited, while the those of the low-credit customer are maintained in the screening mechanism, promoted in the checking mechanism and lessened in the insurance mechanism. We identify the conditions under which the supplier decides to choose each of the mechanisms. Finally, we show that if the market credit status is relatively poor, the supplier prefers to adopt only the screening mechanism. Otherwise, the supplier attains more leeway to decide whether to transfer risk via the insurance mechanism or to undertake risk via the screening and checking mechanisms based on the tension between the credit incentive effect and the default risk gap effect.

Macroprudential Policy on Banking Sector in Indonesia

This study investigates the implementation of macroprudential policy on banking sector and society. The research applied a descriptive analysis by using an in-depth interview with Bank Indonesia, representative of commercial bank, and society. The result showed that macroprudential policy has no impact on individual, but it had an impact on industrial banking specifically on bank credit lending which caused by LTV regulation. The society responses to the LTV policy is that the majority do not object to the imposition of a maximum limit for housing credit enacted by bank because of the relatively long credit period. Furthermore, another instrument of macroprudential such as GWM-LFR does not have an impact on banking sector and society but capital buffer instrument assuming a sluggish economy condition is assessed to have an impact on lending by banks.

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.

An inventory model for non-instantaneous deteriorating items with credit period and carbon emission sensitive demand: a signomial geometric programming approach

ABSTRACTThis study considers sustainability issues and default risks in the context of joint inventory control and trade credit financing for Non-Instantaneous Deteriorating Items (NIDIs) in a supplier-retailer-customer system, in which the supplier offers an upstream full trade credit to the retailer and the retailer, in turn, provides a downstream partial trade credit to her/his customers. Demand rate is sensitive to the amount of carbon emissions, the length of the credit period suggested by the retailer to its customers and selling price. The main objective of this study is to optimize credit period, order quantity, and replenishment cycle time in order to maximize retailer’s total profit and minimize carbon emissions at the same time. For solving the proposed problem, we apply an approximation method to simplify the profit function and transform the problem into a constrained Signomial Geometric Programming (SGP) problem, then a global optimization approach is used for solving the model.Finally, a numerical illustration and sensitivity analysis are performed to demonstrate the problem and the solution procedure. Some useful managerial insights are obtained from computational results. The results show that the retailer will increase its total profit by considering trade credit policy and non-instantaneous deteriorating phenomenon.

A collaborative model for coordination of monopolistic manufacturer's promotional efforts and competing duopolistic retailers' trade credits

In recent years, competition among enterprises has been significantly increased. Trade credit and promotional effort are two important tools that have been extensively used for increasing competitive advantage. In today's business environment, retailers compete each other on new factors such as the length of credit period offered to end customers. In this paper, the performance of a supply chain (SC) consisting of a monopolistic manufacturer and two competing retailers has been analyzed under a promotional-effort credit-period dependent demand. The promotional efforts made by the manufacturer and the trade credits offered by competing retailers stimulate the market demand. The investigated SC is modeled under the decentralized, centralized and coordinated decision-making structures. In the decentralized model, three game structures are proposed to reflect the retailers' behaviors according to their market dominance: (1) retailers' Cournot behavior, (2) retailers' Collusion behavior, and (3) retailers' Stackelberg behavior. In the centralized model, the optimal decisions on promotional efforts and credit periods are determined to maximize the profits of the entire channel. However, the results indicate that the centralized solution will not necessarily be acceptable to all members as it does not consider the individual profit of each SC member. To remedy shortcomings of the centralized model and coordinate the channel, a novel collaborative model is proposed in order to not only increase the whole SC profits, but also guarantee participation of all SC members. Finally, a numerical example along with a comprehensive sensitivity analysis is carried out to compare the performance of the proposed models.

Smallholder preferences and willingness-to-pay measures for microcredit

PurposeThe purpose of this paper is to examine smallholders’ preferences and willingness to pay for microcredit products with varying attribute combinations, in order to contribute to the debate on the optimal design of rural microcredit.Design/methodology/approachData used in this study are based on a discrete choice experiment from 552 randomly selected respondents. Mixed logit and latent class models are estimated to examine the choice probability and sources of preference heterogeneity. Endogenous attribute attendance models are applied to account for attribute non-attendance (ANA) phenomenon, focusing on separate non-attendance probability as well as joint non-attendance probability.FindingsThe results demonstrate that preference heterogeneity and ANA exist in the smallholder farmers’ microcredit choices. Averagely, smallholder farmers prefer longer credit period, smaller credit size, lower transaction costs and lower interest rate. Guarantor collateral method and installment repayment positively affect their preferences as well. Moreover, respondents are found to be willing to pay more for the attributes they consider important. The microcredit providers are able to attract new customers under the current interest rates, if the combination of attributes is appropriately adjusted.Originality/valueThis study contributes to the debate by assessing the preference trade-off of different microcredit attributes more comprehensively than in previous analyses, by taking preference heterogeneity and ANA into account.

Does investment in trade credit matter for profitability? Evidence from publicly listed agro-food firms

The paper examines the relationship between trade credit investment and firm profitability, employing a panel of publicly listed agro-food firms in the United States for the period 2001-2014. Whilst almost all firms in the sample invest in trade credit, there is statistically significant variation in the level of trade credit investment and credit period within the United States public agro-food industry. The pooled ordinary least squares, fixed effects and random effects estimations established a significant positive effect of trade credit investment on firm profitability. Due to endogeneity concerns, an instrumental variable fixed effects model is estimated and the results also confirm a statistically and economically significant positive effect of trade credit investment on firm profitability. The results are robust to different econometric estimation techniques and to the use of non-market based measure (return on assets) and market based measure (Tobin’s q) of firm performance. The paper concludes that investing in trade credit significantly increases profitability of agro-food firms as suggested by the financing, transaction/operation and commercial theories of trade credit. Notwithstanding, firms’ trade credit investment decisions should be guided by cost-benefit tradeoff.

