Hui-Ling Yang

Two-warehouse inventory models for deteriorating items with shortages under inflation

Abstract In this paper, the two-warehouse inventory problem for deteriorating items with constant demand rate and shortages under inflation is considered. In contrast to the traditional deterministic two-warehouse inventory model with shortages at the end of each replenishment cycle, an alternative model in which each cycle begins with shortages and ends without shortages is proposed here. The optimal solution not only exists but also is unique. Comparing these two two-warehouse inventory models, the study shows that the proposed model is less expensive to operate than the traditional one in the case of the inflation rate is greater than zero. Hence, under the consideration of inflationary effect, the proposed model is less expensive. Finally, some numerical examples for illustration are provided.

Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand

In this paper, we extend the inventory lot-size models to allow for inflation and fluctuating demand (which is more general than constant, increasing, decreasing, and log-concave demand patterns). We prove that the optimal replenishment schedule not only exists but is also unique. Furthermore, we show that the total cost associated with the inventory system is a convex function of the number of replenishments. Hence, the search for the optimal number of replenishments is simplified to finding a local minimum. Finally, several numerical examples are provided to illustrate the results.

Deterministic lot-size inventory models with shortages and deterioration for fluctuating demand

We establish various inventory replenishment policies. We then analytically identify the best alternative among them based on the minimum total relevant costs. Finally, we prove that the relevant cost is convex with the number of replenishments. Consequently, the search for the optimal replenishment number is reduced to finding a local minimum.

Deterministic economic order quantity models with partial backlogging when demand and cost are fluctuating with time

In todays time-based competition, the unit cost of a high-tech product declines significantly over its short life cycle while its demand increases. In this paper, we extend the classical economic order quantity model to allow for not only time-varying demand but also fluctuating unit cost. In addition, we also allow for shortages and partial backlogging. We then prove that the optimal replenishment schedule not only exists but also is unique. In addition, we also show that the total cost is a convex function of the number of replenishments, which simplifies the search for the optimal number of replenishments to find a local minimum. Moreover, we further simplify the search process by providing an intuitively good starting search point.

An optimal recursive method for various inventory replenishment models with increasing demand and shortages

We establish various inventory replenishment policies to solve the problem of determining the timing and number of replenishments. We then analytically compare various models, and identify the best alternative among them based on minimizing total relevant costs. Furthermore, we propose a simple and computationally efficient optimal method in a recursive fashion, and provide two examples for illustration.

On an EOQ model for deteriorating items with time-varying demand and partial backlogging

For seasonal products, fashionable commodities and high-tech products with a short product life cycle, the willingness of a customer to wait for backlogging during a shortage period is diminishing with the length of waiting time. Recently, Chang and Dye developed an inventory model in which the backlogging rate declines as the waiting time increases. In this paper, we complement the shortcoming of their model by adding the non-constant purchase cost into the model. In addition, we show that the total cost is a convex function of the number of replenishments. We further simplify the search process by providing an intuitively good starting value, which reduces the computational complexity significantly. Finally, we characterize the influences of the demand patterns over the replenishment cycles and others.

Inventory lot‐size policies for the bass diffusion demand models of new durable products

Abstract The Bass model and its revised forms have been used for forecasting dynamic demand growth in retail service, industrial technology, consumer durable goods, and others. However, the inventory models currently available do not recognize the Bass diffusion demand pattern. In this paper, we first establish the necessary and sufficient conditions to solve the problem in determining the timing and number of replenishments for the Bass model. We then develop several fundamental theoretical results. Furthermore, a one‐dimensional iterative method is proposed to find the optimal replenishment schedule. Finally, we provide an intuitively accurate estimate for the optimal number of replenishments, which significantly reduces computational complexity in finding the optimal replenishment number.

A forward recursive algorithm for inventory lot-size models with power-form demand and shortages

Abstract Barbosa and Friedman (L.C. Barbosa, M. Friedman, Management Science 24 (8) (1978) 819) establish an optimal replenishment policy for power-form demand rate. In this paper, we extend their inventory lot-size model to allow for shortages. The goal is to find the optimal number and time of replenishments in order to keep the total relevant cost as low as possible during a finite planning horizon. We develop a simple forward recursive algorithm to determine the optimal replenishment timing. Furthermore, we propose an intuitively accurate estimate for the optimal number of replenishments, which significantly reduces computational complexity in finding the optimal replenishment number. A numerical example is provided to illustrate the solution procedure.

A backward recursive algorithm for inventory lot-size models with power-form demand and shortages

In 1978, Barbosa and Friedman established a ‘general root law’ for power-form demand rate. Shortages are prohibited. However, in reality, shortages may occur and the planning time horizon is usually finite as the product life cycle is short. Therefore, the author here extends their inventory lot-size model to allow for shortages during a finite planning time horizon and propose an alternative algorithm in a backward manner to determine the optimal replenishment timing without using iterative search schemes. The study not only shows that the total relevant cost is a strictly convex function of the replenishment number, but also provides the condition for determining the optimal replenishment number. Finally, a numerical example is given for illustration.

Capacitated inventory replenishment policy with linear trend demand

Abstract We consider a capacitated inventory system with a linear increasing trend in demand. Backlogs and shortages are not allowed. Replenishments are assumed to be instantaneous and the planning horizon is finite. The objective is to find the optimal replenishments number and time scheduling in order to keep the total relevant cost as low as possible. Based on some fundamental theoretical results, we propose a method to solve the problem and provide a numerical example for illustration.