Time-dependent Partial Backlogging Research Articles

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.

Optimal replenishment policies of an EOQ model for non-instantaneous Weibull deteriorating items with ramp-type of demand under shortages

This paper discusses the effects of ramp-type of demand on an EOQ model for non-instantaneous Weibull deteriorating items under time-dependent partial backlogging. Here, we consider a retailer who purchases and sells a single product over an infinite time horizon faces a ramp-type of demand. Shortages are allowed and partially backlogged. The time to the deterioration of the item is distributed as Weibull. Total cost and the optimum number of replenishments are taken here as decision variables. The objective is to obtain the optimal replenishment policies that minimise the total cost. For demonstrating the model numerical samples are explained in the following sections.

An Order-Level Inventory Model for a Deteriorating Item with Time-Quadratic Demand and Time-Dependent Partial Backlogging with Shortages in All Cycles

SYNOPTIC ABSTRACTThe purpose of this work is to study an inventory model for a deteriorating item considering time-quadratic demand and time-dependent partial backlogging, which depends on the length of the waiting time for the next replenishment over a finite time horizon and variable replenishment cycle. The model is solved analytically to obtain the optimal solution of the problem. The sufficient condition of the optimal solution is also studied. It is then illustrated with the help of numerical examples.

A comparative study on two-warehouse inventory model for deteriorating items with shortages

This paper deals with infinite time horizon economic order quantity two-warehouse inventory model for deteriorating items with shortages. Shortages are allowed and the unsatisfied demand is partially backlogged. The backlogging rate is a fraction of the on-hand inventory. We consider demand as a function of time. The objective of this model is to minimise the total cost of the retailer. Numerical examples are presented to determine the developed model and the solution procedure. Time dependent partial backlogging model is compared with complete backlogging model.

An optimal inventory replenishment policy for a deteriorating item with time-quadratic demand and time-dependent partial backlogging with shortages in all cycles

The paper deals with an optimal inventory replenishment policy for a deteriorating item considering time-quadratic demand and time-dependent partial backlogging which depends on the length of the waiting time for the next replenishment over a finite time horizon and variable replenishment cycle. The model is solved analytically to obtain the optimal solution of the problem. It is then illustrated with the help of numerical examples.

A Production Inventory Model with Flexibility and Reliability under mλ-measure

In this paper, a production inventory model is developed with flexibility and reliability consideration of production process under mλ-measure which is linear combination of Possibility measure and Necessity measure. The model has incorporated selling price dependent demand, an imprecise cost parameters and time dependent partial backlogging. The critical values of fuzzy profit function with respect to mλ–measure are introduced and are employed to construct the fuzzy chance-constrained programming model. The objective function is optimized using a genetic algorithm and confidence limits of fuzzy profit function are obtained for numerical illustration with the sensitivity analysis

An EOQ model for a deteriorating item with time-varying demand and time-dependent partial backlogging

This paper describes an EOQ model for a deteriorating item considering time-dependent demand and time-dependent partial backlogging, which depends on the length of the waiting time for the next replenishment over a finite time horizon and variable replenishment cycle. Equal replenishment cycle length in case of fixed planning horizon is relaxed in this model. Also, backlogging rate is taken to be dependent on waiting time of the customers, instead of waiting line of the customers. This seems to be better representation since impatient customers naturally want to know how long time they have to wait for receiving their goods, not how many customers are ahead. The model is solved analytically to obtain the optimal solution of the problem for a general time-dependent demand pattern. It is then illustrated with the help of numerical examples.

A two warehouse inventory model for deteriorating items with time dependent partial backlogging and variable demand dependent on marketing strategy and time

This paper deals with a deterministic inventory model for single deteriorating items with two separate storage facilities (own and rented warehouses) due to limited capacity of the existing storage i.e., own warehouse. The demand rate of this item is dependent on continuous time, selling price of the item and the frequency of advertisement in the popular electronic and print media and also through the sales representatives. The replenishment rate is infinite. The stock is transferred from the rented warehouse to own warehouse in continuous release pattern and the associated transportation cost is taken into account. Shortages, if any, are allowed and partially backlogged with a rate dependent on the duration of waiting time up to the arrival of next lot. The corresponding problem has been formulated as a constrained non-linear mixed integer problem. Finally, the model has been illustrated with a numerical example and to study the effect of changes of different system parameters on initial stock level, maximum shortage level, cycle length, frequency of advertisement along with the maximum profit of the system, sensitivity analyses have been carried out by changing one parameter at a time and keeping the other parameters at their original values.

Modeling customer impatience in a newsboy problem with time-sensitive shortages

Abstract Customers across all stages of the supply chain often respond negatively to inventory shortages. One approach to modeling customer responses to shortages in the inventory control literature is time-dependent partial backlogging. Partial backlogging refers to the case in which a customer will backorder shortages with some probability, or will otherwise solicit the supplier’s competitors to fulfill outstanding shortages. If the backorder rate (i.e., the probability that a customer elects to backorder shortages) is assumed to be dependent on the supplier’s backorder replenishment lead-time, then shortages are said to be represented as time-dependent partial backlogging. This paper explores various backorder rate functions in a single period stochastic inventory problem in an effort to characterize a diversity of customer responses to shortages. We use concepts from utility theory to formally classify customers in terms of their willingness to wait for the supplier to replenish shortages. Under mild assumptions, we verify the existence of a unique optimal solution that corresponds to each customer type. Sensitivity analysis experiments are conducted in order to compare the optimal actions associated with each customer type under a variety of conditions. Additionally, we introduce the notion of expected value of customer patience information (EVCPI), and then conduct additional sensitivity analyses to determine the most and least opportune conditions for distinguishing between customer behaviors.

On “An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging” by Dye and Ouyang

In 2005, Dye and Ouyang proposed an EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging, and then established the unique optimal solution to the problem when building up inventory is not profitable. However, they did not provide the optimal solution to the problem when building up inventory is profitable. In this note, we establish an appropriate model in which building up inventory is profitable, and then provide an algorithm to find the optimal solution to the problem. A numerical example is used to illustrate the proposed model.

An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging

In the present paper, we extend Padmanabhan and Vrat's model by proposing a time-proportional backlogging rate to make the theory more applicable in practice. The existence and uniqueness of the solutions of the relevant systems are examined. Subsequently, a numerical example is presented to illustrate the application of developed model.

An inventory model with deteriorating items, quantity discount, pricing and time-dependent partial backlogging

Wee (International Journal of Production Economics 59 (1999) 511), in his interesting paper presented a deterministic inventory model with the following characteristics. Quantity discount schemes for the unit cost, partial backlogging at a fixed rate, deterioration of stock in time and demand rate being a linear function of the selling price. In this article we generalize the work of Wee (1999). More specifically, we consider a model where the demand rate is a convex decreasing function of the selling price and the backlogging rate is a time-dependent function, which ensures that the rate of backlogged demand increases as the waiting time to the following replenishment point decreases.

Optimal stopping and restarting production times for an EOQ model with deteriorating items and time-dependent partial backlogging

Yan and Cheng (J. Operational Res. Soc. 49 (1998), 1288–1295) presented a general production–inventory model with production rate, product demand rate and deterioration rate, all considered as functions of the time. Their model allows for shortages and partial backlogging of the unsatisfied demand at a constant rate. In this paper, we extend the results of Yan and Cheng to cover the case where the backlogging rate is a time-dependent function and we propose an algorithm for the solution of this problem. We also propose some conditions which we believe to be necessary for the validity for some of Yan's and Cheng's statements. The paper closes with numerical examples which cover each one of the cases considered in the paper.