On a finite horizon production lot size inventory model for deteriorating items: An optimal solution

2001 ◽  
Vol 132 (1) ◽  
pp. 210-223 ◽  
Author(s):  
Zaid T. Balkhi
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Finite Horizon ◽  
Deteriorating Items ◽  
Lot Size ◽  
Production Lot Size

scholarly journals Purchasing Inventory Models for Deteriorating Items with Quadratic Demand

2019 ◽  
Vol 20 (2) ◽  
pp. 204
Author(s):  
C. K. Sivashankari
Keyword(s):  
Optimal Solution ◽  
Deteriorating Items ◽  
Time Dependent ◽  
Lot Size ◽  
Inventory Cost ◽  
Replenishment Policy ◽  
Parameter Values ◽  
Visual Basic 6.0 ◽  
Production Lot Size ◽  
Dependent Demand

This paper deals with purchasing inventory replenishment policy for deteriorating items consider with the time-dependent quadratic demand and time-dependent backlogging. Two models were formulated and solved. First, it is for deteriorating items with quadratically time-dependent demand for deteriorating items. Second, quadratically time-dependent demand for deteriorating items and shortages. A mathematical model is developed to the fourth-order equation for each model, and the optimal production lot size, which minimizes the total cost is derived. Sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the system. Numerical examples are taken to illustrate the procedure of finding the optimal inventory cost, cycle time, and optimal lot size. The numerical experiment in this model was coded in Microsoft Visual Basic 6.0.

scholarly journals A finite horizon production model with variable production rates and constant demand rate

2002 ◽  
Vol 6 (2) ◽  
pp. 71-78 ◽  
Author(s):  
Zvi Goldstein
Keyword(s):  
Production Rate ◽  
Finite Horizon ◽  
Production Model ◽  
Maximum Speed ◽  
Lot Size ◽  
Production Problem ◽  
Demand Rate ◽  
The Cost ◽  
Production Lot Size ◽  
Variable Production

In this paper we present a finite horizon single product single machine production problem. Demand rate and all the cost patterns do not change over time. However, end of horizon effects may require production rate adjustments at the beginning of each cycle. It is found that no such adjustments are required. The machine should be operated either at minimum speed (i.e. production rate = demand rate; shortage is not allowed), avoiding the buildup of any inventory, or at maximum speed, building up maximum inventories that are controlled by the optimal production lot size.

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.

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