scholarly journals Effect of price-sensitive demand and default risk on optimal credit period and cycle time for a deteriorating inventory model

2020 ◽  
Author(s):  
Asim Paul ◽  
Magfura Pervin ◽  
Sankar Kumar Roy ◽  
Gerhard-Wilhelm Weber ◽  
Abolfazl Mirzazadeh
Keyword(s):  
Cycle Time ◽  
Default Risk ◽  
Optimal Solution ◽  
Global Maximum ◽  
Selling Price ◽  
Future Directions ◽  
Credit Period ◽  
Proposed Model ◽  
The Stability ◽  
The Mathematical Model

In this paper, we formulate and solve an economic order quantity model with default risk. Our main purpose is to investigate retailer's optimal replenishment time and credit period for deteriorating items under selling price-dependent demand while maximizing profit per unit time. Here, shortages are allowed and items are partially backlogged for interested customers. We show that optimal replenishment time and credit period not only exist but they are also unique. We solve the proposed problem analytically. An algorithm is presented to derive the optimal solution of the model. The mathematical model is evaluated by numerical examples. We use Mathematica to obtain a global maximum solution to the optimal cycle time and the optimal credit period for the proposed model. A sensitivity analysis with respect to major parameters is performed in order to examine the stability of our model. At the end of the paper, conclusions are drawn and an outlook of possible future directions is depicted.

Vendor-Buyer Supply Chain Models With Supplier Default Risk Under Selling Price and Trade Credit Period Dependent Demand

2018 ◽  
pp. 156-173
Author(s):  
Chetansinh R. Vaghela ◽  
Nita H. Shah
Keyword(s):  
Supply Chain ◽  
Default Risk ◽  
Trade Credit ◽  
Stackelberg Game ◽  
Model Parameters ◽  
Selling Price ◽  
Lot Size ◽  
Credit Period ◽  
Proposed Model ◽  
Dependent Demand

This chapter focuses on uncooperative supply chain inventory models when a supplier offers a credit period to the retailer for a fixed period of time. The models are studied with trade credit in Nash game and Supplier-Stackelberg game respectively. First, the authors have presented optimal results for centralized and decentralized decisions with selling price dependent demand and without trade credit. Second, the authors have obtained optimal results under the two games using classical optimization. The total joint profit of the supply chain is maximized with respect to initial lot size, selling price, and trade credit period. Numerical examples are provided to authenticate the proposed model and to provide some managerial insights. Also through sensitivity analysis, important model parameters are examined.

scholarly journals A Lot-Size Model for Deteriorating Items under Conditions of a One-Time Only Extended Credit Period

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Nita H. Shah
Keyword(s):  
Mathematical Model ◽  
Cycle Time ◽  
Deteriorating Items ◽  
Special Period ◽  
Lot Size ◽  
Credit Period ◽  
Size Model ◽  
The Mathematical Model ◽  
Special Cycle ◽  
Theoretical Results

Now-a-days, the offer of credit period to the customer for settling the account for the units purchased by the supplier is considered to be the most beneficial policy. In this article, an attempt is made to formulate the mathematical model for a customer to determine optimal special cycle time when the supplier offers the special extended credit period for one time only during a special period. A decision policy for a retailer is developed to find optimal special cycle time. The theoretical results and effects of various parameters are studied by appropriate dataset.

scholarly journals The Operational Planning Model of Transhipment Processes in the Port

2016 ◽  
Vol 28 (2) ◽  
pp. 81-89 ◽  
Author(s):  
Mia Jurjević ◽  
Svjetlana Hess
Keyword(s):  
Business Performance ◽  
Container Terminal ◽  
Optimal Solution ◽  
Operational Planning ◽  
Business Decisions ◽  
Traffic System ◽  
Cargo Handling ◽  
Proposed Model ◽  
Successful Business ◽  
The Mathematical Model

Modelling of a traffic system refers to the efficiency of operations for establishing successful business performance by examining the possibilities for its improvement. The main purpose of each container terminal is to ensure continuity and dynamics of the flow of containers. The objective of this paper is to present a method for determining the amount of certain types of containers that can be transhipped at each berth, with the proper cargo handling, taking into account minimum total costs of transhipment. The mathematical model of planning the transhipment and transportation of containers at the terminal is presented. The optimal solution, obtained with the method of linear programming, represents a plan for container deployment that will ensure effective ongoing process of transhipment, providing the lowest transhipment costs. The proposed model, tested in the port of Rijeka, should be the basis for makingadequate business decisions in the operational planning of the container terminal.

scholarly journals Pricing Decision within an Inventory Model for Complementary and Substitutable Products

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 568 ◽  
Author(s):  
Ata Allah Taleizadeh ◽  
Masoumeh Sadat Babaei ◽  
Shib Sankar Sana ◽  
Biswajit Sarkar
Keyword(s):  
Optimization Method ◽  
Selling Price ◽  
Complementary Products ◽  
Substitutable Products ◽  
Pricing Decision ◽  
Proposed Model ◽  
Total Profit ◽  
Order Quantities ◽  
The Stability ◽  
Classical Optimization

A combination of substitutable and complementary products is very important for any business industry to make all-round profit from different aspects. How deterioration affects complementary products or substitutable products is discussed in this study. This study investigates the pricing and inventory decisions for complementary and substitutable items which are deteriorating in nature. Four models are analyzed where the demand of one product is dependent upon the selling price and the price of another product. This paper tries to compute the optimum prices and order quantities to optimize the total profit, which is the main aim. Theoretically, this model is solved by a classical optimization method. Numerical examples demonstrate the applicability of this model. Results conclude that the total profit is dependent on the degree of substitutability and complementarity. A sensitivity analysis of optimal solutions is given to test the stability of the proposed model.

