An EOQ model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages

We have developed an order level inventory system for deteriorating items with demand rate as a ramp type function of time. The finite production rate is proportional to the demand rate and the deterioration rate is independent of time. The unit production cost is inversely proportional to the demand rate. The model with no shortages case is discussed considering that: (a) the demand rate is stabilized after the production stopping time and (b) the demand is stabilized before the production stopping time. Optimal costs are determined for two different cases.

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A study of inflation effects on an EOQ model for Weibull deteriorating/ameliorating items with ramp type of demand and shortages

Yugoslav journal of operations research ◽

10.2298/yjor110830008v ◽

2013 ◽

Vol 23 (3) ◽

pp. 441-455 ◽

Cited By ~ 1

Author(s):

M. Valliathal ◽

R. Uthayakumar

Keyword(s):

Computer Software ◽

Optimal Solution ◽

Solution Procedure ◽

Inventory Level ◽

Decision Variable ◽

Deterioration Rate ◽

Eoq Model ◽

Replenishment Policy ◽

Demand Rate ◽

Ramp Type Demand

This paper deals with the effects of inflation and time discounting on an inventory model with general ramp type demand rate, time dependent (Weibull) deterioration rate and partial backlogging of unsatisfied demand. The model is studied under the replenishment policy, starting with shortages under two different types of backlogging rates, and their comparative study is also provided. We then use the computer software, MATLto find the optimal replenishment policies. Duration of positive inventory level is taken as the decision variable to minimize the total cost of the proposed system. Numerical examples are then taken to illustrate the solution procedure. Finally, sensitivity of the optimal solution to changes of the values of different system parameters is also studied.

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Order Level Inventory Models for Deteriorating Seasonable/Fashionable Products with Time Dependent Demand and Shortages

Mathematical Problems in Engineering ◽

10.1155/2009/679736 ◽

2009 ◽

Vol 2009 ◽

pp. 1-24 ◽

Cited By ~ 13

Author(s):

K. Skouri ◽

I. Konstantaras

Keyword(s):

Inventory Model ◽

Time Dependent ◽

Inventory Models ◽

Deterioration Rate ◽

Replenishment Policy ◽

Demand Rate ◽

Increasing Demand ◽

Ramp Type Demand ◽

Unsatisfied Demand ◽

Dependent Demand

An order level inventory model for seasonable/fashionable products subject to a period of increasing demand followed by a period of level demand and then by a period of decreasing demand rate (three branches ramp type demand rate) is considered. The unsatisfied demand is partially backlogged with a time dependent backlogging rate. In addition, the product deteriorates with a time dependent, namely, Weibull, deterioration rate. The model is studied under the following different replenishment policies: (a) starting with no shortages and (b) starting with shortages. The optimal replenishment policy for the model is derived for both the above mentioned policies.

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