A Theory of Optimized Resource Allocation from Systems Perspectives

Transcription

1 Systems Research and Behavioral Science Syst. Res. 26, 289^296 (2009) Published online 6 March 2009 in Wiley InterScience ( & Research Paper A Theory of Optimized Resource Allocation from Systems Perspectives Ying Xiong 1 and Sohail S. Chaudhry 2 * 1 Zhejiang University, Hangzhou , China 2 Villanova School of Business, Villanova University, Villanova, PA 19085, USA A construction project is an example of a complex systems engineering problem. In this paper, we have characterized a construction project in the context of the theory of six forces on the factors of production. This new approach was defined by giving consideration to the characteristics of the construction project s resource allocation. An economic efficiency index was also used to assess resource allocation of a construction project. Based on this approach, a theory of optimized resource allocation of the construction project is proposed. Copyright # 2009 John Wiley & Sons, Ltd. Keywords theory of six forces on factors of production; engineering project; resource allocation; systems research; systems engineering; technological economics INTRODUCTION The planning, scheduling and controlling of a construction project is an example of a complex system engineering problem (Yang et al., 2006). Typically, such a problem requires a long construction cycle, a vast sum of capital input and the coordination of various resources to accomplish the project. However, the existing research in resource constrained project scheduling problems emphasizes particularly on the construction of the model and the solution methodology (Herroelen et al., 1998; Kolisch and Hartmann, 2006; Tseng and Chen, 2006; * Correspondence to: Sohail Chaudhry, Villanova School of Business, Villanova University, Villanova, PA 19085, USA sohail.chaudhry@villanova.edu Kastor and Sirakoulis, 2008). Thus, it is necessary to provide a unified and scientifically sound methodology to guide managers in the allocation of various resources that are utilized in a construction project. The models described and used in literature usually are aimed at some specific projects of a particular type. The lack of universality is the fundamental reason why such studies cannot be fully applied and/or extended to other practical projects. Consequently, this issue has become an exigent subject in the construction field to develop a theory of the optimized resource allocation of the construction project from a different point of view. Such a process can assist in the guidance of the resource allocation model of construction project and the design of the resource allocation method. Hence, we propose a Copyright # 2009 John Wiley & Sons, Ltd.

2 RESEARCH PAPER combination of the practice of the construction project with the Theory of Six Forces on Factors of Production that is an important theory of the technological economics (Xu, 1986). More specifically, the paper proposes the theory of the optimized resource allocation of the construction project that is based on the theory of six forces on factors of production (Xu, 2006). The plan of the paper is as follows: in the next section, we specify and integrate the six forces on factors of production within a construction project. The section following it discusses the issues related to resource allocation in a construction project. In the final section, the evaluation standard of the optimized resource allocation of the construction project is presented. RESOURCES UTILIZED IN A CONSTRUCTION PROJECT The theory of factors of production is an important fundamental theory in technological economics (Xu, 1986). According to this theory, any work or production must possess six forces simultaneously. These forces are labour, capital, material, nature, transport and time, which are actually six production factors or resources. The construction project cannot be executed without the consideration of these six forces. The labour force in a construction project implies the occupation and consumption of the labour during the construction of a project. From the view of the physical form, the occupation of the labour means the personnel involved during the construction that include the workers, managers and so on, while the consumption of the labour represents the efforts (including the physical and mental labour) made by those personnel at the work site. From this point of view, then the occupation of the labour suggests the ownership of the current assets such as wages, while the consumption of the labour signifies the cost such as the labour wages. Unlike as in the general industrial production, the labour input in a construction project does not occur only once, and the occupation and consumption of labour input is not uniformly distributed during the project life cycle. For a construction Syst. Res. enterprise, the managers are often permanent; however, the workers that are engaged in actual construction are frequently hired temporarily based on the construction schedule. Consequently, the allocation of human resources must determine not only the amount but the timing of the occupation as well. The basic principle is to decrease the idle hours of the personnel during the construction period as the existence of such hours implies that there is labour occupation without consumption, which is a waste of the human resources. The capital force in a construction project delegates the allocation and consumption of the capital during the construction. When viewed from the physical perspective, the allocation of the capital indicates the utilization of the construction equipment and machinery during the construction process and the consumption of the capital signifies the consumption caused by the allocation of the construction equipment and machinery. From the perspective of the value form, the occupation of the capital implies the occupation of the fixed assets, such as the construction equipment and machinery, and the consumption of the capital denotes the basic depreciation and the major repair expenditure associated with such fixed assets. As was the case of the human resources, the allocation of the capital force during the construction also needs to decide both the amount and the timing of the allocation. At the same time, the idle hours of the machines and equipments should be decreased as much as possible during the process of allocation. The material force in a construction project signifies the allocation and consumption of the materials during the construction. From the view of the physical form, the occupation of materials implies the allocation of materials that are required for construction, including various raw materials, semi-finished goods and energy, while the consumption of materials indicates the use of these materials. From the view of the value form, the occupation of materials means the allocation of the current assets associated with the materials and the consumption of materials represents the costs of the abovementioned materials. Typically, the construction 290 Ying Xiong and Sohail Chaudhry

