Oil production task allocation (OPTA) is affected by various factors, and each one has a different impact on oil production. Therefore, the fair distribution of production task to each production branch is really a hard work for an oil company, so a fair allocation based on contribution rate (ABCR) has been proposed to solve this problem in this paper. The algorithm of ABCR, unlike other existing algorithms, takes into account the differences of members’ contribution (DMC), which can be expressed by member contribution rate (MCR) based on the certainty and uncertainty factors. Two steps are implemented to gain the differences of members’ contribution. First, we use Principal Component Analysis (PCA) to reduce factors for certain factor and construct a new factor with Analytic Hierarchy Process (AHP) for uncertain factor. Then, the MCR is evaluated by AHP. Based on member contribution rate, member goal, and alliance target, a fair allocation can be obtained by ABCR. Finally, we propose an evaluation criterion for allocation. Case study shows that the resource allocation results of ABCR not only are more reasonable than those of the other methods but also can prevent unfair allocation and enhance the production environment, thereby improving the enthusiasm for production.
Traditionally, alliance activities can play a constructive role to each member and maximize the benefits of alliance. As benefits increase, some questions follow. For example, the fair allocation of benefits will become more difficult. No wondering that each member will try to grab as more benefits as it can. Therefore, it is a great challenge to find an allocation algorithm for members in alliance benefits and ensure that each member is profitable. Fair allocation algorithm seems to be a satisfactory solution. Fairness has been taken into account as one of the important additional criteria in many application domains, such as resource allocation [
In traditional fair allocation algorithms, member goal and alliance target are commonly the two effect factors. However, recently researchers have found that the two effect factors are not the only effect factors in a fair task allocation [
Some simple solutions of allocation usually allocate the benefit by proportional allocation. The proportional allocation is generally the most intuitive procedure. In some cases, the accuracy of the assignment results is not very strict; this method is still often used in actual programs. However, this issue of fair allocation is not comprehensive.
Shapley value [
Many challenges exist in our studying of oil production task allocation algorithm.
(1) The effect factors of the next year’s oil production task have significant differences from those of the last year. The change of each factor is unpredictable. And these factors can be divided into certain factors and uncertain factors.
(2) To the best of our knowledge, the existing fair allocation algorithm cannot be directly applied to address our problem because the existing allocations algorithms ignore the dummy factors unfair allocation in alliance activities [
(3) It is very important to achieve fairness allocation in the oil production task collocation, but the process of distribution is difficult. To realize fairness allocation, member contribution rate (MCR) is considered in our algorithm.
(4) The MCR can be generated from some certain factors and some uncertain factors of the oil company. This poses a difficulty because obtaining the information is expensive. Therefore, an effective circumvent way to solve this difficulty is to create some combination factors, which include some selected certain factors and a constructed uncertain factor, to evaluate the member contribution rate in task allocation.
In our oil production task allocation program, we assume that we know the previous production task of each branch and decide to cooperate to produce in next year. According to the production contribution rates of oilfield branches, respective production capacity, and the production tasks of the oilfield branch, to allocate the oil production task fairly to each oilfield branch is possible.
To solve this problem, we propose an allocation algorithm based on member contribution rate, which can rationally allocate tasks or benefits of members in alliance. This strategy not only gave an evaluation method for the differences of members’ contribution (DMC) in alliance activities, but also designed an allocation algorithm called fair allocation based on contribution rate (ABCR). We express the DMC by member contribution rate (MCR), which is used to express the members’ difference in alliance based on the certainty and uncertainty factors of the construction. There are two steps in implementing the differences of members’ contribution. First, we use Principal Component Analysis (PCA) [
The contribution of this paper can be summarized as below.
(1) A fair allocation algorithm based on member contribute rate was proposed in this paper. This algorithm not only can achieve fairness in the oil production task allocation easily, but also can be applied to other similar projects.
