A Fuzzy Production Inventory Model for Deteriorating Items with Shortages

In this paper we have developed a supply chain production inventory model for deteriorating items with shortage under Fuzzy environment. 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. In reality it is seen that we cannot define all parameters precisely due to imprecision or uncertainty in the environment. So, we have defined the inventory parameter deterioration rate as triangular fuzzy numbers. The signed distance method and graded mean integration method have been used for defuzzification. Numerical examples are taken to illustrate the procedure of finding the optimal total inventory cost, stock level and backlog level. Sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the system.

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A production inventory model with deteriorating items and shortages

Yugoslav journal of operations research ◽

10.2298/yjor0402219s ◽

2004 ◽

Vol 14 (2) ◽

pp. 219-230 ◽

Cited By ~ 6

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.

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Production inventory model for controllable deterioration rate with shortages

RAIRO - Operations Research ◽

10.1051/ro/2019042 ◽

2019 ◽

Author(s):

Umakanta Mishra ◽

Jacobo Tijerina-Aguilera ◽

Sunil Tiwari ◽

Leopoldo Eduardo Cárdenas-Barrón

Keyword(s):

Optimal Solution ◽

Solution Procedure ◽

Inventory Model ◽

Production Cycle ◽

Proper Solution ◽

Deterioration Rate ◽

Preservation Technology ◽

Production Policy ◽

Production Inventory ◽

Theoretical Results

This paper deals with an economic production quantity (EPQ) inventory model for deteriorating items under preservation technology. The preservation technology is used to protect the items from deterioration. Three different production levels are considered. It is assumed that initially the production rate is at lower rate and it increases gradually over the period. This is just in order to reduce the holding cost by avoiding the larger stock quantity in the beginning of production cycle. The shortages are permitted and fully backordered. The objective of the production inventory model is to determine optimal production policy which minimizes the manufacturer’s total cost. Theoretical results are established in order to demonstrate the existence of the optimal solution and a proper solution procedure is presented. A numerical example and a sensitivity analysis are presented to validate the theoretical results. Also, some managerial insights are provided.

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

Yugoslav journal of operations research ◽

10.2298/yjor150202002y ◽

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.

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