3 Syst. Res. project consists of several activities according to certain precedence relationships, and the utilization of material resources does not occur only once, that is at the beginning of the construction but, rather, these materials are placed into use on a gradual basis throughout the construction process, since the materials used will vary during each stage of the construction process. The nature force in a construction project means the allocation and consumption of the construction site during the construction. Again, from the view of the physical form, the occupation of the nature force suggests the allocation of various spaces at the construction site, while the consumption of the nature force denotes the use of various spaces on the construction site. From the view of the value form, the occupation of the nature force describes the allocation of the fixed assets, such as land, the construction site, etc., and the consumption of the nature force represents the use of the fixed assets. Apart from the allocation and consumption of itself, the nature force will indirectly affect the economic effect of any project s execution by affecting the productivity of the construction. For example, if the working areas are small, then this will have a direct impact on the working conditions on the labour force and thus, lead to the possibility of decrease in labour productivity. The transport force in a construction project is the allocation and consumption of the flow of human resources, material flow and information flow during construction. The flow of human resources includes the procedural and organizational relationships of the construction activities, the personnel allocation of various activities and other factors. The material flow covers the purchase, storage and the utilization of the raw materials. The information flow describes the collection, arrangement, transmission and processing of various information regarding the time, cost and quality. From the view of the physical form, the occupation of the transport force means the allocation of the flow of human resources, material flow and information flow, while the consumption of the transport force describes the consumption of the above-mentioned flows. From the view of the value form, the occupation of the transport force means the allocation of the current assets associated with the flow of human resources, material flow and information flow, and the consumption of the transport force denotes the related costs. The time force in a construction project purports the scheduling during the construction phase, which includes duration and the start time. From the view of the physical form, the occupation of the time force represents the allocation of time, while the consumption of the time force suggests the consumption of time. From the view of the value form, a time value of capital is usually used to calculate and evaluate the expenses in construction project. In this way, the occupation of the time force indicates the allocation of the time value of the capital, while the consumption of the time force signifies the consumption of the time value of capital. From the above analysis, it is clear that the execution of a construction project cannot be carried out without considering all of these six forces. Consequently, these six forces constitute the required resources involved in any construction project. RESOURCE ALLOCATION IN THE CONSTRUCTION PROJECT RESEARCH PAPER Characteristics of Resource Allocation in a Construction Project The allocation of the six types of resources during a construction project can be classified into two categories. First, those resources whose allocation is related to the overall project, such as the nature force and transport force. Such allocations are usually established before the beginning of the construction. Second, those resources whose allocation covers each activity during construction process, such as the labour force, material force, capital force and time force. Their allocation usually occurs at the beginning of the construction process, so as to guarantee a successful implementation. The allocation of the resources to the overall project is a one-time decision while the allocation of the resources that covers the activities of the construction project Optimized Resource Allocation from Systems Perspectives 291

