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.     

EOQ inventory model for items with Weibull distribution deterioration,time-varying demand and partial backlogging

The paper presents an EOQ inventory model that is depleted not only by time-varying demand but also by Weibull distribution deterioration, in which shortages are allowed and partially backordered. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Further, the optimal procedure was independent of the form of the demand rate. It is then illustrated with the help of four numerical examples. The sensitivity analysis is also studied.     

A production-inventory model under stock-dependent demand, Weibull distribution deterioration and shortage

In the present article, we establish two production inventory models (Model I and Model II) for deteriorating items when the demand rate depends on the instantaneous inventory level. The production rate depends not only on the stock level but also on the demand. In both the models, we consider the Weibull distribution deterioration. Model I is developed and solved without allowing shortages whereas Model II is developed and solved allowing shortages that are backlogged. Three numerical examples are given to illustrate the solution procedure of the two models. Sensitivity analysis is also carried out.     

Supply chain models for deteriorating products with ramp type demand rate under permissible delay in payments

In this paper an order level inventory model for deteriorating items with general ramp type demand rate under conditions of permissible delay in payments is proposed. In this model shortages are allowed and partially backlogged. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Its study requires exploring the feasible ordering relations between the time parameters appeared, which leads to three models. For each model the optimal replenishment policy is determined. The sufficient conditions of the existence and uniqueness of the optimal solutions are also provided. Suitably selected numerical examples highlight the obtained results. Sensitivity analysis of the optimal solution with respect to major parameters of the system has been carried out and the implications are discussed.     

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.     

Inventory systems for deteriorating items with shortages and a linear trend in demand-taking account of time value

This paper derives an inventory model for deteriorating items with the demand of linear trend and shortages during the finite planning horizon considering the time value of money. A simple solution algorithm using a line search is presented to determine the optimal interval which has positive inventories. Numerical examples are given to explain the solution algorithm. Sensitivity analysis is performed to study the effect of changes in the system parameters.Scope and purpose The traditional inventory model considers the ideal case in which depletion of inventory is caused by a constant demand rate. However, in real-life situations there is inventory loss due to deterioration. In a realistic product life cycle, demand is increasing with time and eventually reaching zero. Most of the classical inventory models did not take into account the effects of inflation and time value of money. But in the past, the economic situation of most of the countries has changed to such an extent due to large scale inflation and consequent sharp decline in the purchasing power of money. So, it has not been possible to ignore the effects of inflation and time value of money any further. The purpose of this article is to present a solution procedure for the inventory problem of deteriorating items with shortages and a linear trend in demand taking account of time value.     

A two‐warehouse inventory model for items with three‐parameter Weibull distribution deterioration,shortages and linear trend in demand

Depending on the type of goods and storage facilities available, perishable goods decay in different manners in terms of the initial point and rate of deterioration. The three‐parameter Weibull distribution is an excellent generalization of exponential decay, with the flexibility of modeling various types of deteriorations. Since inventory management of perishable goods involves expensive storage facilities, the retailer with small storage may have to rent a warehouse. In this paper, we discuss a two‐warehouse inventory model where deteriorations in the two warehouses follow independent three‐parameter Weibull distributions. Transfer of units is from the rented warehouse to the own warehouse, and incurs a positive cost per unit. Demand is a non‐decreasing linear function of time, shortages are backlogged and replenishment is instantaneous. A solution procedure for obtaining optimal values of initial inventory level and cycle time is presented. Sensitivity analysis is carried out. The effect of using other related deterioration distributions is illustrated.     

Optimal replenishment policy for perishable items with stock-dependent selling rate and capacity constraint

In this paper, a deterministic inventory model is developed for deteriorating items with stock-dependent demand and finite shelf/display space. Furthermore, we allow for shortages and the unsatisfied demand is partially backlogged at the exponential rate with respect to the waiting time. We provide solution procedures for finding the maximum total profit per unit time. In a specific circumstance, the model will reduce to the case with no shortage. Further, we use numerical examples to illustrate the model.     

Deterministic inventory model with two levels of storage,a linear trend in demand and a fixed time horizon

A deterministic inventory model is developed for a single item having two separate storage facilities (owned and rented warehouses) due to limited capacity of the existing storage (owned warehouse) with linearly time-dependent demand (increasing) over a fixed finite time horizon. The model is formulated by assuming that the rate of replenishment is infinite and the successive replenishment cycle lengths are in arithmetic progression. Shortages are allowed and fully backlogged. As a particular case, the results for the model without shortages are derived. Results are illustrated with two numerical examples.Scope and purposeThroughout the world, the production of food grains is periodical. Normally, in countries where state control is less, the demand of essential food grains is lowest at the time of harvest and goes up to the highest level just before the next harvest. This phenomenon is very common in developing third world countries where most of the people are landless or marginal farmers. At the time of harvest, they share some grain/product with landowners and as soon as the small inventory is exhausted, they are forced to buy food grains from the open market. As a result, demand for food grains increases with time in a period along with the number of the people whose initial stock of food grains gets exhausted.In this paper, a two-storage inventory model with time-dependent demand and fixed time horizon is developed and solved by a mathematical programme based on gradient method. This methodology of model development and its solution are quite general and it can be applied to inventory models of any product whose production is periodical and demand increases linearly with time.     

Decision process for multiobjective,multi-item production-inventory system via interactive fuzzy satisficing technique

Multiobjective and single-objective inventory models of stochastically deteriorating items are developed in which demand is a function of inventory level and selling price of the commodity. Production rate depends upon the quality level of the items produced and unit production cost is a function of production rate. Deterioration depends upon both the quality of the item and duration of time for storage. The time-related deterioration function follows a two-parameter Weibull distribution in time. In these models, results are derived for both without shortages and partially backlogged shortages. Here, objectives for profit maximization for each item are separately formulated with different goals and compromise solutions of the multiobjective production/inventory problems are obtained by goal programming method. The models are illustrated with numerical examples and results for different formulations are compared. The results for the models assuming them to be a single house integrated business are also obtained using a gradient-based optimization technique and compared with those obtained from the respective decentralized models. Taking man-machine interaction into consideration, interactive solutions are derived for one of the said models—multiobjective model with shortages using interactive fuzzy satisficing method. Pareto optimum and satisficing results are derived for some numerical data.