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

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1175-1200 ◽  
Author(s):  
Avik Mukherjee ◽  
Gour Chandra Mahata
Keyword(s):  
Default Risk ◽  
Trade Credit ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Dynamic Decision Making ◽  
Credit Policy ◽  
Credit Period ◽  
Deterioration Rate ◽  
Demand Rate ◽  
Credit Financing

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.

scholarly journals An Inventory System for Deteriorating Products with Ramp-Type Demand Rate under Two-Level Trade Credit Financing

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
G. Darzanou ◽  
K. Skouri
Keyword(s):  
Existence And Uniqueness ◽  
Trade Credit ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Inventory System ◽  
Credit Policy ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Credit Financing ◽  
Ramp Type Demand

An inventory system for deteriorating products, with ramp-type demand rate, under two-level trade credit policy is considered. Shortages are allowed and partially backlogged. Sufficient conditions of the existence and uniqueness of the optimal replenishment policy are provided, and an algorithm, for its determination, is proposed. Numerical examples highlight the obtained results, and sensitivity analysis of the optimal solution with respect to major parameters of the system is carried out.

scholarly journals Optimal replenishment, pricing and preservation technology investment policies for non-instantaneous deteriorating items under two-level trade credit policy

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Chandan Mahato ◽  
Gour Chandra Mahata
Keyword(s):  
Trade Credit ◽  
Market Competition ◽  
Deteriorating Items ◽  
Credit Policy ◽  
Business World ◽  
Credit Period ◽  
Technology Investment ◽  
Deterioration Rate ◽  
Preservation Technology ◽  
Preservation Technology Investment

<p style='text-indent:20px;'>In the business world, both the supplier and the retailer accept the credit to make their business position strong, because the credit not only strengthens their business relationships but also increases the scale of their profits. In this paper, we consider an inventory model for non-instantaneous deteriorating items with price sensitive demand, time varying deterioration rate under two-level trade credit policy. Besides, to reduce deterioration rate, retailers invest some cost to prevent product degradation/decay, known as preservation technology, is also inserted. Consumption of such items within shelf life prevents to deterioration, which can be achieved by bulk sale. In order to stimulate the selling, trade-credit policy is also considered here. In the sequel, not only the supplier would offer fixed credit period to the retailer, but retailer also adopt the trade credit policy to the customers in order to promote the market competition. The retailer can accumulate revenue and interest after the customer pays for the amount of purchasing cost to the retailer until the end of the trade credit period offered by the supplier. The main objective is to determine the optimal replenishment, pricing and preservation technology investment strategies including whether or not invest in preservation technology and how much to invest in order to maximize the average profit of the system. It is proved that the optimal replenishment policy not only exists but is unique for any given selling price and preservation technology cost. An algorithm is presented to derive the optimal solutions of the model. Numerous theorems and lemmas have been inserted to obtain the optimal solution. Finally, numerical examples and managerial implications are incorporated to validate the proposed model.</p>

scholarly journals A Global Optimizing Policy for Decaying Items with Ramp-Type Demand Rate under Two-Level Trade Credit Financing Taking Account of Preservation Technology

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
S. R. Singh ◽  
Swati Sharma
Keyword(s):  
Trade Credit ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Credit Policy ◽  
Preservation Technology ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Credit Financing ◽  
Delay In Payments ◽  
Ramp Type Demand

An inventory system for deteriorating items, with ramp-type demand rate, under two-level trade credit policy taking account of preservation technology is considered. The objective of this study is to develop a deteriorating inventory policy when the supplier provides to the retailer a permissible delay in payments, and during this credit period, the retailer accumulates the revenue and earns interest on that revenue; also the retailer invests on the preservation technology to reduce the rate of product deterioration. Shortages are allowed and partially backlogged. Sufficient conditions of the existence and uniqueness of the optimal replenishment policy are provided, and an algorithm, for its determination, is proposed. Numerical examples draw attention to the obtained results, and the sensitivity analysis of the optimal solution with respect to leading parameters of the system is carried out.

Optimal trade credit and replenishment policies for non-instantaneous deteriorating items

2020 ◽  
Vol 54 (6) ◽  
pp. 1793-1826
Author(s):  
Anuj Kumar Sharma ◽  
Sunil Tiwari ◽  
V.S.S. Yadavalli ◽  
Chandra K. Jaggi
Keyword(s):  
Solution Method ◽  
Trade Credit ◽  
Optimal Solution ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Selling Price ◽  
Credit Policy ◽  
Demand Rate ◽  
Fuzzy Inventory ◽  
The Impact

The present study presents a fuzzy inventory model for non-instantaneous deteriorating items under conditions of permissible delay in payments. In the current paper, we incorporate the condition in which, the supplier accepts the partial payment at the end of the credit period and the reaming amount after that period under the term and condition. Here, the demand rate is a function of the selling price. Also, it is assumed that shortages are allowed and are fully backlogged. The present paper also considers that the interest earned (IE) on the fixed deposit amount, i.e., revenue generated by fulfilling the shortage, balance amount, after settling the account is higher than that of usual interest rate (Ie). Hence, the objective of this study is to determine the retailer’s optimal policies that maximize the total profit. Also, some theoretical results are obtained, which shows that the optimal solution not only exists, it is unique also. The impact of the new proposed credit policy is investigated on the optimality of the solution for the non-instantaneous deteriorating products. The validation of the proposed model and its solution method is demonstrated through the numerical example. The results indicate that the inventory model, along with the solution method, provides a powerful tool to the retail managers under real-world situations. Results demonstrate that it is essential for the managers to consider the inclusion of new proposed credit policy significantly increases the net annual profit.

