Three-parameter Weibull Distribution Deterioration Research Articles

An Optimal Policy for Deteriorating Items With Generalized Deterioration, Trapezoidal-Type Demand, and Shortages

This paper focuses an optimal policy of an inventory model for deteriorating items with trapezoidal type demand rate and the three-parameter Weibull distribution deterioration rate. The model allows shortages which are completely backlogged in order to achieve better preserving amenity. The authors present some optimal solutions which leads to determine the total inventory cost in which the collective behavior of customers hinges on the waiting time. An easy-to-use optimization technique is included to find the shortage time point and order quantity to minimize the total system cost. Taking into account the above-mentioned assumptions, different kinds of numerical examples are considered to illustrate the theoretical behavior of the framed optimization model. The sensitivity analysis is made for this problem with variation of parameters. The study shows that the optimal solution not only exists but also is unique and is less expensive to operate if the factors of three-phase variation, representing the growth, the steady, and the decline phases of demand with respect to time are considered.

A note on an economic order quantity model with time-dependent demand, three-parameter Weibull distribution deterioration and permissible delay in payment

Khanra et al. (2011, Applied Mathematics and Computation, 218, 1-9) established recently an Economic Order Quantity (EOQ) model with rate of deterioration and the rate of demand are constant and time dependent quadratic function of time respectively when the supplier offers the retailer a delay period. It is obvious that the significance of the depletion of any inventory is due to the rate of deterioration partly and the rate of demand mainly. In real life situation, the rate of deterioration is not always constant, but it is an increasing function of time. In our proposed model, we have considered a deteriorating item that follows a three-parameter Weibull distribution deterioration. Shortages are not permitted in our model. This model is validated by a numerical example and the sensitivity analysis of the optimal solution with respect to the parameters of the model is carried out.

Joint pricing, advertisement, preservation technology investment and inventory policies for non-instantaneous deteriorating items under trade credit

To maximize profit in a competitive market environment, for retailers, it became necessary to optimize preservation, pricing, and marketing strategies together with inventory ordering policies. This study deals with the problem of optimizing price, advertisement frequency, preservation technology (PT) investment and ordering policies simultaneously for non-instantaneous deteriorating items whose deterioration rate can be reduced by investing in PT, while demand depends on both selling price and frequency of advertisement. The supplier allows some credit period to settle the account, and under this policy, three possible cases considered separately. We adopt three-parameter Weibull distribution deterioration and partial backlogs of shortages in a general framework to formulate the model. An iterative algorithm is provided to obtain the optimal solution, then the proposed model is illustrated through numerical examples. The concavity of the total profit function with respect to decision variables shown graphically. Sensitivity analysis has been conducted to investigate the impact of each parameter. PT investment and credit period are beneficial for the retailer, and also can earn more profit through advertisement. Value-added food products, such as bottled fruit juice, soft drinks, packed fruits, bread, cake, processed meat, etc., needs preservation technology and their demand depends on the price as well as marketing. Profit maximization of such items can be studied with the help of new model developed in this paper.

Two-warehouse partial backlogging inventory model with ramp type demand rate, three-parameter Weibull distribution deterioration under inflation and permissible delay in payments

Abstract Decay or deterioration of physical goods while in stock is a natural phenomenon in many inventory systems. The three-parameter Weibull distribution is an excellent generalization of exponential decay, which can be used for items with any initial value of the rate of deterioration and for items which starts deteriorating only after a certain period of time. To reduce the amount of deterioration and the limited storage facility in own warehouse (OW) the retailer’s is moving their excess items to store in a rented warehouse (RW). Generally it is seen that for any new brand of consumer goods coming to the market, the demand rate increases with time up to a certain period and then ultimately stabilize and becomes constant. This kind of stabilization has been termed as ’ramp-type’ demand rate. So, in this paper, we have developed two warehouse inventory models with ramp type demand rate and three-parameter Weibull distribution deterioration (ThPWD) under inflationary conditions, where permissible delay in payment is available for retailer if outstanding amount is compensated within the given credit period. Since, not all customers are willing to wait for backlogged during the shortage period, in this investigation shortages are also allowed and partially backlogged. The purpose of this study is not only to find retailer’s optimal replenishment policies but also to minimize the total average cost. Finally, a numerical example is presented to illustrate the proposed model and sensitivity analysis of the optimal solutions with respect to major parameters is carried out using the Mathematica-8.0 software.

