物流資源分配的多目標(biāo)優(yōu)化模型英文原文及翻譯

1、MULTI-TARGET OPTIMIZATION MODEL OF LOGISTICS RESOURCES ALLOCATIONZI-KUI LIN 1， LEI CHEN 2Department of logistics management, Beijing Jiao tong University, Beijing ,ChinaE-MAIL: ，Abstract: Considering the balance between the cost of enterprise logistics resource and

2、 service levels, and took into account the internal and external enterprise resources, establishing a multi-objective model with the decision about resource outsourcing. Solving the model withrestriction method, the possible solution is acquired and evaluated. Displaying the best outsourcing decisio

3、n in different objectives of circumstances the same is the optimal allocation of resources programmer. Finally, the example shows the application of the model in decision programming. Key words: Logistics resources; Resource Allocation; Optimization; Multi-target programming 1. IntroductionWith the

4、intense competition in the global economy, enterprises pursue more effective development to ensure their status in the market. Logistics is also getting more and more attention from enterprises. Both logistics enterprises and internal logistics of enterprises have played important roles in the busin

5、ess development strategy. It has become a matter which need careful consideration that how to allocate the logistics resources rationally to ensure their own cost savings as well as customers satisfaction to the logistics services. This paper would establish a Multi-target programming model to study

6、 how to allocate the logistics resources rationally with two targets: logistics costs and customers satisfaction to logistics services 1. Enterprise resources in the form of material can be divided into tangible and intangible knowledge resources. Material resources include physical resources, human

7、 resources and financial resources. The logistics of resource allocation will be studied from the perspective of material resources in this article 2. The allocation of resources refers to allocating resources among different uses. Selection of resources for future use determines the composition of

8、social products. The fact that allocation of resources has become a problem is due to two reasons. First, the supply of social resources is limited (namely the scarcity of resources), while the desire of human demands is unlimited; Secondly, certain resources often have many different options for us

9、e. The internal logistics of enterprises face such a problem: logistics resources of enterprises are limited, but when faced with the case that different projects need logistics services, how to allocate the resources? Similarly, the logistics enterprises often have such a problem as well: when faci

10、ng different customers, how to arrange the logistics resources to meet the customers needs and achieve maximum gains at the same time? In the field of logistics there are many examples which can be generally called anti-back phenomena. As a sort of service, logistics itself needs to consume resource

11、s, resulting in business costs. Its cost is inevitable, but can be reduced and controlled through reasonable plans. We have found that the phenomenon of Antinomy exist between logistics service and logistics cost. Customers satisfaction with the achievement of logistics services would inevitably res

12、ult in an increase in logistics cost. On the other hand, the increased logistics cost, which means sufficient logistics resources will make customers be satisfied with logistics services. Therefore, considering the logistics costs and the targets of logistics services, it is meaningful to study to s

13、tudy logistics distribution of resources and to achieve the balance of the two targets. 2. Multi-target Optimization Model of Logistics Resources Allocation 2.1. Model Description The model pursues these two goals: the lowest total costs of enterprises and the highest level of service. Resources of

14、Logistics enterprises mainly include equipment, facilities and staff; logistics enterprises deal with not a single item, but several projects with different demands so as to reach the two contradictory goals simultaneously with limited resources 3. Model structure as shown in Figure 1: In addition t

15、o the basic structure in Figure 1, logistics resources of enterprises are divided into internal resources and external resources, which take into account of outsourcing decision-making of enterprises and decide whether to use external resources in certain projects by weighing these two targets in th

16、e decision making process. Improvement of the model shown in Figure 2: 2.2. Assumptions 1) Resources in logistics enterprises are limited, and are divided into internal resources and external resources. The main resources in this model are: equipment, facilities and staff.2) The faced projects can b

17、e counted from 1 to n. Their demands for all types of resources vary from the upper limit to the lower limit. Each project has to be completed before the deadline. The model assumes that the lower time limit for projects to have access to resources can be completed by the deadline; and the upper lim

18、it, within the shortest possible time; the project demands for resources have saturation, reaching the upper limit means that the demands have been fully satisfied, and access to more resources makes no sense.3) The resource allocation of logistics has the two targets: cost and service level. The ph

19、enomenon named anti-back exists among the benefits. Total costs consist of various costs caused by using resources for all projects. This model weighs the level of service by means of measuring the time to complete the project. It is assumed that the more were there resources, the faster could we co