4 RESEARCH PAPER typically requires a series of decisions over time. The main reason for this is that the activities involved in a construction project are organically related to each other by the precedence constraints and resource constraints. These resources need to be allocated to various activities sequentially based on the start times of these activities. The theory proposed in this paper is mainly aimed to guide the allocation problem of the these resources which include the allocation problem related to the labour force, material force, capital force and time force for different activities. The allocation of the labour force, material force and capital force mainly focuses on determining the amount and timing of the resources allocated to the various activities. Whereas, the allocation of the time force mainly concentrates on determining the duration and start time of each activity such as the activity schedule of the project. These characteristics of the allocation of these resources are elucidated below. (1) There is a mutual restriction and influence between the allocation of time force and the allocation of the labour force, material force and capital force. On one hand, the quantity of the labour force, material force and capital force assigned to the project determines the duration of activities in the allocation of time force. For example, if the duration of a certain activity was determined to be 10 workerdays, then this can be accomplished in 5 days if two workers are hired as opposed to if five workers are hired, the duration of the activity can be reduced to 2 days. On the other hand, the start time of the activities in the allocation of time force determines the time of the labour force, material force and capital force input. This characteristic reflects the fact that the allocation of different resources that does not occur independently, but relates to each other in the way that allocation of a certain resource would have a greater influence on the allocations of the rest. Also, the resource allocation of a construction project can have two schemes. One is the time force allocation scheme, usually known as the activity schedule of construction, and the other is Syst. Res. the allocation scheme for the labour force, material force and capital force, commonly known as resources planning. Both schemes can express the allocation results of all the resources. (2) The resource allocation schemes in the construction project are of diverse form. The principle of inter-replacement among the six forces in the theory of six forces on factors in production shows that every production factor can not only be replaced to each other inside itself, and be replaced to each other among the other factors (Xu, 1986; Xu, 2006). The resources in the construction project also satisfy this principle. For instance, the replacement of the labours described above reflects the quantity replacement of the human resources within itself. If the construction machine is used to replace the manual work of the labour, then it is called the mutual replacement between the resources of labour force and capital force. Similarly, different start time of activities reflects the mutual replacement of the time force resource. The resources replacement on quantity of the labour force, material force and capital force in the construction project is defined as the performing mode of the activities. Each mode has three representation: (i) the pairing between the duration of an activity and corresponding quantity of the materials under fixed workload, which reflects the equilibrium relationship between the duration of the activity and the quantity of materials input, and can be described as shown in Figure 1(a); (ii) the pairing between the duration of an activity and corresponding quantity of the capital under fixed workload, which represents the equilibrium relationship between the duration of the activity and the quantity of capital input, and can be represented by Figure 1(b) and (iii) the pairing between workload and corresponding required materials under fixed activity duration, which denotes the equilibrium relationship between the workload and the quantity of materials input, and is depicted in Figure 1(c). In general, these three modes can be transformed to each other. The performing 292 Ying Xiong and Sohail Chaudhry

5 Syst. Res. RESEARCH PAPER Figure 1. Performing mode of an activity mode of an activity usually can be classified into three categories: crashing mode, normal mode and delaying mode (Shtub et al., 2006). Compared to the normal mode, the duration of the activity is shorter but requires more resources in the crashing mode. In contrast, the duration of the activity is longer but requires fewer resources in the delaying mode than that in the normal mode. The mutual replacement of the time force resource is called the mode of activity schedule of the activity. Generally, when the resource constraints are not considered, the start time of an activity can be scheduled within the time window between the earliest start time and the latest start time. The difference between the latest start time and the earliest start time is called the total float of the activity. Therefore, the mode number of the activity schedule equals to the total float of the activity. If the resource constraints are of concern, then the mode number of the activity schedule will be smaller than or equal to the total float. Consequently, the resource allocation of the construction project is actually the selection of the performing mode and the activity schedule mode for different activities, and different combination of these two modes constitutes different resource allocation scheme of the construction project. (3) There exists physical allocation and value allocation of the resources in the construction project. The principle of physical value in the theory of six forces on factors in production shows that there exist two forms simultaneously for any production factor. They are the physical form and the value form. The resource allocation in the construction project also has the allocation of physical form and value form. The physical form allocation focuses on the quantity and time assigned to the activity, while the value form allocation is concerned with the quantity of actual value (capital) input. This depends on three factors that are the quantity, price and time of the materials input. It is the physical form allocation that really works during the production, so it should be considered first every time. However, the value form allocation cannot be ignored for the reason that Optimized Resource Allocation from Systems Perspectives 293