(2) Member contribution rate, which expresses the contribution rate of each member in alliance activities, is defined. Unlike other approaches, this definition quantifies each member’s contribution in affiliate activity.
(3) A fairness criterion was designed firstly. It can solve the problem that it is not clear how to evaluate and compare these allocation algorithms implemented.
The rest of this paper is organized as follows. We proposed an improved fair allocation based on member’s contribution rate in Section
For
For example, in oil production task allocation, we usually know the production capacity of each oilfield branch, as well as its technical and management information in task allocation. That is to say, there is no need or it is impossible to know the production capacities of the different combinations of each oilfield branch. In other words, it is not necessary to consider the subcoalition; we only consider the “all oilfield branches coalition” in our task allocation. Thus, to achieve the fair allocation of oil production tasks, we made the following assumptions.
Our task allocation argues that the contribution of different members in the alliance activities is inconsistent.
Our task allocation ignores the role of subcoalitions of
Member contribution rate (MCR) that can be calculated by some certainty and uncertainty effect factors of oil production is used to determine the differences of member contribution (DMC). In the alliance activity there are two steps to obtain the MCR. First, we use PCA [
The algorithm of ABCR is planned to be composed of three parts: member contribution rate, member goal, and alliance target. The framework of ABCR was designed as in Figure
Framework of ABCR.
After data collection and preparation, the next step is to determine the allocation factors, which includes three parts: member goal, alliance target, and member contribution rate. NBS and PA mainly rely on member goal and alliance target, while in ABCR member contribution rate is also an indispensable condition.
In step 3, while member goal (
Utilizing the idea of Nash bargaining solution, assuming that cooperative principle is the prerequisite and the next cooperation allocation results can be decided by previous results, and taking into account the difference of member contribution rate in alliance, a fair allocation model can be extended as
To obtain the solution of model (
(1) If
(2) Model (
(3) Usually, to make the solution convincing, it is needed to consider the role of subcoalitions
(4) Model (
(5) If the expected allocation of each member is less than that of actual allocation, model (
Before implementing a fair allocation by ABCR, certain influencing factors and uncertain influencing factors are all collected firstly. Then the values of certain factors should be normalized and the uncertain factors should be abstracted as a new characteristic factor and quantified.
Alliance activities are often very complex, as well as the characteristics of members. Factors that affect the contribution of each member are divided into certain factors and uncertain factors.
On the one hand, only a few certain factors play key roles in alliance activities. In order to select the key factors from original certain factors, factors reduction is a necessary process. On the other hand, some uncertain factors may play an important role, too. Therefore, factors construction is also a very important process, which generates one or more key factors from all original uncertain factors. It can be implemented by AHP.
After factor reduction and factor construction, the values of MCR can be obtained by combining the key certain factors and the constructed factors.
The evaluation of MCR is implemented by a quantitative method of DMC based on comparative advantage. The calculation process of MCR can be summed up as follows.
(1) Model the problem as a hierarchy in alliance activities.
(2) Evaluate the hierarchy, which is usually used to express the effect of this hierarchy.
(3) Establish priorities by determining the weight of each member in alliance.
Assuming that there are
If the number of data and the task are negatively correlated, this factor becomes negative and is defined as
It is easy to see that
For the negative factor, the eigenvector of the
(4) Contribution Rate Calculation
The contribution rate is calculated as
According to MCR, the member goal, and the alliance target, the solution of allocation based on MCR is obtained by model (
Model the problem as a hierarchy.
Calculate the comprehensive weight of each member’s contribution to alliance.
Determine the alliance target and the threat points of members.
Obtain the fair allocation solution by ABCR.
It is relatively easy to present a variety of possible “fair” allocations, but what is really different is to accurately assess these allocations. In order to illustrate the rationality of our fair allocation algorithm, we have designed the following assessment indicators. It is worth noting that there are no united assessment criteria for a fair allocation algorithm in previous studies.
