scholarly journals The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade Credit

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 596 ◽  
Author(s):  
Kun-Jen Chung ◽  
Jui-Jung Liao ◽  
Shy-Der Lin ◽  
Sheng-Tu Chuang ◽  
Hari Mohan Srivastava
Keyword(s):  
Taylor Series ◽  
Approximation Method ◽  
Optimal Solution ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Optimal Solutions ◽  
Taylor Series Approximation ◽  
Annual Total ◽  
Cash Discount ◽  
Relevant Cost

In the year 2004, Chang and Teng investigated an inventory model for deteriorating items in which the supplier not only provides a cash discount, but also allows a permissible delay in payments. The main purpose of the present investigation is three-fold, as follows. First, it is found herein that Theorem 1 of Chang and Teng (2004) has notable shortcomings in terms of their determination of the optimal solution of the annual total relevant cost Z ( T ) by adopting the Taylor-series approximation method. Theorem 1 in this paper does not make use of the Taylor-series approximation method in order to overcome the shortcomings in Chang and Teng (2004) and alternatively derives all the optimal solutions of the annual total relevant cost Z ( T ) . Secondly, this paper systematically revisits the annual total relevant cost Z ( T ) in Chang and Teng (2004) and presents in detail the mathematically correct ways for the derivations of Z ( T ) . Thirdly, this paper not only shows that Theorem 1 of Chang and Teng (2004) is not necessarily true for finding the optimal solution of the annual total relevant cost Z ( T ) , but it also demonstrates how Theorem 1 in this paper can locate all of the optimal solutions of Z ( T ) . The mathematical analytic investigation presented in this paper is believed to be useful for correct managerial considerations and managerial decisions.

A Fuzzy Inventory Model for Weibull Deteriorating Items with Price-Dependent Demand and Shortages under Permissible Delay in Payment

2012 ◽  
Vol 1 (2) ◽  
pp. 53-79
Author(s):  
Chandra K. Jaggi ◽  
Sarla Pareek ◽  
Anuj Sharma ◽  
Nidhi
Keyword(s):  
Cycle Length ◽  
Optimal Solution ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Selling Price ◽  
Profit Function ◽  
Permissible Delay In Payment ◽  
Fuzzy Inventory ◽  
Dependent Demand ◽  
Fuzzy Inventory Model

In this paper, a fuzzy inventory model is formulated for deteriorating items with price dependent demand under the consideration of permissible delay in payment. A two parameter Weibull distribution is taken to represent the time to deterioration. Shortages are allowed and completely backlogged. For Fuzzification of the model, the demand rate, holding cost, unit purchase cost, deterioration rate, ordering cost, shortage cost, interest earn and interest paid are assumed to be triangular fuzzy numbers. As a result, the profit function will be derived in fuzzy sense in order to obtain the optimal stock-in period, cycle length and the selling price. The graded mean integration method is used to defuzzify the profit function. Then, to test the validity of the model a numerical example is considered and solved. Finally, to study the effect of changes of different parameters on the optimal solution i.e. average profit, order quantity, stock-in period, cycle length and selling price, sensitivity analysis are performed.

scholarly journals A production inventory model with deteriorating items and shortages

2004 ◽  
Vol 14 (2) ◽  
pp. 219-230 ◽  
Author(s):  
G.P. Samanta ◽  
Ajanta Roy
Keyword(s):  
Cycle Time ◽  
Production Control ◽  
Continuous Production ◽  
Optimal Solution ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Production Cycle ◽  
Stock Level ◽  
Deterioration Rate ◽  
Time Sensitivity

A continuous production control inventory model for deteriorating items with shortages is developed. A number of structural properties of the inventory system are studied analytically. The formulae for the optimal average system cost, stock level, backlog level and production cycle time are derived when the deterioration rate is very small. Numerical examples are taken to illustrate the procedure of finding the optimal total inventory cost, stock level, backlog level and production cycle time. Sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the system.

scholarly journals An EOQ model for deteriorating items under supplier credits when demand is stock dependent

2010 ◽  
Vol 20 (1) ◽  
pp. 145-156
Author(s):  
Nita Shah ◽  
Poonam Mishra
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Critical Parameters ◽  
Eoq Model ◽  
Constant Rate ◽  
Cash Discount

In many circumstances retailer is not able to settle the account as soon as items are received. In that scenario supplier can offer two promotional schemes namely cash discount and /or a permissible delay to the customer. In this study, an EOQ model is developed when units in inventory deteriorate at a constant rate and demand is stock dependent. The salvage value is associated to deteriorated units. An algorithm is given to find the optimal solution. The sensitivity analysis is carried out to analyze the effect of critical parameters on optimal solution.