20、mplete projects. Consequently, the service level could be weighed according to the degree of saturation. 4) Also this model considers whether adopt the outsourcing. For each project, outsourcing means that resources of the entire projects should all be attained by outsource, but not that part of res

21、ources are provided within enterprises while others leased through outsource. 5) Supposing various resources are independent to each other, their impacts on the target were not relevant.2.3. Model Establishment The mathematical model of multi-target programming can be established as4,5,6: min, max i

22、s an N-dimensional vector variable. is objective function in logistics system. is objective function of customer satisfaction. The constraint inequality is .The constraint equation is In the N-dimensional space, the viable solution for the domain is , which has 1 2 -restrictive conditions and non-bi

23、nding negative. Two-objective functions of logistics optimize the allocation resources can be expressed as min = (1) max = (2) , expressed as the quantity whose number is in own logistics resources whose quantity is .Those resources are obtained by the project . ,expressed as the costs whose number

24、is in the sort of resources whose number is ., expressed as the quantity whose number is in outsourcing logistics resources whose quantity is .Those resources are obtained by the project . , expressed as the costs whose number is in the sort of outsourcing resources whose number is . , expressed as

25、fixed costs in outsourcing by the Project (such as the costs of negotiation). , expressed as the variable between 1 and 0 which means whether adopt outsourcing. , expressed as the weight of service level of project in all L.O.S evaluations. , expressed as the weight of the No. kind of resources whos

26、e sort is of project in all L.O.S evaluations. , expressed as the total quantity of the No. kind of own resources whose sort is . The outsourcing resources are enough. , expressed as the minimum limit of the No. kind of resources whose sort is demanded by project i . , expressed as the maximum limit

27、 of the No. kind of resources whose sort is demanded by project . So there are constraints as follow: (3) (4) (5) (6) (7) (8) (9) Formula (1) is expressed as a function that minimizes the total costs. Total costs constitute of various kinds of costs prepared for all projects. Project-outsourcing is

28、liable to occur and it will take some fixed costs such as costs used for negotiation. Formula (2) is with the purpose to maximize customer satisfaction and with the quantified level of customer service instead of customer satisfaction. The model is mainly measured by the access to the resources of p

29、rojects .This model figures out that the more resources obtained the faster efficiency of the sum of completion projects, so the access to resources saturation can be used to measure the level of customer satisfaction. Formula (3) is expressed as quantitative restriction of various own resources. It

30、 also considers that limitation of resources doesnt exist when we adopt outsourcing. Formula (4) and formula (5) are expressed as minimum requirements of the demands made by various resources and the quantity that has reached the degree of saturation. Formula (6) and formula (7) can be expressed as

31、weight. Formula (8) can be expressed as nonnegative restriction. Formula (9) is used to decide whether we adopt outsourcing. When we set the value as 0, it means that the project is outsourcing. 2.4. Model SettlementI Analysis for Solution In view of the choices of outsourcing, this model can serve

32、as a basis which could conclude whether there is enough own resources of enterprises. The three possible solutions of the model are as follows: 1. All projects all use their own resources and have a higher level of service. This result shows that enterprises own sufficient resources, but we think, f

33、rom the management perspective, enterprises resources have not been fully utilized, and enterprises dont make full use external resources. 2. Most of the projects use their own resources, meanwhile a few projects use outsourcing resources. This result shows that the enterprise resources owned are mo

34、re adequate, and also make full use of the external resources. At this point, we need to assess which items should use owned resources, and which ones use the outsourcing resources to achieve the level of service required and also the most reasonable cost. 3. A small part of projects use their own r

35、esources, meanwhile the most use outsourcing resources. This shows that enterprises are short of owned resources, can not cope with too many projects, and need to expand the size of their own resources or change their corporate strategy not to be blind to undertake projects. This model mainly invest

36、igates in the second case to look for a reasonable balance between the two targets that conflict each other. II Methods for solution Multi-target programming can deal with two or more conflicted goals at the same time, so the solution of the Multi-target programming is the Pareto optimal vector. The

37、 multi-target programming solution denotes that a set of quantized targets study out several sets of no-inferior solutions by means of mathematical programming in a restrict condition 7. This model will generate a set of no-inferior solutions by means of Constraint Method 8.We usually hunt out for a

38、 set of no-inferior solutions in solving process to solve problems by means of translating Multi-target optimization into Single-objective optimization. In case of function space that be made up of and , if we add constraint condition to one of object functions （ ， is set as an initialization of, fo

