Optimal acquisition and inventory control can often make the difference between successful and unsuccessful remanufacturing. However, there is a greater degree of uncertainty and complexity in a remanufacturing system, which leads to a critical need for planning and control models designed to deal with this added uncertainty and complexity. In this paper, a method for optimal acquisition and inventory control of a remanufacturing system is presented. The method considers three inventories, one for returned item and the other for serviceable and recoverable items. Taking the holding cost for returns, recoverable and remanufactured products, remanufacturing cost, disposal cost, and the loss caused by backlog into account, the optimal inventory control model is established to minimize the total costs. Finally, a numerical example is provided to illustrate the proposed methods.
With the increasing awareness of environmental protection worldwide, the green trend of conserving the Earth’s resources and protecting the environment is overwhelming. The conversation of resources is being considered from many aspects of product development and use, such as redesign, reuse, recycle, and remanufacture of products and components. Remanufacturing is a powerful product recovery option which generates products as good as new ones from old discarded ones [
Various strategic and operational aspects of used products remanufacturing have been investigated in the last decades. However, for remanufacturing, the main problem is the collection of used products with good quality at the right time and at the right inventory level [
With the used product collection available, another important decision in remanufacturing is how many quantities of the available cores should be determined. Jayaraman [
Used product acquisition and quantity planning have been widely recognized as an efficient tool of remanufacturing [
Motivated by the foregoing discussion, this paper presents an optimal method for used product acquisition and inventory control. The state variable is defined by the recoverable inventory and the serviceable inventory of remanufactured products, the decision variable is defined by the number of returned products per stage, and the Bellman equation is constructed by minimizing the expected cost during the finite stages. And the optimal acquisition and inventory control levels of the remanufacturing system can be obtained with the policy iteration method. Following the presentation of the proposed method, the method is demonstrated via a numerical example.
In this section, the framework, assumptions, and the proposed model for used products acquisition and inventory management are presented.
A remanufacturing system begins with the collection of the used product or parts, also named as core, followed by its remanufacturing and delivery of the remanufactured product to the client [
Inventory control framework of a remanufacturing system.
There are several unique characteristics which predominantly and naturally occur in the remanufacturing environment that further complicate the remanufacturing management [
Mindful that these problems add complexity to this field of research, the objective of this paper is to determine the optimal acquisition and inventory control to guarantee a required service level and to minimize the total costs.
Several operations, such as collection and inspection of used products, remanufacturing of as-good-as-new products, and disposal of used products unsuitable for the remanufacturing process, are considered within the system. However, a number of assumptions are made throughout this analysis in order to simplify the system and facilitate the modeling process by helping to focus on the most important factors. The assumptions are summarized as follows: Market demands of remanufactured products are stochastic variables. Taking into account that used products should be tested after collection and then be remanufactured, capacity of collection and inspection activities is considered to be infinite. Remanufacturing cost is a linear function of the state of returned products, and remanufacturing quantity is a linear function of batch quantity of return. The proportion of returned products which are disposed is stochastic, and the impact of used products disposal on remanufacturing production planning is not considered. Remanufacturing activity starts and ends in the same stage and ignores the uncertainties of production lead time.
As described above, the : the total stages of the production plan,
The state variable is defined by the recoverable inventory and the serviceable inventory of remanufactured products
The state transition equation is
As the remanufacturing processing quantity is a linear function of batch quantity of retur,
The total cost of stage
subject to
In this model, the state variable
With the
For
Therefore, the optimal acquisition quantity
The objective is to determine the optimal inventory control
According to the theory of dynamic programming, the Bellman equation of the objective function, which can represent the recursive relation, is shown as follows:
So, the above discussed model can be formulated as follows:
This model formulation can be divided into two phases for production planning. Firstly, the optimal acquisition quantity may be determined, and then the optimal inventory control model needs to be established to minimize the total costs.
The proposed model is a dynamic programming model, which is difficult to solve, especially that the state at next period is not completely determined by the state and policy decision at current period (i.e., need to obtain the optimal decisions per period). We present a policy iteration approach to obtain near optimal solution for the problem. The approach starts with an arbitrary policy (an approximation to the optimal policy works best) and carries out the following steps: firstly,
It is assumed that the total stages number
Parameter settings of constants for the model.
|
|
|
|
|
|
---|---|---|---|---|---|
3 | 1.5 | 1.5 | 11 | 0.5 | 3 |
Parameter settings of variables for the model.
|
|
| |
---|---|---|---|
|
8 | 6 | 0.5 |
|
10 | 8 | 0.5 |
From the history data, the probability distribution of demands can be forecast for each stage. So, we can obtain the expectation of demand
The distribution of the demands of remanufactured products in stage 1.
Demands of remanufactured |
1 | 2 | 3 |
---|---|---|---|
Distribution |
0.4 | 0.4 | 0.2 |
The distribution of the demands of remanufactured products in stage 2.
Demands of remanufactured |
1 | 2 | 3 |
---|---|---|---|
Distribution |
0.1 | 0.6 | 0.3 |
According to Tables
In the second stage, we can list all the probable inventory states, and according to the optimal inventory control model established in Section
The probable state and its expected cost of stage 2.
State ( |
Disposal quantity |
Expected cost of stage 2 |
---|---|---|
(0, 0) | 1.65 | 32.406 |
(0, 1) | 1.65 | 27.030 |
(0, 2) | 1.65 | 28.531 |
(1, 0) | 0.65 | 35.406 |
(1, 1) | 0.65 | 29.531 |
(1, 2) | 0.65 | 31.031 |
The probable state and its expected cost of stage 1.
State ( |
Disposal quantity |
Expected cost of stage 1 |
Accumulative total expected cost |
---|---|---|---|
(0, 0) | 1.65 | 28.025 | 55.055 |
In the above analysis, the parameters are modified by the data from real remanufacturing works of used machine tools. The uniform distribution of the state variable
The success of a remanufacturing business is very dependent on the acquisition and inventory management in order to satisfy the demand for remanufactured products. In this paper, optimal acquisition and inventory control method is proposed for a remanufacturing system with uncertain demand. The state variable is defined by the recoverable inventory and the serviceable inventory of remanufactured products, and the objective is to determine the quantities that have to be remanufactured in these periods in order to minimize the total cost. This method can be used for remanufacturing enterprise to make the production plan in the uncertain environment.
With the development of remanufacturing, the returns amount will be large and the state of returned products will be more and more unpredictable. Thus, this model has much to be desired; in a further research, the sensibility of the optimal production-inventory policy on changes of quantity of return products should be examined. The interaction between the state of recycling products and the cost of remanufacturing processing should also be given deeper consideration.
The work described in this paper was supported by the National Natural Science Foundation of China (51205295) and the National Science and Technology Supporting Program (no. 2012BAF02B01). These financial contributions are gratefully acknowledged. The authors also thank the anonymous reviewers whose reviews helped in improving the paper.