Given some value
We call this relative ratio the relative growth rate (RGR).
Given some value
We call this difference the fairness degree (FD) of the
If we have a data set containing the values
Then,
Suppose an oil company has three oilfield branches, the oil production in last year was 1.4012, 2.2618, and 1.6535 million tons, and the oil production task of this oil company in next year is 5.8482 million tons. Some certain effect factors of each oilfield branch can be obtained, such as the production capacity in last year, the number of active wells, the production of old wells, the production cost, the water content, natural decline rate, comprehensive decline rate, and the remaining recoverable reserves (the details are omitted for reasons of confidentiality).
In addition, some uncertain effect factors can be obtained and the details are omitted for the same reasons. There are some main uncertain effect factors, such as the degree of drilling equipment, the level of production management, the geographical location, and technical staff level. The production capacity of each oilfield branch may be quite different. Hence, it is very important to allocate the oil production task to each oilfield branch fairly.
To solve this problem, three steps are taken in ABCR.
Production capacity and natural decline rate are two main certain factors that are selected from certain effect factors by PAC. Uncertain factors include the location of drilling platform, the equipment level, the technical staff level, and the production management level. The key uncertain factors are extracted by AHP (Figure
Factor construction and factor reduction.
With the main factors, natural production, natural decline rate, and RW of uncertainty factors, the MCR of each branch can be determined by AHP.
Firstly, evaluate the priorities of the criterion layer to the target layer.
After determining the relative importance of the three factors shown in Figure
Structure for member weight evaluation.
In this situation, the natural rate of decline and the actual workload are more important. The actual workload refers to the distribution of reservoirs, the geographical location of each branch, the oil company’s personnel structure, and other comprehensive factors. The comparison matrix can be calculated as follows:
To determine the weight of the distribution of natural production in alliance, the corresponding normalized feature vector is
The consistency ratio of this matrix is 0.0171. It means that this matrix can pass the consistency test and is properly to be used for calculation.
Secondly, evaluate the priorities of the project layer to the criterion layer.
According to the actual data, we can compare the relative advantages, but we need to pay attention to the interpretation of the data. In distribution of the old oil well production, the natural production in last year reflects the production capacity of the oil factory. Therefore, the larger the natural production, the larger the production capacity of the oil factory. The natural decline rate reflects the enterprise resources consumption rate, so the lower the natural decline rate, the lower the enterprise resources consumption rate. And the actual workload reflects the benefit of the enterprise, so the smaller the actual workload, the smaller the benefit of the enterprise.
The paired comparison matrixes about three influencing factors in these oil production branch factories are constructed as follows:
① The paired comparison matrixes of three branches to the natural production can be calculated as follows:
② The paired comparison matrixes of three branches to the natural decline rate can be calculated as follows:
③ The paired comparison matrixes of three branches to the actual workload can be calculated as follows:
Thirdly, the calculation of MCR.
The MCRs of three oil branches are calculated as follows:
Table
Member contribution rate calculation.
No. branch | Selected factors | Constructed factors | Member contribution rate | |||
---|---|---|---|---|---|---|
Natural production of old well (unit: million tons) | Natural decline rate | Actual workload | ||||
Value | Proportion | Value | Proportion | |||
1 | 1.4012 | 0.2636 | 2.15% | 200 | 0.3333 | 0.2626 |
2 | 2.2618 | 0.4254 |
|
250 | 0.4167 | 0.5669 |
3 | 1.6535 | 0.3110 |
|
150 | 0.2500 | 0.1676 |
After obtaining these data, the allocations of ABCR, NBS, and PA were obtained, respectively. The allocation values and their RGR are shown together in Table
NPOW allocations of PA, NBS, and ABCR.
