As the length of time between product renewals decreases, the enterprises that make innovative products face new challenges. The production cost structure of innovative products can be changed by collecting product returns, which can be economically valuable for enterprises. Enterprises face both production and demand randomness; hence, it is important to improve the traditional optimal production decision-making model that considers the randomness of demand only. This paper divides innovative products into structural innovation products and improved innovation products. The paper studies the optimal single-period production decision between reused parts and conventional new parts in complementary and substitute relationships. It further gives the analytical expressions for satisfying the optimal production and provides some numerical examples. The research results indicate that when producing innovative products, whether based on structural or improved innovation, with the variance of the quantity of the recycled parts increasing, the optimal purchase quantity of the conventional parts will increase but the expected profits for the innovative products will decrease. With integrated substitution and complementation based on improved innovation, enhancing the fluctuation in the number of recycled parts has a greater impact on the optimal purchase quantity of the substitute conventional parts than that of the complementary parts.
The product production process is key to reducing an enterprise’s inventory and to improving enterprise profitability, and there is much research on this issue. The accuracy of product output decisions has a significant impact on profitability. Some studies show that market demand uncertainty is a major factor in causing inaccurate output decisions in semiconductor manufacturing enterprises [
Traditionally, studies on enterprise management decisions focus on the cost optimization, enterprise production, inventory, and purchase decisions. As the product lifecycle becomes increasingly shorter, the amount of waste products generated has an increasingly serious impact on the environment. It is difficult for the innovative enterprise to balance enterprise development and environmental protection. The former strategy focuses on profit growth, while the latter focuses on sustainable development. Now, many enterprises must develop a product recycling strategy. Using recycled parts changes the enterprise cost structure. Such reuse can both meet environmental laws and other requirements and bring potential economic benefits. Generally, product output decisions do not account for the influence of recycled parts, an issue known as product reverse logistics [
There are many decision-making studies on traditional product production. However, few studies focus on decisions relating to innovative product production. Unlike traditional products, enterprises often use new parts to produce innovative products. Innovative products are generally characterized by a short lifecycle and by rapid replacement. This situation generates a lot of waste, which is costly for the enterprises. Previous enterprise innovation studies do not have a micro focus, but rather they consider aspects such as the innovation preprocess and the relationship between innovation and enterprise performance. Those studies that investigate the commercialization process of innovation focus on the macro characteristics only, such as the impact of new products on the economy. This paper explores uncertainty decisions based on the innovative product output using recycled parts from a relatively micro perspective. Hence, under the uncertainty condition of the recycling of remanufacturing components, this paper considers the coordination between remanufacturing and new components.
The model assumes the following. The production, sales, recycling, and other relevant functions are accomplished independently by one enterprise. The enterprise is a centralized decision-making system. The cost of the recycled parts is
The lifecycle of the innovative products is short. If such products have not sold out in a certain time period, then it is generally considered as an innovation failure. When the production exceeds the demand, the penalty value for each product is
The number of recycled parts, represented by random variable
The enterprises that make innovative products use two methods: structural innovation and improved innovation. The products based on structural innovation are new products that are regrouped from existing parts. The products based on improved innovation are new products that require both old parts and some new parts. These two methods show that there is a substitutability or a complementary relationship between recycled parts and conventional new parts when the enterprises produce the innovative products. Under a substitutability condition, the innovative products are produced using recycled parts or using new parts purchased conventionally. Under a complementary condition, the innovative products are produced using both recycled parts and new parts purchased conventionally. Both are indispensable. This paper focuses on making decisions to optimize the profits of the enterprises that produce innovative products using these two methods.
Figure
Relationship between demand
Here, according to the division shown in Figure
Here, actual demand
Relationship between demand
Here, according to the division in Figure
Here, actual demand
Relationship between demand
Here, according to the division in Figure
The profit function can be expressed as
Thus, the expected profit
In this formula,
So, we can get
To find optimal decision
In this formula,
Obviously, expected profit
Optimal purchase quantity
The profit function can be expressed as
Thus, expected profit
So, we can get
To find optimal decision
After the calculation, the root of
Accordingly, if
The optimal purchase quantity
The profit function can be expressed as
Thus, the expected profit
So, we can get
To find optimal decisions
If
It can be verified that
So,
Optimal purchase quantities
The influence that part recovery uncertainty has on the optimal solution can be studied by setting the values of some parameters. According to [
Optimal strategy and profit by recovered quantity: part substitution.
