Development of an EPQ Model for Deteriorating Product with Stock and Demand Dependent Production rate under Variable Carrying Cost and Partial Backlogging

In the present article, an economic production quantity (EPQ) model is developed for deteriorating product with time dependent demand and the time dependent inventory carrying cost. Here,it is assumed that the production rate at any instant depends on both the stock and the demand of the product. To make the model more realistic, the shortages are allowed and partially backlogged. The backordering rate is taken as a decreasing function of waiting time for the next refill.The main objective of the present study is to find the optimal total cost per unit time of the production system. To validate the optimal resuts, numerical example is provided. To analyze the effect of variations in the optimal resuts with respect to change in one parameter at a time, sensitivity analysis is carried out and the results are presented graphically

A deterministic inventory model for deteriorating items with selling price dependent demand and three-parameter Weibull distributed deterioration

In this paper, an attempt is made to develop two inventory models for deteriorating items with variable demand dependent on the selling price and frequency of advertisement of items. In the first model, shortages are not allowed whereas in the second, these are allowed and partially backlogged with a variable rate dependent on the duration of waiting time up to the arrival of next lot. In both models, the deterioration rate follows three-parameter Weibull distribution and the transportation cost is considered explicitly for replenishing the order quantity. This cost is dependent on the lot-size as well as the distance from the source to the destination. The corresponding models have been formulated and solved. Two numerical examples have been considered to illustrate the results and the significant features of the results are discussed. Finally, based on these examples, the effects of different parameters on the initial stock level, shortage level (in case of second model only), cycle length along with the optimal profit have been studied by sensitivity analyses taking one parameter at a time keeping the other parameters as same

Two Warehouse Inventory Model for Deteriorating Products with Stock Dependent Demand and Shortages

In this paper a deterministic inventory model for two warehouses has been developed. In two warehouses the first is the owned warehouse with a fixed capacity of W units and the other one is rented warehouse with unlimited stocking capacity. The deterioration occurs in both the warehouses. First the demand is fulfilled from the inventory in rented warehouse and after thatthe inventory in owned warehouse has been used. The shortages are allowed in owned warehouse only and the excess demand is partially backlogged. For the generality of the model we presented the equations for total cost of the system. A numerical example and sensitivity analysis with respect to different associated parameters has also been presented to illustrate the model

Analysis of an Inventory Model with Time-dependent Deterioration and Ramp-type Demand Rate: Complete and Partial Backlogging

The proposed model based on the global market strategies as for how the demand vary of the new seasonal products when they entered in the markets. The model has developed for the seasonal products or new consumer goods. The demand rate has considered Ramp-type based on the seasonal products having a time-dependent deterioration rate. The mathematical formulation of the proposed model is given. The present article consists two inventory model differ to each other as (a) in the first model stock-out situation is considered as completely backlogged; (b) in the second model partial backlogged stock-out situation is inserted. To obtain the optimal solution solved the proposed model analytically and shown the convexity of the proposed models graphically by using Mathematica 9.0. Numerical examples are given to test and verify the theoretical results. Ultimately, the sensitivity of the optimal solution with respect to major parameters with concluding remarks are discussed

Inventory Model for Quadratic Demand and Deteriorating Items Following Weibull Distribution with Trade Credit Policy

In this paper, an inventory model for deteriorating items following two parameter Weibull distribution with trade credit policy is developed, while demand is viewed as quadratic function of time. The supplier gives the retailer a trade credit period. Trade credit is a frequently used method of payment implemented by suppliers, and it generally leads to greater revenue and ultimately, higher income. The suggested inventory model seeks to calculate the ideal replenishment cycle duration in order to maximize the overall profit per unit of time.  Shortages are permitted and partially backlogged. Two categories are applied to the mathematical model. Case I: When the payment to settle the account is made on or before the positive inventory. Case II: When the payment to settle the ac-count is made after the inventory reaches to zero. The model is illustrated through numerical experiments, sensitivity analysis, and graphical depiction

DETERIORATING ITEM INVENTORY MODEL WITH SHORTAGES, VARIABLE HOLDING COST AND TIME DEPENDENT QUADRATIC DEMAND: AN OPTIMIZATION APPROACH USING WITH AND WITHOUT CONTROLLABLE RATE OF DETERIORATION

The purpose of this study is to develop time dependent quadratic demand and variable holding cost, a model of inventory system, for instantaneous deteriorating items with the consideration of the facts that the deteriorating rate can be controlled by using the preservation technology (PT). A solution procedure is presented to find the optimal solution of the cost function. Shortages are allowed and partially backlogged. The backlogging rate is assumed to be dependent on the length of the waiting time for the next replenishment. The longer the waiting time is, the smaller the backlogging rate would be. Results have been validated with relevant examples. Sensitivity analysis is performed to show the effect of changes in the parameters on the optimum solution for both the cases that is with and without using the preservation technology respectively. The analysis of the model shows that the solution of the model is quite stable and can be applied for optimizing the inventory cost of deteriorating items for the business enterprise

Inventory ordering policies for mixed sale of products under inspection policy, multiple prepayment, partial trade credit, payments linked to order quantity and full backordering

The situation where serviceable products are sold together with a proportion of deteriorating products to consumers is rarely discussed in the literature. This article proposes an inventory model with disparate inventory ordering policies under a situation where a portion of serviceable products and a portion of deteriorating products are sold together to consumers (i.e. mixed sales). The ordering policies consider a hybrid payment strategy with multiple prepayment and partial trade credit schemes linked to order quantity under situations where no inventory shortage is allowed and inventory shortage is allowed with full backorder. The hybrid payment policy offered by a supplier is introduced into the classical economic ordering quantity model to investigate the optimal inventory cycle and the fraction of demand that is filled from the deteriorating products under inspection policy. Further, a new solution method is proposed that identifies optimal annual total profit with mixed sales assuming no inventory shortage and inventory shortage with full backorder. The impact of an inspection policy is investigated on the optimality of the solution under hybrid payment strategies for the deteriorating products. The validation of the proposed model and its solution method is demonstrated through several numerical examples. The results indicate that the inventory model along with the solution method provide a powerful tool to the retail managers under real-world situations. Results demonstrate that it is essential for the managers to consider inclusion of an inspection policy in the mixed sales of products, as the inspection policy significantly increases the net annual profit