Time Dependent Demand Rate Research Articles

A Production Inventory Model for Fractionally Time-Dependent Demand Rate with Weibull Deterioration and Partially Backlogged Items

A Production Inventory Model for Fractionally Time-Dependent Demand Rate with Weibull Deterioration and Partially Backlogged Items

An Inventory Model for Perishable Items with Cubic Deterioration Rate Having Shelf-Life Price, Stock, and Time-Dependent Demand Rate

An Inventory Model for Perishable Items with Cubic Deterioration Rate Having Shelf-Life Price, Stock, and Time-Dependent Demand Rate

On the Effect of a Fixed Cost on an Inventory Model with Time – Dependent Parameters

An economic order quantity model with a time-dependent demand, a fixed cost and a time-dependent holding cost is developed. It provides quantitative insight into a serious practical problem where costs are incurred even when an order is not placed. The effect of a fixed cost on the inventory model is examined. Previous models incorporating time-dependent demand rate assume that the holding cost is constant for the entire inventory cycle. The holding cost is considered as an increasing function of time spent in storage. Differential calculus is used for finding the optimal solution. A numerical example is used to validate the proposed model. Sensitivity analysis is carried out to analyze the effect of changes in the optimal solution with respect to changes in various parameters.

Replenishment decision for ameliorating inventory with time dependent demand and partial backlogging rate

Replenishment decision for ameliorating inventory with time dependent demand and partial backlogging rate

An EOQ model for deteriorating item with continuous linear time dependent demand with trade of credit and replenishment time being demand dependent

This study is about an inventory model with continuous linear time dependent demand rate with constant rate of deterioration in the consideration of partial backorder including delay in payment and time period is demand dependent. Demand is the fundamental attribute for consideration of inventory related problem. In reality, there is some inter connection of demand function among various time interval for which the demand cannot change drastically at some critical point during the appearance of another state of system. Thus, it is quite natural that the demand function should be continuous in nature in inventory management problem. So, here the most prominent part of our present study is the consideration of time dependent continuous demand in the proposed model. A supportive numerical example of the proposed model is illustrated for insightful investigation. The solution method and sensitivity analysis has also been presented.

Theoretical developments and application of variational principle in a production inventory problem with interval uncertainty

The goal of this work is two folded: (i) theoretical development of optimality condition of a variational problem with interval uncertainty; (ii) application of the established results in a production inventory model with interval uncertainty. To serve the purpose of first fold, the definitions of optimizers of an interval valued variational problem (IVVP) are proposed by using interval order relations. Then both the necessary and sufficient optimality conditions of an IVVP with single as well as several variables are derived. In this derivation, the obtained necessary conditions are named as c-r Euler equations and sufficient conditions are named c-r as Legendre conditions. To achieve the purpose of second fold, a production inventory model is formulated by considering interval valued time dependent production and demand rates. Then the corresponding IVVP of the proposed model is obtained and its optimal policy is studied with the help of established c-r Euler’s equations and c-r Legendre conditions. Finally, to illustrate the optimal policy of the proposed model, a numerical example is considered and optimality of its obtained results are verified graphically.

Fuzzy EOQ Model for Time Varying Deterioration and Exponential Time Dependent Demand Rate under Inflation

In this study we have discussed a fuzzy eoq model for deteriorating products with time varying deterioration under inflation and exponential time dependent demand rate. Shortages are not allowed in this fuzzy eoq model and the impact of inflation is investigated. An inventory model is used to determine whether the order quantity is more than or equal to a predetermined quantity for declining items.The optimal solution for the existing model is derived by taking truncated taylor’s series approximation for finding closed form optimal solution. The cost of deterioration, cost of ordering, cost of holding and the time taken to settle the delay in account are considered using triangular fuzzy numbers. In this study the fuzzy triangular numbers are used to estimate the optimal order quantity and cycle duration. Furthermore we have used graded mean integration method and signed distance approach to defuzzify these values. To validate our model numerical examples are discussed for all cases with the help of sensitivity analysis for different parameters. Finally, a higher decay rate results in a shorter ideal cycle time as well as higher overall relevant cost is established. The presented model can be used to predict demand as a quadratic function of time,stock level time dependent demand, selling price, and other variables.

A Fuzzy type Backlogging Production Inventory Model for Perishable Items with Time Dependent Exponential Demand Rate

Production inventory models have an important role in production planning and scheduling. In any economic production quantity (EPQ) model, the production rate is dependent on demand. In this paper we have established a production inventory model for perishable items with partial backlogging and time dependent exponential demand rate. Allowing shortage, it is partially backlogged. The unsatisfied demand is backlogged and it is considered a function of waiting time. The aim of our study is to optimizing the total profit during a given cycle. A numerical example is given in showing the applicability of the developed model.