scholarly journals Two – Warehouse Inventory System Model for Deteriorating Items Considering Partial Upstream Trade Credit Financing

2021 ◽  
pp. 69-80
Author(s):  
Z. H. Aliyu ◽  
B. Sani
Keyword(s):  
Sensitivity Analysis ◽  
Credit Risk ◽  
Trade Credit ◽  
Optimal Solution ◽  
Inventory System ◽  
System Model ◽  
Credit Period ◽  
Business Transaction ◽  
Credit Financing ◽  
Relevant Cost

In this study, we developed an inventory system model under two – level trade credit where the supplier considers the retailer as credit risk but the retailer considers the customers as credit worthy. Therefore, the retailer is given a trade credit period on  proportion of the goods ordered whenever he/she pays for proportion of the goods immediately after delivery. In the same vein, the retailer passes the same grace to the customers but without attaching any condition as the customers are assumed credit worthy. This partial upstream trade credit is offered to reduce the risk of failure in payment on the business transaction especially that most retailers are involved in bulk orders. The relevant cost functions are determined and a numerical example is given. Sensitivity analysis was carried out to see the effect of changes in parameters on the optimal solution of the model.

A Fuzzy EOQ Model for Deteriorating Items With Allowable Shortage and Inspection Under the Trade Credit

2018 ◽  
pp. 233-249
Author(s):  
Chandra K. Jaggi ◽  
Bimal Kumar Mishra ◽  
T. C. Panda
Keyword(s):  
Trade Credit ◽  
Method Comparison ◽  
Deteriorating Items ◽  
Order Quantity ◽  
Centroid Method ◽  
Deterioration Rate ◽  
Eoq Model ◽  
Permissible Delay In Payment ◽  
Demand Rate ◽  
Fuzzy Cost

This chapter develops an economic order quantity model for deteriorating items with initial inspection, allowable shortage under the condition of permissible delay in payment by fuzzify the demand rate, deterioration rate and inspection parameter of non-defective parameter based on as triangular fuzzy numbers to fit the real word. The total fuzzy cost function has been defuzzified using signed distance and centroid method. Comparison between these two methods has also been discussed. The validity of the model has been established with the help of a hypothetical numerical example.

scholarly journals Study of Inventory Model for Deteriorating Items With Exponential Demand Function

2016 ◽  
Vol 34 ◽  
pp. 89-100
Author(s):  
Manik Mondal ◽  
Mohammed Forhad Uddin ◽  
Kazi Anowar Hussain
Keyword(s):  
Opportunity Cost ◽  
Demand Function ◽  
Trade Credit ◽  
Unit Cost ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Bisection Method ◽  
Credit Policy ◽  
Deterioration Rate ◽  
Linear Demand

This paper develops an inventory model for deteriorating items consisting the ordering cost, unit cost, opportunity cost, deterioration cost and shortage cost. In this inventory model instead of linear demand function nonlinear exponential function of time for deteriorating items with deterioration rate has been considered. The formulated model has numerically solved by bisection method. The effects of inflation and cash flow are also taken into account under a trade-credit policy of discount with time. In order to validate the model, numerical examples have been solved by bisection method using Matlab. Further, the sensitivity of different parameters is considered in order to estimate the cash flow.GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 89-100

Optimal replenishment decision for retailers with variable demand for deteriorating products under a trade-credit policy

2020 ◽  
Vol 54 (6) ◽  
pp. 1685-1701 ◽  
Author(s):  
Biswajit Sarkar ◽  
Bikash Koli Dey ◽  
Mitali Sarkar ◽  
Sun Hur ◽  
Buddhadev Mandal ◽  
...  
Keyword(s):  
Trade Credit ◽  
Numerical Study ◽  
Global Optimum ◽  
Optimal Decision ◽  
Selling Price ◽  
Credit Policy ◽  
Credit Period ◽  
Deterioration Rate ◽  
Solution Methodology ◽  
Dependent Demand

In this study one obtained the optimal decision of a retailer for the replenishment rate with selling-price and credit-period dependent demand to maximize the profit. A time-varying deterioration rate was considered for those products. A credit-period was offered by the retailer to the end customer to settle the whole payments. The aim of the model was to obtain the maximum profit for the retailer based model. A solution methodology with an algorithm was used to obtain the global optimum profit. An illustrative numerical example was given to test the practical applicability of the model. Numerical study indicated that the profit was at a maximum when the permissible delay-period for payment offered by the suppliers was lies between the permissible delay-time, and the cycle time, offered by the retailer.

scholarly journals Estimation of inventory for deteriorating items with non-linear demand considering discount and without discount policy

2016 ◽  
Vol 13 (2) ◽  
pp. 151-164
Author(s):  
Manik Mondol ◽  
M. Forhad Uddin ◽  
M. S. Hossain
Keyword(s):  
Cash Flow ◽  
Opportunity Cost ◽  
Demand Function ◽  
Trade Credit ◽  
Unit Cost ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Credit Policy ◽  
Deterioration Rate ◽  
Linear Demand

This paper develops an inventory model for deteriorating items consisting the ordering cost, unit cost, opportunity cost, deterioration cost and shortage cost. In this inventory model instead of linear demand function nonlinear exponential function of time for deteriorating items with deterioration rate has been considered. The effects of inflation and cash flow are also taken into account under a trade-credit policy of discount and without discount with time. In order to validate the model, numerical examples have been solved by bisection method deploying Matlab.  Further, in order to estimate the cash flow the sensitivity of different parameters is considered.

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