39、r example.Then, Multi-target optimization can be translated into Single-objective optimization that aims at . We could use Linear Programming Theory which could get a maximum or minimum value. If we change the value of within the limits of maximum or minimum values, well get the entire confines of e

40、stablished space. And for the same reason, well get the confines of space by means of holding in function . No-inferior solutions always fluctuate among a segment of confines. We could get optimum solution within the set of no-inferior solutions to satisfy the decision maker. There are two targets c

41、onflicting with each other, so we cant entirely get a optimum solution by using quantized model. If we use Constraint Method to solve the model, we could figure out the scope of targets in consecutive mode to offer decision makers a much more reasonable blue-print. This paper uses the lingo software

42、 9 to find out various programs for the model.3. Example 3.1. Description Enterprises have their own logistics resources, and enterprises can also choose to outsource to third parties and make use of external resources. Of course, the cost of outsourcing resources is inevitable higher than that of u

43、sing its own resources. But under the condition of the lack of their owned resources, in order to reach a certain level of customer satisfaction, outsourcing will have to be chose. Then we will give an example to verify the practicality of the model. In this example, the enterprise has three project

44、s. Three types of logistics resources (forklift, staff, and storeroom) are needed to complete the project. Parameters for the example are shown in the tablebelow. The maximum and minimum limit of demands prepared for all projects could be obtained by analyzing various ingredients according to physic

45、al truth in Table 1. The data in Table 2 could be figured out according to historical data. The data in Table 3 could be figured out by investigation. The weighing data in Table 4 and Table 5 could be figured out according to quantitative analysis and qualitative analysis. This case aims at proving

46、the practicability of this model, of which data are the simulation data. 3.2. To solve the case by Constraint Method Logistics enterprises usually carry on projects depending on their consistent service level. Theyll offer different service according to different projects. Now, lets solve the case b

47、y Constraint Method: in the condition (), well figure out the optimum solution to get the final chart of solution of two-targets optimization shown in Table 7.When the value of reaches the minimum, accordingly, well get the value of which is expressed as the degree of customer satisfaction. When the

48、 value of reaches the maximum, accordingly, well get the value of which is expressed as the total costs. Enterprises will offer different service according to different projects. We translate Multi-target optimization into Single-objective optimization by means of regarding cost function as objectiv

49、e function in the restrict condition of and the range（65.8%-100%）of . Then we set r a proper value to make sure how many no-inferior solutions the system generates. When we set = 4, therell be 4 sets of no-inferior solutions. With the value of increased, we set step width as 10%. This model will fig

50、ure out the optimum solution of single-target function in cases of the same value of . The result is shown in Table 8: The result indicates that the enterprise has to adopt outsourcing to increase its service level because of lack of resources. It also displays the “anti-back” of total costs and ser

51、vice level at the same time. Decision-makers should decide the proper scheme to make full use of internal and external resources according to the fixed targets, different service level and different costs. 4. Conclusion This paper considers two conflicting objectives the cost and service level, we c

52、an get how to achieve the optimal allocation of resources in the conflicting objectives through the establishment of multi-target programming model. In the model, we take into account the enterprises owned resources and external resources at the same time, and resolve the problem whether the project

53、 is outsourced or not under different circumstances. This model can be considered as a qualitative factor when the project is outsourced. Combining with various qualitative factors， eventually we can obtain a reasonable outsourcing decision-making. Results can be educed from the model can be drawn:

54、one, in different service levels, the best outsourcing, which are as follows. First, in the different levels of services, the optimal decision-making and allocation of resources result in the optimal cost. Second, under the requirement of different cost, the best outsourcing decision-making and the

55、optimal allocation of resources result in the highest level of service. The enterprises management strategies should have a focus between the costs and service level. Decision-making can be based on business strategy, and use this model to find out the optimal solution. The model can be further refi

56、ned in this article, and the deep researches can be made from several aspects, such as the outsourcing decision-making, logistics resource pricing, the weight of the project resources and so on. These aspects all can be improved and researched on the basis of this model. References 1 Zhitai Wang，The

57、 New Modern Logistics M, The Capital University of Economics and Business Press , Beijing, 2005. 2 Ning Chen and Xueyan Zhang, “Model of Resource Allocation Efficiency in Enterprise Multi-project Management” J. Industrial Engineering，Vol 9，No.5, pp.92-96, Sep.2006.3 Vaidyanathan Jayaraman, “A Multi-objective Logistics Model for a Capacitated Service Facility Problem” J, Int J of Physical Dist