Weibull Deterioration Research Articles

Two-warehouse partial backlogging inventory models with three-parameter Weibull distribution deterioration under inflation

Abstract In many inventory systems, the effects of deterioration of physical goods have drawn much attention of various researchers in recent years. The more the deterioration is, the more the order quantity would be. According to such consideration, taking the deterioration rate into account is necessary. Thus, in this paper, I develop the two-warehouse partial backlogging inventory model introduced in Yang (2006) to incorporate three-parameter Weibull deterioration distribution. The objective is to derive the optimal replenishment policy that minimizes the net present value of total relevant cost per unit time. Two alternative models are compared based on the minimum cost approach. The study shows that the optimal solution not only exists but also is unique. Model 2 is still less expensive to operate than Model 1 in the proposed model. Finally, some numerical examples and sensitivity analysis on parameters are made to validate the results of the proposed inventory system.

An EOQ model for three parameter Weibull deterioration with permissible delay in payments and associated salvage value

This paper deals with the development of an inventory model for Weibull deteriorating items with constant demand when delay in payments is allowed to the retailer to settle the account against the purchases made. Shortages are not allowed and the salvage value is associated with the deteriorated units. In this paper, we consider two cases; those are for the case payment within the permissible time and for payment after the expiry of permissible time with interest. Numerical examples are provided to illustrate our results. Sensitivity analysis are carried out to analyze the effect of changes in the optimal solution with respect to change in one parameter at a time.

Inventory Model for Ramp type items with Trade Credit under Extra ordinary purchase

We have endeavoured here to depict an interactive inventory model between producer (supplier) and prospective buyer (vendor) in the presence of an extraordinary purchase and credit period with two parameter weibull deterioration for items with ramp type demand. The case of shortages is also studied.Additonally, we deal with the problem of a supplier disposing a large inventory level through an offer to a prospective buyer in the form of a credit period. From our model we confirm that the behaviour of replenishment period and trade credit period and change of the total variable cost observed from numerical evidence should be interpreted with caution in any business organisation.

An EOQ model with time dependent Weibull deterioration and ramp type demand

Article history: Received 1 September 2010 Received in revised form 20 November 2010 Accepted 22 November 2010 Available online 22 November 2010 This paper presents an order level inventory system with time dependent Weibull deterioration and ramp type demand rate where production and demand are time dependent. The proposed model of this paper considers economic order quantity under two different cases. The implementation of the proposed model is illustrated using some numerical examples. Sensitivity analysis is performed to show the effect of changes in the parameters on the optimum solution. © 2011 Growing Science Ltd. All rights reserved.

An inventory model with generalized type demand, deterioration and backorder rates

This study is motivated by the paper of Skouri et al. [Skouri, Konstantaras, Papachristos, Ganas, European Journal of Operational Research 192 (1) (2009) 79–92]. We extend their inventory model from ramp type demand rate and Weibull deterioration rate to arbitrary demand rate and arbitrary deterioration rate in the consideration of partial backorder. We demonstrate that the optimal solution is actually independent of demand. That is, for a finite time horizon, any attempt at tackling targeted inventory models under ramp type or any other types of the demand becomes redundant. Our analytical approach dramatically simplifies the solution procedure.

Imperfect production process with exponential demand rate, Weibull deterioration under inflation

In this research, an integrated production inventory model is developed from the perspective of both the manufacturer and the retailer. The model assumes exponential demand rate, production rate is demand dependent under the inflation, imperfect production process and multiple deliveries. We have assumed that the produced items deteriorates at a constant rate at the producer’s end due to the proper storages conditions, and as the items reaches the retailer’s end follows the Weibull deterioration. Shortages are allowed at the retailer’s part only and the unfulfilled demand is partially backlogged. A numerical example along with sensitivity analysis is given to illustrate the model. Integrated cost policy is compared with the independent decisions made by the manufacturer and the retailer’s and the necessary conclusions are made. Mathematica5.2 is being used to reach the optimal policies.

Effects of ramp type demand and Weibull deterioration rate on retailers' optimal pricing and lot-sizing policies for deteriorating items with partial backlogging

This paper discusses a deterministic inventory model for Weibull deteriorating items with partial backlogging under ramp type demand function. Shortages are allowed. Here we consider replenishment cycles, the time at which shortage begins; replenishment time and the optimal selling price are taken as decision variables. The objective of this model is to maximise the total profit (TP) which includes the sales revenue, purchase cost, the set up cost, holding cost, shortage cost and opportunity cost due to lost sales. We extend the results to ameliorating items also. Numerical examples are given to illustrate the model.

Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate

In this paper, an inventory model with general ramp type demand rate, time dependent (Weibull) deterioration rate and partial backlogging of unsatisfied demand is considered. The model is studied under the following different replenishment policies: (a) starting with no shortages and (b) starting with shortages. The model is fairly general as the demand rate, up to the time point of its stabilization, is a general function of time. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The optimal replenishment policy for the model is derived for both the above mentioned policies.

An integrated production-inventory deteriorating model for pricing policy considering imperfect production, inspection planning and warranty-period- and stock-level-dependant demand

In marketing, enterprises try all motivated selling strategies to stimulate customers to buy a product. One of these selling strategies is a warranty policy that provides a return promise of free replacement. The buyer may place more orders because of the display of the product. An increasing demand resulting from these motivated factors influences the replenishment planning. In operational process, quality level resulting in relevant activities may cause changes of operational planning. The purpose of this study is to investigate an integrated production inventory deteriorating model considering the pricing policy, the imperfect production, the inspection planning, the warranty-period and the stock-level-dependant demand with the Weibull deterioration, partial backorder and inflation. We incorporate a single-retailer single-manufacturer cooperation from the perspectives of both the manufacturer and the retailer. The classical optimisation technique and the heuristic method are used to derive the optimum solutions. A numerical example and sensitivity analysis are presented.

Economic Order Quantity model with Weibull deterioration distribution, shortage and ramp-type demand

A single-item single-period Economic Order Quantity model for deteriorating items with a ramp-type demand and Weibull deterioration distribution is considered. The shortages in inventory are allowed and backlogged completely. The model is developed over an infinite planning horizon and the optimal replenishment policy is derived by minimizing the total inventory cost per unit time. The numerical solution of the model is obtained, and the sensitivity of the parameters involved in the model is also examined.

Optimal replenishment scheduling for inventory items with Weibull distributed deterioration and time-varying demand

This paper proposes a dynamic programming model for solving replenishment scheduling problems. The model is developed based on the following assumptions: the inventory items are subject to deterioration of two-parameter Weibull distribution, the demand rate is exponentially distributed over time, shortages are allowed, and the effects of inflation and time-value of money are taken into consideration. The solutions of the model determine the optimal replenishment schedule over a finite horizon so that the present worth of the total cost is minimized. The solution procedure is illustrated by two numerical examples. The strength of the proposed model is supported by carrying out a comparison study with an existing model. The proposed model permits variation in both the replenishment intervals and the service levels between order cycles. As a result, it generates a better solution than other optimization models having fixed order intervals and fixed service levels. In addition, the Weibull deterioration used in the model is a generalized form of exponentially decaying functions, and hence it is applicable to the management of a wider range of deteriorating items in practice, like agricultural products, blood, drugs, fashion goods, high-tech and electronic components, volatile liquids, and radioactive substances

An EOQ inventory model for items with Weibull deterioration, shortages and time varying demand

An inventory model is considered in which inventory is depleted not only by demand, but also by deterioration. Hence, in this paper, we derive the EOQ model for inventory of items that deteriorates at a Weibull distributed rate, assuming the demand rate with a continuous function of time. Moreover, the proposed model cannot be solved directly in a closed form, thus we used the computer software IMSL MATH/LIBRARY (1989) to find the optimal service level and the optimal replenishment cycle time. Further, we also verify that the sufficient conditions of optimality of the service level and the replenishment cycle time are satisfied under certain conditions. Finally, three numerical examples and sensitivity analyses are provided to assess the solution procedure.

An EOQ inventory model with time-varying demand and Weibull deterioration with shortages

An inventory model is considered in which inventory is depleted not only by demand, but also by deterioration. Hence, in this paper, we derive the EOQ model for inventory of items that deteriorate at a Weibull-distributed rate, assuming the demand rate with a continuous function of time. Moreover, the proposed model cannot be solved directly in a closed form, thus we used the computer software IMSL MATH/LIBRARY (1989) to find the optimal reorder time. Further, we also find that the optimal procedure is independent from the form of the demand rate. Finally, we also assume that the holding cost is a continuous, non-negative and non-decreasing function of time in order to generalize the EOQ model. Moreover, four numerical examples and sensitivity analyses are provided to assess the solution procedure.

Optimal issuing policy in production lot size system for items with Weibull deterioration

Abstract The effect of two issuing policies, LIFO and FIFO, on the inventory level in a production lot size model for items with varying rate of deterioration is studied An implicit form of inventory level under each policy is developed for each phase of a cycle which is shown to be consistent with known extreme cases A numerical solution procedure employing the Runge-Kutta method and Simpson's Rule is developed to select a preferable policy in terms of the amount deteriorated per unit time.