No. | NPOW of last year | Results of fair allocation (B=5.8482, unit: million tons) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
PA | NBS | ABCR | ||||||||
Value ( |
RGR ( |
|
Value ( |
RGR ( |
|
Value ( |
RGR ( |
| ||
1 | 1.4012 | 1.5413 | 0.1 | 0.162 | 1.9434 | 0.387 | 0.1244 | 1.5961 | 0.1391 | 0.1235 |
2 | 2.2618 | 2.4880 | 0.1 | 0.4669 | 2.3210 |
|
0.5407 | 2.3778 | 0.0513 |
|
3 | 1.6535 | 1.8189 | 0.0987 | 0.069 | 1.5838 |
|
0.1243 | 1.8743 | 0.1335 | 0.034 |
It can be seen from Table
Furthermore, comparing the results of these three different algorithms, it can be found that the best result can be obtained by multiple factors allocation. The results of three methods are compared in Table
The characteristics of fair allocations algorithm.
Characteristics | Level | |
---|---|---|
PA | (1) Member goal and alliance target are needed |
A |
|
||
NBS | (1) Member goal and alliance target are needed |
A |
|
||
ABCR | (1) Beside member goal and alliance target, member weights are also needed |
A+ |
The main advantages of ABCR are summed up as follows:
(1) Avoiding irrational proportional allocation. For example, suppose oil company sets a course for 10% growth compared with the production in last year. The natural decline rate of the No. 3 branch is the highest. The value is 16.01% (boldfaced in Table
(2) When compared with NBS, it is easier for ABCR to release potential of production capacity in strong branches. In fact, the actual production capacity of the No. 2 branch is 16.18% higher than that of the No. 1 branch. However, according to the allocation result of Nash bargain solution, the production task of the No. 2 branch is only 6.46% higher than that of No. 1 branch.
(3) Also, suppose oil company sets a course for 10% growth compared with the production in last year and the natural decline rate of the No. 2 branch is the lowest. The valve is 0.69% (italicized in Table
This paper presents a fair allocation algorithm called ABCR. In this algorithm, we consider three elements of fair allocation: member contribute rate, member goal, and alliance target. In order to determine the member contribution rate, we divide the factors that affect fair allocation into two categories: certain factors and uncertain ones. We get the main certain factors by PCA, get the overall uncertain factors by AHP, and then combine them to determine the member contribution rate of each member in alliance activities. In addition, in order to assess the fairness of this proposed algorithm, a criterion evolution method for fairness is proposed. In case study, actual production data is applied to three different allocation algorithms, the results of which show that the rationality of our fair allocation algorithm is the best. Finally, we justify our fair allocation algorithm by comparing its characteristics with those of the other two allocation algorithms.
There were two main research motivations that drove this work. The first motivation is whether there exists a fair allocation algorithm to characterize variable or uncertain factors. To the best of our knowledge, ABCR is a rational solution to tackle this problem. The second motivation is that there exist many studies about fair allocation, but there is less discussion about fairness criteria evaluation. Therefore, we present an easy fairness criteria evaluation method and a case study shows that our proposed fairness allocation algorithm is rational.
To summarize, this work makes an in-depth study of certain and uncertainties factors that affect production task, as well as using factor selection and factor construction to determine the main factors that affect production task to determine the contribution rate of members in affiliate activities, combined with member goals and alliance target to determine the results of fair allocation. Based on the adaptation scenario of the fair allocation algorithm, we believe that this proposed allocation algorithm is very suitable in practice. Nevertheless, considering the results of this work, we believe that a more complex scenario also needs this model to distribute the oil production task, so it is very meaningful to extend the domain of the proposed model to other application scenarios, such as the multi-league cooperation allocation problem.
Some data were omitted due to a confidentiality agreement between the research team and the Northwest Oil Field Branch, China Petroleum & Chemical Corporation. The signed agreement is valid from December 18, 2012, to December 17, 2021.
The authors declare that they have no conflicts of interest regarding the publication of this paper.
This work is supported by the Northwest Oilfield Branch, China Petrochemical Corporation [Grant no. 34400000-12-ZC0607-0017].