Joint inspection and inventory control for deteriorating items with time-dependent demand and deteriorating rate

In this paper, we consider inventory control problems for deteriorating items with maximum serviceable lifetime under mixed sales situation, both of the demand and the deterioration rate are depending on time. A model is presented to formulate the process of mixed sales that deteriorated items are sold to consumers together with serviceable items, where penalty cost for the sales of deteriorated products is included. From the literature search, this study is one of the first researches on the joint inspection and inventory control policies under the mixed sales situation with time-dependent demand and deterioration rate. An additional ordering contract is designed to improve the inventory holder’s profit. The optimal ordering time and ordering quantities are characterized for the additional ordering contract. We show that it would be more beneficial for the inventory holder to employ an additional order. Furthermore, two different inspection policies are considered in this study: (i) one inspection during the cycle; (ii) continuous monitoring in the cycle. The numerical results show that the net profit would increase if one inspection or continuous monitoring is conducted. These results provide useful insights to guide decision-making in inventory control problems of deteriorating products.

An EPQ model with time proportion deterioration and ramp type demand under different payment schemes with fuzzy uncertainties

To ensure the order of goods and to attract the retailers and small vendors through discounts, the advance payment is a well-practised real life phenomenon in present market scenario and is being well studied in the field of inventory modelling and supply chain. Almost all inventory models depend upon the demands of the customers. Thus, demand is an important characteristic. The items may decay or deteriorate with time and loss their values partly or in full. The parameters might fluctuate due to various reasons and is more realistic to consider the uncertainty of the parameters rather than their fixed values. A deteriorating inventory model for a single item without shortage is developed in this paper. The crisp models are developed without and with advance payment schemes having time dependent ramp type demand and time proportion deterioration rate. The corresponding fuzzy models are formulated in which several parameters involved are taken as pentagonal fuzzy numbers to incorporate the uncertainties. We used the Regular Weighted Point method to convert the fuzzy numbers into the crisp numbers in order to make the computations affordable. We presented some numerical examples and studied the changing effects of different inventory parameters. Managerial insights are also described.

Multi-item a supply chain production inventory model of time dependent production rate and demand rate under space constraint in fuzzy environment

In this paper, we have developed an integrated production inventory model for two echelon supply chain consisting of one vendor and one retailer. Production rate and demand rate of retailer and customer are time dependent. Idle time cost of the vendor has been considered. Multi-item inventory has been considered. In integrated inventory model average cost has been calculated under limitation on stroge space. Two echelon supply chain fuzzy inventory model has been solved by various techniques like as Fuzzy programming technique with hyperbolic membership functions (FPTHMF), Fuzzy non-linear programming technique (FNLP) and Fuzzy additive goal programming technique (FAGP), weighted Fuzzy non-linear programming technique (WFNLP) and weighted Fuzzy additive goal programming technique (WFAGP). A numerical example is illustrated to test the model. Finally to make the model more realistic, sensitivity analysis has been shown.

A production stock model for a distributed deteriorating product with both price and time dependent demand rate under inflation and late paying allowing shortages

A production stock model for a distributed deteriorating product with both price and time dependent demand rate under inflation and late paying allowing shortages

A Production Stock Model for a Distributed Deteriorating Product with both Price and Time Dependent Demand Rate under Inflation and Late Paying Allowing Shortages

This paper develops a production stock model for deteriorating products with shortages under the effect of inflation and late paying in which demand is a function of selling price and time. In this article, the model is considered with different deterioration distributions and various time dependent holding costs. This model aids in maximising the total inventory cost by finding the two production periods, the consumption period and the shortage period. Numerical example is presented to understand the developed model. Also, the effect of changes in different parameters on the optimal total cost is graphically presented.

Replenishment Decision for Ameliorating Inventory with Time Dependent Demand and Partial Backlogging Rate

Replenishment Decision for Ameliorating Inventory with Time Dependent Demand and Partial Backlogging Rate

Inventory Model for Deteriorating Items with Seasonal Price and Time Dependent Ramp type Demand

In real life, deteriorating items are considered as the high profit products due to seasonal behaviour in demand. Another observation for the demand is the dependency over price as well as time. Many seasonal items have single opportunity of replenishment and the replenished inventory is used for successive number of demand seasons. In this paper, simultaneous procurement and pricing policies are considered for the seasonal deteriorating items with ramp type, price and time dependent demand rate. Time dependent partial backlogging is considered. Managerial insights are extracted from analytical results, numerical example and sensitivity analysis.