APPLICATION OF RATIONAL APPROXIMATION IN CALCULATION OF THE SECOND DERIVATIVE OF THE GRAVITY FIELD

Geophysics ◽  
1971 ◽  
Vol 36 (3) ◽  
pp. 571-581 ◽  
Author(s):  
B. N. P. Agarwal ◽  
Tarkeshwar Lal
Keyword(s):  
Gravity Field ◽  
Rational Approximation ◽  
Taylor Series ◽  
Approximation Method ◽  
Weight Coefficient ◽  
Second Derivative ◽  
Laplace's Equation ◽  
Frequency Responses ◽  
Taylor Series Approximation ◽  
Series Approximation

A rational approximation method has been introduced to increase the convergence of the Taylor series, which is the fundamental basis for calculation of the second derivative of the gravity field or any field satisfying Laplace’s equation. Six weight coefficient sets, three each using rational and Taylor series approximations for the same number of rings, have been developed. The frequency responses of the proposed weight coefficient sets establish the superiority of rational approximation over Taylor series approximation. The amplitude responses of all derived coefficient sets, along with those of some of the existing coefficient sets, are also presented.

scholarly journals A partial backlogging inventory model for non-instantaneous deteriorating items with stock-dependent consumption rate under inflation

2010 ◽  
Vol 20 (1) ◽  
pp. 35-54 ◽  
Author(s):  
Jinh Chang ◽  
Feng Lin
Keyword(s):  
Solution Process ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Optimal Order ◽  
Partial Backlogging ◽  
Demand Rate ◽  
Dependent Demand Rate ◽  
Dependent Demand

In this paper, we derive a partial backlogging inventory model for noninstantaneous deteriorating items with stock-dependent demand rate under inflation over a finite planning horizon. We propose a mathematical model and theorem to find minimum total relevant cost and optimal order quantity. Numerical examples are used to illustrate the developed model and the solution process. Finally, a sensitivity analysis of the optimal solution with respect to system parameters is carried out.

scholarly journals Optimal replenishment policy for fuzzy inventory model with deteriorating items and allowable shortages under inflationary conditions

2016 ◽  
Vol 26 (4) ◽  
pp. 507-526
Author(s):  
Chandra Jaggi ◽  
Sarla Pareek ◽  
Aditi Khanna ◽  
N Nidhi
Keyword(s):  
Net Present Value ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Distance Method ◽  
Ordering Policy ◽  
Total Profit ◽  
The Impact

This study develops an inventory model to determine ordering policy for deteriorating items with constant demand rate under inflationary condition over a fixed planning horizon. Shortages are allowed and are partially backlogged. In today?s wobbling economy, especially for long term investment, the effects of inflation cannot be disregarded as uncertainty about future inflation may influence the ordering policy. Therefore, in this paper a fuzzy model is developed that fuzzify the inflation rate, discount rate, deterioration rate, and backlogging parameter by using triangular fuzzy numbers to represent the uncertainty. For Defuzzification, the well known signed distance method is employed to find the total profit over the planning horizon. The objective of the study is to derive the optimal number of cycles and their optimal length so to maximize the net present value of the total profit over a fixed planning horizon. The necessary and sufficient conditions for an optimal solution are characterized. An algorithm is proposed to find the optimal solution. Finally, the proposed model has been validated with numerical example. Sensitivity analysis has been performed to study the impact of various parameters on the optimal solution, and some important managerial implications are presented.

scholarly journals Integrated inventory model involving quality improvement investment and advance-cash-credit payments

2021 ◽  
Author(s):  
Chih-Te Yang ◽  
Chien-Hsiu Huang ◽  
Liang-Yuh Ouyang
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Decision Makers ◽  
Optimal Solutions ◽  
Order Quantity ◽  
Defective Items ◽  
Numerical Examples ◽  
Proposed Model ◽  
Production Inventory ◽  
Total Profit

This paper investigates the effects of investment and inspection policies on an integrated production–inventory model involving defective items and upstream advance-cash-credit payment provided by the supplier. In this model, retailers offer customers a downstream credit period. Furthermore, the defective rate of the item can be improved through capital co-investment by the supplier and retailer. The objective of this study was to determine the optimal shipping quantity, order quantity, and investment alternatives for maximizing the supply chain's joint total profit per unit time. An algorithm was developed to obtain the optimal solution for the proposed problem. Several numerical examples are used to demonstrate the proposed model and analyze the effects of parameters changes on the optimal solutions. Finally, management implications for relevant decision makers are obtained from the numerical examples.

OPTIMAL DETERIORATING ITEMS INVENTORY MODEL WITH A THREE-ECHELON SUPPLY CHAIN STRATEGIC ALLIANCE

2010 ◽  
Vol 27 (06) ◽  
pp. 693-711 ◽  
Author(s):  
JONAS C. P. YU
Keyword(s):  
Supply Chain ◽  
Strategic Alliances ◽  
Strategic Alliance ◽  
Optimal Solution ◽  
Integrated Approach ◽  
Global Optimum ◽  
Inventory Model ◽  
Heuristic Technique ◽  
Relevant Cost ◽  
Independent Model

This study develops a mathematical inventory model for deteriorating item taking into account a vertical integration of a three-echelon supply chain (one supplier, one distributor, and one retailer) through strategic alliances. The objective is to minimize the joint total relevant cost for the integrated inventory model. A simple but efficient heuristic technique is used to derive the optimal solution. A numerical example and sensitivity analysis on the optimal results are presented to validate the results of the proposed integrated model. The proposed mathematical model has demonstrated how an integrated approach to decision making can achieve a global optimum and outperform three typically individual models (i.e., independent model, dominant supplier's model and dominant retailer's model).

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