scholarly journals Optimal Replenishment Policy for Weibull-Distributed Deteriorating Items with Trapezoidal Demand Rate and Partial Backlogging

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Lianxia Zhao
Keyword(s):  
Optimal Solution ◽  
Solution Procedure ◽  
Deteriorating Items ◽  
Optimal Order ◽  
Partial Backlogging ◽  
Total Cost ◽  
Replenishment Policy ◽  
Demand Rate ◽  
The Stability ◽  
Theoretical Results

An inventory model for Weibull-distributed deteriorating items is considered so as to minimize the total cost per unit time in this paper. The model starts with shortage, allowed partial backlogging, and trapezoidal demand rate. By analyzing the model, an efficient solution procedure is proposed to determine the optimal replenishment and the optimal order quantity and the average total costs are also obtained. Finally, numerical examples are provided to illustrate the theoretical results and a sensitivity analysis of the major parameters with respect to the stability of optimal solution is also carried out.

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 An Inventory Model under Trapezoidal Type Demand, Weibull-Distributed Deterioration, and Partial Backlogging

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lianxia Zhao
Keyword(s):  
Sensitivity Analysis ◽  
Waiting Time ◽  
Optimal Solution ◽  
Inventory Model ◽  
Partial Backlogging ◽  
Inventory Models ◽  
Numerical Examples ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Theoretical Results

This paper studies an inventory model for Weibull-distributed deterioration items with trapezoidal type demand rate, in which shortages are allowed and partially backlogging depends on the waiting time for the next replenishment. The inventory models starting with no shortage is are to be discussed, and an optimal inventory replenishment policy of the model is proposed. Finally, numerical examples are provided to illustrate the theoretical results, and a sensitivity analysis of the major parameters with respect to the optimal solution is also carried out.

scholarly journals Replenishment Model with Entropic Order Quantity for Deteriorating Items under Inflation

2021 ◽  
pp. 34-47
Author(s):  
P. K. Tripathy ◽  
Anima Bag
Keyword(s):  
Cost Minimization ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Optimal Order ◽  
Selling Price ◽  
Order Quantity ◽  
Total Cost ◽  
Purchase Cost ◽  
Holding Cost ◽  
Special Approach

The purpose of the current paper is to determine an optimal order quantity so as to minimize the total cost of the inventory system of a business enterprise. The model is developed for deteriorating items with stock and selling price dependent demand under inflation without permitting shortage. Optimal solution is achieved by cost minimization strategy considering replenishment cost, purchase cost, holding cost and deterioration cost with a special approach to entropy cost for bulk size purchasing units. The effectiveness of the proposed model has been avowed through empirical investigation. Sensitivity analysis has been accomplished to deduce managerial insights. Findings suggest that an increased inflationary effect results in increment in the system total cost. The paper can be extended by allowing shortage. The model can be utilized in the business firms dealing with bulk purchasing units of electric equipments, semiconductor devices, photographic films and many more.

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

2013 ◽  
Vol 23 (3) ◽  
pp. 441-455 ◽  
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.

scholarly journals Optimal order policy for deteriorating items in response to temporary price discount linked to order quantity

2009 ◽  
Vol 40 (4) ◽  
pp. 383-400 ◽  
Author(s):  
Liang-Yuh Ouyang ◽  
Chih-Te Yang ◽  
Hsiu-Feng Yen
Keyword(s):  
Cost Saving ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Optimal Order ◽  
Market Demand ◽  
Order Quantity ◽  
Price Discount ◽  
Total Cost ◽  
Holding Cost ◽  
Special Order

This paper investigates the possible effects of a temporary price discount offered by a supplier on a retailer's replenishment policy for deteriorating items, whereby the price discount rate depends on the order quantity. The purpose of this study is to develop a decision process for retailers to assist in determining whether to adopt a regular or special order policy. Furthermore, the optimal quantity of a special order policy for a selected case is determined by maximizing the total cost saving between special and regular orders for the duration of the depletion time. This research establishes an algorithm to determine the optimal solution and utilizes several numerical examples to illustrate the theoretical results and subsequently conducts a sensitivity analysis of the optimal solution with respect to the main parameters. Finally, the results reveal that (1) the optimal special order quantity is determined by trading off the benefits of the price discount against the additional holding cost, (2) the retailer benefits in terms of total cost saving if the remnant inventory is as low as possible when adopting a special order policy, (3) for the retailer it is preferable to adopt the special order policy if the unit purchase cost, market demand rate and/or ordering cost increase, and (4) the retailer will order a lower quantity and the total cost saving will decrease when either the holding cost rate or deterioration rate is high. Thus, this study provides the basis for enterprises to make inventory decisions.

Ordering Policy in a Two-Warehouse Environment for Deteriorating Items under Inflationary Conditions

2014 ◽  
pp. 320-338
Author(s):  
Chandra K. Jaggi ◽  
Sarla Pareek ◽  
Aditi Khanna ◽  
Ritu Sharma
Keyword(s):  
Global Economy ◽  
Aggregate Demand ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Inventory Problem ◽  
Inventory Costs ◽  
Ordering Policy ◽  
Demand Rate ◽  
Warehousing Systems ◽  
The Cost

In this chapter, the two-warehouse inventory problem is considered for deteriorating items with constant demand rate and shortages under inflationary conditions. In today’s unstable global economy, the effects of inflation and time value of money cannot be ignored as it increases the cost of goods. To safeguard from the rising prices, during the inflation regime, the organization prefers to keep a higher inventory, thereby increasing the aggregate demand. This additional inventory needs additional storage space that is facilitated by a rented warehouse. Further ahead, in the real business world, to retain the freshness of the commodity, most of the organizations adopt the First-In-First-Out (FIFO) dispatching policy. FIFO policy yields fresh and good conditioned stock thereby resulting in customer satisfaction, especially when items are deteriorating in nature. However, the two warehousing systems usually assume that the holding cost of items is more in Rental Warehouse (RW) than the Owned Warehouse (OW) due to modern preserving techniques. Therefore, to reduce the inventory costs, it is economical to consume the goods of RW at the earliest. This approach is termed the Last-In-First-Out (LIFO) approach. The objective of the present chapter is to develop a two warehouse inventory model with FIFO and LIFO dispatching policies under inflationary conditions. Further, comparison between FIFO and LIFO policies has been exhibited with the help of a numerical example. Sensitivity analysis has also been performed to study the impact of various parameters on the optimal solution.

scholarly journals Determining the Optimum Ordering Policy in Multi-Item Joint Replenishment Problem Using a Novel Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wen-Tsung Ho
Keyword(s):  
Cycle Time ◽  
Heuristic Algorithms ◽  
Optimal Solution ◽  
Lead Times ◽  
Joint Replenishment ◽  
Joint Replenishment Problem ◽  
Ordering Policy ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Time Division

This work investigates the joint replenishment problem (JRP) involving multiple items where economies exist for replenishing several items simultaneously. The demand rate for each item is known and constant. Shortages are not permitted and lead times are negligible. Many heuristic algorithms have been proposed to find quality solutions for the JRP. In this paper, cycle time division and recursive tightening methods are developed to calculate an efficient and optimal replenishment policy for JRP. Two theorems are demonstrated to guarantee that an optimal solution to the problem can be derived using cycle time division and recursive tightening methods. Restated, cycle time division and recursive tightening methods theoretically yield the optimal solution in 100% of instances. The complexity of cycle time division and recursive tightening methods is justO(NlogN), whereNrepresents the number of items involved in the problem. Numerical examples are included to demonstrate the algorithmic procedures.

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