Inventory model for deteriorating items with price and time-dependent seasonal demand

Deteriorating items are considered as the main source of revenue. Many deteriorating items pusses the seasonal demand pattern. Generally, the sellers made a bulk purchase during the season and used the replenished inventory over a number of successive demand seasons. Thus, the inventory models for deteriorating item with a seasonal demand will provide valuable managerial insights. We developed a deterministic inventory model with price and time-dependent seasonal demand rate for items undergoing constant deterioration. Replenished inventory is used for more than one successive season and after depletion, at the end of the season order is placed for next replenishment. Shortages are considered only for one season. Time-dependent partial backlogging is considered for shortages. Analytical results for the optimality of the profit function with respect to decision variables in closed-form expressions are presented. Solution procedure and analytical results are verified with a numerical example.

Solution of a sustainable bi-objective book-producers' problem using statistical approach

This article leads to statistical approach on bi-objective economic production quantity (EPQ) inventory problem especially on two book producers' problem under unit selling price and production run time dependent demand rate. The concept of 'early product-early demand' and 'low price-high demand' policy has been employed for developing this bi-objective inventory problem. The discounts on marked unit selling price have been offered at the time of selling the books on spot for both the producers also. In this model we are optimising the objective functions of both producers for this it is considered as bi-objective model. However, behind any computational process there might have the effects of extraneous variables for which we have used correlation approach to solve the model. In addition, we use goal attainment (GA) approach to solve the bi-objective problems first and then generate dataset from sensitivity analysis of the model. Moreover, we compute the correlation coefficients matrix for both joint and independent relations of the objective functions. The decision is made on the basis of testing of hypothesis over the decision maker's (DM) zone of intelligence. Finally, the dot plots are made for justification of the model.

An EOQ inventory model for deteriorating items with time-dependent deterioration rate, ramp-type demand rate and shortages

This paper presents an economic order quantity (EOQ) model for deteriorating items having time proportional deterioration rate, time dependent ramp-type demand rate and shortages. Shortages are allowed to occur in the inventory system and completely backlogged. The ramp-type demand rate is deterministic and varies with time up to a certain point and then becomes constant. The three-parameter Weibull distribution rate indicates the change in deterioration rate with respect to time and takes into account of the items which are already deteriorated while receiving into an inventory system as well as items those might start deteriorating in future. To start with, the model is developed for shortages, but is also valid for the seasonal items and newly launched high tech products like computers, laptops, mobile phones and automobiles, etc. The purpose of this study is to develop an optimal policy, so that the average total cost is minimised by optimising the procurement time point. Furthermore, the solution procedure and the numerical example are provided to illustrate the proposed model. Finally, sensitivity analysis of the various parameters on optimal solution is carried out.

A fuzzy imperfect production and repair inventory model with time dependent demand, production and repair rates under inflationary conditions

This research work derives an integrated inventory model for imperfect production/remanufacturing process with time varying demand, production and repair rates under inflationary environment. This inventory model deals with the joint manufacturing and remanufacturing options. There is a collection process devoted to collect used items with the aim to remanufacture them. Both production and repair runs generate imperfect items. The repair process remanufactures used and imperfect items. Further, it is also considered that the remanufactured item that is classified as good has exactly same quality as that of new one. Demand rate is supposed as time dependent. The production rate is assumed to be demand dependent and therefore it is also time dependent. The repair rate is supposed to be a function of time. All system costs are contemplated in uncertain environment. Therefore, the costs are considered as fuzzy nature. Theoretical results are illustrated thru a numerical example. Finally, a sensitivity analysis is performed in order to know the impact of different parameters on the optimal policy.

An EOQ inventory model for deteriorating items with time-dependent deterioration rate, ramp type demand rate and shortages

This paper presents an economic order quantity (EOQ) model for deteriorating items having time proportional deterioration rate, time dependent ramp-type demand rate and shortages. Shortages are allowed to occur in the inventory system and completely backlogged. The ramp-type demand rate is deterministic and varies with time up to a certain point and then becomes constant. The three-parameter Weibull distribution rate indicates the change in deterioration rate with respect to time and takes into account of the items which are already deteriorated while receiving into an inventory system as well as items those might start deteriorating in future. To start with, the model is developed for shortages, but is also valid for the seasonal items and newly launched high tech products like computers, laptops, mobile phones and automobiles, etc. The purpose of this study is to develop an optimal policy, so that the average total cost is minimised by optimising the procurement time point. Furthermore, the solution procedure and the numerical example are provided to illustrate the proposed model. Finally, sensitivity analysis of the various parameters on optimal solution is carried out.