Optimal replenishment policy for items with three-parameter Weibull deterioration, stock-level dependent demand and partial backlogging

Our focus in this paper is on determining an optimal replenishment policy for items with three-parameter Weibull distribution deterioration and inventory-level dependent demand. We developed and analyzed the model under the assumption of partial backlogging. The three-parameter Weibull hazard rate captures the impact of already deteriorated items that are received into the inventory, as well as those items that may start deteriorating in future. The inventory-level demand reflects a real market demand for product whose sales is enhanced by stock on display. We study a case base examples to gain some quantitative insight into the proposed model and we perform sensitivity analysis to draw some managerial implications.

An Optimal Policy with Three-Parameter Weibull Distribution Deterioration, Quadratic Demand, and Salvage Value Under Partial Backlogging

This paper deals with an EOQ (Economic Order Quantity) model for deteriorating items having the following characteristics: 1) Deteriorating items follow a three-parameter Weibull distribution deterioration rate; 2) Shortages are allowed and are partially backlogged; 3) Salvage value of items is incorporated; 4) Demand is deterministic and a time-dependent quadratic function of time. The principal objective of the introduced model is to minimize the average total inventory cost by finding an optimal replenishment policy. The effectiveness of the model is validated with a numerical example and the sensitivity analysis of the optimal solutions to changes in the values of the various parameters associated with the model has been performed.

An Inventory Model With Three-Parameter Weibull Deterioration, Quadratic Demand Rate and Shortages

SYNOPTIC ABSTRACTThis article presents an economic order quantity (EOQ), model for items with three-parameter Weibull distribution deterioration and quadratic demand trend. The model is developed and analyzed under quasipartial backlogging, i.e., in a situation when a shortage occurs, a good number of customers are willing to wait for the product to become available again. The quadratic demand rate is deterministic and it depicts different phases of market demand, including accelerated rise or fall in demand. The instantaneous rate of deterioration is an increasing function of time. We provide simple analytical tractable procedures for deriving the model and give numerical examples to illustrate the solution procedure. Sensitivity analysis is performed to show how the optimal values of the policy variables in the model change as various model parameters are changed.

Optimal payment policy with price-dependent demand and three parameters dependent deterioration rate under the influence trade credit

In this paper we developed an inventory model for an optimal payment policy for deteriorating items under the influence of trade credit. Demand rate of the product is considered as the function of selling price. Here, we consider the deteriorating item that follows three-parameter Weibull distribution deterioration. Finally, the optimal solution is illustrated with help of numerical example and the sensitivity analysis is carried out with respect to different parameters.

An Economic order quantity model for Items with Three-parameter Weibull distribution Deterioration, Ramp-type Demand and Shortages

In this paper, we develop an economic order quantity inventory model for items with three-parameter Weibull distribution deterioration and ramp-type demand. Shortages are allowed in the inventory system and are completely backlogged. The demand rate is deterministic and varies with time up to a certain point and eventually stabilized and becomes constant. The instantaneous rate of deterioration is an increasing function of time. We provide simple analytical tractable procedures for deriving the model and give numerical examples to illustrate the solution procedure. Our adoption of ramp-type demand reflects a real market demand for newly launched product.

A replenishment policy for items with price-dependent demand, time-proportional deterioration and no shortages

In this article, an order-level inventory system for deteriorating items has been developed with demand rate as a function of selling price. The demand and the deterioration rate are price dependent and time proportional, respectively. We have considered a perishable item that follows a three-parameter Weibull distribution deterioration. Shortages are not permitted in our model. The optimal solution is illustrated with a numerical example and the sensitivity analysis of parameters is carried out.

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 inventory model for items with ramp type demand, three-parameter Weibull distribution deterioration and starting with shortage

In this present paper an inventory model is developed with ramp type demand, starting with shortage and three - parameter Weibull distribution deterioration. A brief analysis of the cost involved is carried out by an example.