Variance | The quantity of substitution parts |
Profit |
---|---|---|
6 | 40.44 | 656.34 |
8 | 40.46 | 655.24 |
10 | 40.48 | 654.19 |
12 | 40.50 | 653.18 |
14 | 40.52 | 652.20 |
16 | 40.54 | 651.26 |
18 | 40.55 | 650.35 |
20 | 40.57 | 649.46 |
From Table
Producing innovative products relies entirely on recycled parts. However, in the actual production, the enterprises keep the production scale of the recycled parts close to the demand scale. Here, this paper sets
Optimal strategy and profit by recovered quantity: part complementarity.
Variance |
|
|
|
|||
---|---|---|---|---|---|---|
Quantity demanded |
Expected profits | Quantity demanded |
Expected profits | Quantity demanded |
Expected profits | |
6 | 100.00 | 239.69 | 104.00 | 280.23 | 113.50 | 215.69 |
8 | 100.00 | 239.58 | 105.46 | 273.27 | 116.00 | 205.58 |
10 | 100.00 | 239.45 | 107.00 | 266.07 | 118.50 | 195.45 |
12 | 100.00 | 239.30 | 109.00 | 257.05 | 118.50 | 195.30 |
14 | 100.00 | 239.14 | 110.00 | 252.07 | 121.00 | 185.14 |
16 | 102.00 | 230.96 | 112.00 | 243.12 | 122.25 | 179.96 |
18 | 103.00 | 226.76 | 113.00 | 238.21 | 128.50 | 154.76 |
20 | 104.00 | 222.56 | 114.00 | 233.32 | 128.50 | 154.56 |
Table
This means that if the expected supply quantity is a certain value, with the supply risk increasing, then the effective output will decrease and will need to be compensated by increasing the purchasing quantity. The profits of the innovation products will decrease as the uncertainty increases. Additionally, if the supply risk of the recycled parts is certain, when the expected supply quantity increases, the optimal purchase quantity of the complementary conventional parts will increase. When the expected supply quantity of the recycled parts is close to the expected demand quantity, the expected profits of the innovative products can reach the maximum.
Parts can be obtained by substitution or by complementarity when producing products based on improved innovation. If
Optimal strategy and profit by recovered quantity: integrated substitution and complementarity.
Variance | Quantity of substitute part |
Quantity of complementary part |
Profit |
---|---|---|---|
6 | 38.41 | 87.66 | 297.32 |
8 | 38.61 | 87.71 | 296.11 |
10 | 38.79 | 87.74 | 295.03 |
12 | 38.95 | 87.77 | 294.04 |
14 | 39.09 | 87.80 | 293.13 |
16 | 39.23 | 87.82 | 292.28 |
18 | 39.36 | 87.84 | 291.48 |
20 | 39.48 | 87.86 | 290.72 |
From Table
This paper studies the optimal output decision for innovative products when the quantity of the recycled parts is uncertain. The model aims to maximize the expected profits for innovative products, accounting for both recycled parts and conventional parts. The model analyzes the optimal decision strategy when the recycled parts and the conventional parts are in a substitute relationship and a complementary relationship, namely, under the circumstances of structural innovation and improved innovation. This paper gives the analytic expressions to meet the optimal production quantity and analyzes the relationship between the optimal production quantity and various parameters. When an enterprise produces innovative products—whether based on structural innovation or improved innovation—as the variance of the quantity of the recycled parts increases, the optimal purchase quantity of the conventional parts will increase but the expected profits of the innovative products will decrease. For integrated substitution and complementarity circumstances in cases of improved innovation, fluctuations in the number of recycled parts have a greater impact on the optimal purchase quantity of the substitute conventional parts than that of the complementary parts. In reality, using recycled parts will effectively reduce costs when enterprises produce innovative products. However, fluctuations in the number of available recycled parts will have an impact on the procurement of other parts. When enterprises make decisions about producing innovative products, they should consider the influence of uncertainties in the supply of recycled parts on the expected profits of the innovative products. This study has some shortcomings. The study only discusses the optimal decision in a single period. A multiperiod analysis would more accurately reflect the reality and should be the subject of a further study.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China (71403066); the State Key Program of National Social Science of China (14AGL004); the Fund of Ministry of Education of China (20122304120021); China Postdoctoral Science Foundation (2013T60351); the Special Foundation of Central Universities Basic Research Fee (HEUCF140907); Heilongjiang Province Postdoctoral Start Fund (LBH-Q13050); and the Scientific and Technological Projects of Heilongjiang Province (GZ11D203).