scholarly journals Retailer’s replenishment policies under conditions of permissible delay in payments

2004 ◽  
Vol 14 (2) ◽  
pp. 231-246 ◽  
Author(s):  
Yung-Fu Huang
Keyword(s):  
Cycle Time ◽  
Real Life ◽  
Optimal Order ◽  
Selling Price ◽  
Order Quantity ◽  
Permissible Delay In Payments ◽  
Credit Period ◽  
Optimal Order Quantity ◽  
Delay In Payments ◽  
S Model

Goyal (1985) is frequently cited when the inventory systems under conditions of permissible delay in payments are discussed. Goyal implicitly assumed that: 1. The unit selling price and the unit purchasing price are equal; 2. At the end of the credit period, the account is settled. The retailer starts paying for higher interest charges on the items in stock and returns money of the remaining balance immediately when the items are sold. But these assumptions are debatable in real-life situations. The main purpose of this paper is to modify Goyal?s model to allow the unit selling price and the unit purchasing price not necessarily be equal to reflect the real-life situations. Furthermore, this paper will adopt different payment rule. We assume that the retailer uses sales revenue during the permissible credit period to make payment to the supplier at the end of the credit period. If it is not enough to pay off the purchasing cost of all items, the retailer will pay off the remaining balance by taking loan from the bank. So, the retailer starts paying for the interest charges on the amount of loan from the bank after the account is settled. Then the retailer will return money to the bank at the end of the inventory cycle. Under these conditions, we model the retailer?s inventory system as a cost minimization problem to determine the retailer?s optimal cycle time and optimal order quantity. Four cases are developed to efficiently determine the optimal cycle time and the optimal order quantity. Numerical examples are given to illustrate these cases. Comparing with Goyal?s model, we also find that the optimal cycle times in this paper are not longer than those of Goyal?s model.

scholarly journals Optimal pricing, ordering, and credit period policies for deteriorating products under order-linked trade credit

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yu-Chung Tsao ◽  
Hanifa-Astofa Fauziah ◽  
Thuy-Linh Vu ◽  
Nur-Aini Masrurohand
Keyword(s):  
Default Risk ◽  
Global Economy ◽  
Trade Credit ◽  
Solution Procedure ◽  
Selling Price ◽  
Discounted Cash Flow ◽  
Credit Period ◽  
Total Profit ◽  
Credit Financing ◽  
Dependent Demand

<p style='text-indent:20px;'>In the modern global economy, trade credit financing is typical in business transactions for both sellers and buyers. The seller offers a credit period to attract new buyers or stimulate demand, and the buyer takes the opportunity to accumulate revenue. To obtain this benefit, the seller prefers trade credit policies that are dependent on the quantity ordered, referred to as order-linked trade credit. The buyer can obtain the benefits from a fully delayed payment if their order is sufficiently large. Similarly, the seller can sell many products while granting a credit period. Otherwise, the buyer receives only partial trade credit, and the seller can take the opportunity of both cash and credit payments. In this study, an economic order quantity (EOQ) inventory model for deteriorating products, under default risk control-based trade credit, is formulated using a discounted cash flow approach. The seller offers to the buyer order-linked trade credit with price-and credit-period-dependent demand. The optimal selling price, credit period policies, and replenishment cycle time are determined simultaneously, while maximizing the present value of the seller's total profit. Moreover, this research provides numerical examples and sensitivity analysis to illustrate the theoretical results, solution procedure, and gain managerial insights. <b>200</b> words.</p>

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

2018 ◽  
Vol 9 (3) ◽  
pp. 52-76
Author(s):  
K.K. Aggarwal ◽  
Arun Kumar Tyagi
Keyword(s):  
Default Risk ◽  
Time Value Of Money ◽  
Credit Period ◽  
Time Value ◽  
Joint Determination ◽  
Proposed Model ◽  
Net Profit ◽  
Inventory Decisions ◽  
Value Of Money

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.

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.

Inventory and pricing decisions for imperfect quality items with inspection errors, sales returns, and partial backorders under inflation

2020 ◽  
Vol 54 (1) ◽  
pp. 287-306 ◽  
Author(s):  
Aditi Khanna ◽  
Aakanksha Kishore ◽  
Biswajit Sarkar ◽  
Chandra K. Jaggi
Keyword(s):  
Optimal Solution ◽  
Selling Price ◽  
Type I ◽  
Discounted Cash Flow ◽  
Screening Process ◽  
Imperfect Quality ◽  
Decision Variables ◽  
Proposed Model ◽  
Price Order ◽  
Inspection Process

In this paper, an optimal replenishment inventory policy for imperfect quality items is presented with a selling price-dependent demand under inflationary conditions using a discounted cash flow (DCF) approach. Due to the presence of defectives in the system, all items go through a 100% inspection process. However, the screening process is also considered to be imperfect and involves errors, namely Type-I and Type-II. In addition, shortages are allowed and are partially backlogged. An optimal solution for the proposed model is derived by maximizing the expected profit function by jointly optimizing three decision variables: selling price, order quantity, and backorder level. To validate the theoretical results, a numerical example along with comprehensive sensitivity analysis is offered. The model has pertinence in industries like textiles, electronics, furniture, footwear, automobiles, and plastics.

Sign in / Sign up

Export Citation Format

Share Document