Joint two-echelon inventory model for optimality of cycle time and inventory decisions with finite production rate under credit period

In the universal competition of business environment, to face the global challenges around the business, it has turn into more traditional of giving trade credit by the vendor to the buyer as part of improving the sales revenue. The buyer need not to pay the vendor immediately whenever buyer received the goods, if a vendor offers credit period to the buyer. In this scenario focusing on the entire supply chain (SC) performance in terms of cycle time, inventory levels, number of shipment and the overall variable cost of the entire SC is essential. Mathematical models are developed for the joint two-echelon inventory system by assuming that production rate is finite. The present work aims to illustrate the optimality of cycle time, levels of inventory, number of shipments and the overall variable cost of the SC under the phenomena of credit period. Finally, numerical examples are solved to illustrate the theoretical results and also the sensitivity analysis is carried out.

Inventory and Credit Decisions Under Inflationary Conditions With Inflation Induced Bad-Debts

This article describes how a credit period, through its influence on demand, becomes a determinant of inventory decisions; therefore, inventory decisions should be determined jointly with credit decisions. Inflation and time value of money affects valuation of investments; hence their effect should not be disregarded in decision-making. Selling on credit exposes a firm to an additional dimension of default risk from customers as a result of inflation. Consequently, this article presents a mathematical model for the joint determination of optimal inventory and credit decisions for a day-terms credit-linked demand by incorporating the effects of inflation and the time value of money. It is assumed that an increase in the rate of inflation leads to an increase in bad-debts. The objective of the model is to maximize the present value of a firm's net profit per unit of time by jointly optimizing the day-terms credit period and order interval. A numerical example, sensitivity analysis, and observations are presented to illustrate the effectiveness of the proposed model.

Working Capital Management and Firms' Profitability in the Midst of an Economic Crisis

The purpose of this article is to identify the relationship between working capital management and corporate performance in adverse economic circumstances. The results show positive relationship between profitability and cash conversion cycle, firm's size, growth and leverage and negative relationship between profitability and components of cash conversion cycle. Analysing the impact of the crisis it can observe that the companies can increase their profitability by reducing the period of credit granted to customers. The significance of this study stems from the fact that it sheds light for the desirable firms' policy during the period of financial constraints. Prior research on this subject has looked into various issues related to the linkage between working capital management and profitability, however, none has examined what this relationship looks like following a prolonged economic crisis.

Integrating credit and replenishment policies for deteriorating items under quadratic demand in a three echelon supply chain

ABSTRACTThis paper deals with a supply chain that is comprised of a single manufacturer, a single distributor and a single retailer. This supply chain is studied and analysed when demand is time and credit period dependent. The items in each member of the chain are subject to deteriorate at a constant rate. The objective is to minimise the total cost of the supply chain with respect to number of shipments among members, cycle time and credit period offered by the distributor to retailer. Scenarios are established and illustrated with numerical examples. Sensitivity analysis is done to deduce managerial insights.

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.

Trade Credit Policy Between Supplier–Manufacturer–Retailer for Ameliorating/Deteriorating Items

This paper is related to the advancement of the inventory models for ameliorating items and focused on the real-life business situation as with the time the deterioration rate of ameliorating items is increased. In the global world, every supply chain entities as suppliers/manufacturers/retailers want to increase the consumption of their goods without any losses. For this, he/she tries to lure manufacturer/retailers by offering some discounts, i.e. credit period for settling the account. The problem states that the manufacturer purchases the ameliorating items from the supplier, where the supplier offers his/her credit period to settle the account. The manufacturer purchases ameliorating items (like pigs, fishes, ducklings, etc.) and take those items as raw material; when the livestock matures the manufacturer sells it to the retailer and offer credit time for settling the account. Reason to propose the model is when the quantities of livestock become larger, then the manufacturer faces difficulty in maintaining all the livestock. In such a situation, the traditional method (without offering credit period) fails to provide the maximum profit to the manufacturer. Therefore, in order to get maximum profit, the manufacturer needs some more realistic scientific outlook for making decisions. The proposed model provides a more realistic assumption of business markets, by offering credit policy. In the introduced model, manufacturer faces amelioration and deterioration rate simultaneously due to the growth and the death of livestock. The amelioration and deterioration rates are assumed as the Weibull distribution type. Shortages allowed only for the retailer, which is partially backlogged. The main goal of this paper is to minimize the total relevant inventory cost for both the manufacturer and the retailers, by finding the optimal replenishment policy. The mathematical formulation with optimal solutions for manufacturer and retailers are given. Convexity and existence of the proposed model via numerical examples and graphical representations are explained. Finally, the conclusions with some future research direction are discussed.

Optimizing a two-warehouse system under shortage backordering, trade credit, and decreasing rental conditions

This study develops an inventory model for the optimization of a two-echelon system with deteriorating loss and shortage backordering, which consists of one supplier and one distributor with a two-warehouse environment, where the storage price of the rented warehouse decreases over time. Some warehouse owners may decrease their storage prices after a certain period as an incentive to distributors. In addition, offering a credit period stimulates suppliers’ sales and reduces on-hand stock levels, and distributors can use this credit period to reduce costs and increase profits. This study determines the optimal production lot size of both players, as well as the number of shipments, in order to minimize the net present value (NPV) of the total joint cost over the planning horizon. In addition, it demonstrates that an optimal solution exists and is unique. A numerical example and sensitivity analyses are provided to illustrate the proposed model. The results of this study provide managerial insights for enterprises that use a rented warehouse to minimize costs by coordinating lot sizes.