6 RESEARCH PAPER an allocation scheme can only be evaluated by the value form allocation. The quantity of the materials assigned to an activity depends on the request of the activity construction, and can be affected by the technical level, mechanization degree and so on. The price of resources depends on the factors other than the construction production, such as the market supply and demand of the production factors, the transportation distances, etc., which are beyond the scope of this paper. The aim of this work is to make the quantity of the input value as small as possible through reasonable arrangement and planning with the fixed quantity and price of the materials. In other words, the paper mainly concentrates on the third factor of the quantity of the value assigned to the project, i.e. the time of the resources input, which directly affects the value input by the time value of capital, given the fixed quantity and price of the materials. The expression input later and return earlier that is always expressed by people is a kind of consideration of the time value of capital. Resource Allocation Mode in a Construction Project According to above analysis, the major content of the resource allocation mode in the construction project is to select performing mode and scheduling mode for each activity. Thus, the formula of this mode can be defined as a dual structure, RM ¼ {PM, SM}, where PM denotes for the performing mode and SM represents the scheduling mode. PM encompasses the performing mode of each activity, i.e. PM ¼ {pm 1,...,pm n }, where n denotes the activity number in a construction project. The performing mode of each activity pm i consists of the quantity of human resources, capital resources and material resources input and the duration of the activity. SM is the set of the start time of each activity, i.e. SM ¼ {ST 1,...,ST n }, where ST i denotes the start time of the activity i. In this expression, the allocation of the time force resource is divided into the performing mode and the scheduling mode. This type of an expression reflects both the allocation of resource quantity and the time of the resource input. If the number of performing mode of activity i is k i, and the total float is TF i under the condition that the resource constraints are ignored (assuming that both the start time and finish time are discrete integers), then the number of resource allocation mode of the activity i is about k i TF i, and the number of resource allocation mode of the construction project which has n activities is about Q n i¼1 k i TF i. Obviously, this is a very large number; however, these modes may not be all feasible. The feasible mode of resource allocation in a construction project must satisfy both the precedence constraints and resource constraints at the same time. Specifically, the precedence constraints imply that the sequence of the activities is determined by construction techniques and organization, while the resource constraints represent the sequence of the activities determined by the supply and demand of the resources. EVALUATION STANDARD OF OPTIMIZED RESOURCE ALLOCATION IN A CONSTRUCTION PROJECT Effect of Resource Allocation in a Construction Project Syst. Res. According to the principle of the economic effect index in technological economics, the economic effect equals to the ratio of the effect to the consumption of the labour. So, what is the effect of the resource allocation in a construction project? The purpose of this allocation is to promote the successful implementation of the construction project and to create the construction product through the construction of the project. The product of the construction created signifies the cost of construction and installation work to the construction enterprises. This cost is actually various payments by the clients, which includes the deserved profit as well as the actual cost of construction and installation work. Two elements need to be decided in terms of the payments that are the amounts and timing, and 294 Ying Xiong and Sohail Chaudhry

7 Syst. Res. they depend on the pricing methods and the payment mode. On the other hand, it is partially incomplete to evaluate the economic effect of resource allocation in a construction project only in terms of payment, since it only considers the actual construction cost of the project and does not take into account the potential profits of finishing the project ahead of time. In such projects which will earn huge profits after operation, completing ahead of time suggests that revenues will be achieved ahead of time, which could not be reflected by the payment. How to covert this revenue that previously was enjoyed only by the clients to the revenue of the contractors? Some methods in practice could bring some helpful references. In practice, some clients add bonus penalty clauses to contracts to ensure the best monetary outcome. If the contractor finishes late, the penalty will be deducted from their fee. If the contractor finishes early, they will receive an early completion bonus. Thus, the clients who do not add such clauses are able to withhold portions of the daily income as the bonus or penalty once the project begins. In this way, the economic effect of the resource allocation of the construction project could be evaluated indirectly. Economic Effect of Resource Allocation in a Construction Project Based on the technological economics, there are two types of operation modes. These are the extensive mode and intensive mode. Considering a type of operation as extensive or intensive mainly depends on the elasticity index of the input, which is the ratio of the growth rate of input to the economic growth rate. If the growth of input exceeds the economic growth, then the operation mode is considered extensive, while if the input does not grow or has a negative growth, then it is considered intensive. The extensive mode achieves the economic benefits (i.e. the difference between the effect and the labour consumption) through increasing the production elements. The intensive mode aims to achieve the economic benefits through increasing the RESEARCH PAPER economic efficiency (i.e. the ratio of the effect to the labour consumption) of the production elements (Xu, 1997). Essentially, the resource allocation of the construction project is intensive, because it increases the economic effect of the project through reasonable scheduling under the premise of the fixed input. As a result, the Economic Efficiency Index (EEI) should be applied to evaluate the economic effect of resource allocation of the construction project. This can be represented as follows: EEI ¼ PVðoutputÞ PVðinputÞ Specifically, EEI denotes the economic efficiency index of the resource allocation of the construction project. PV (output) and PV (input) signify the present value of output and input of the resource allocation of the construction project respectively. Evaluation Standard of Optimized Resource Allocation in a Construction Project The economic meaning of the EEI of resource allocation in a construction project is quite obvious. The numerator PV (output) designates the production of construction created by the construction enterprise. The denominator PV (input) reflects the value of resource input by the construction enterprise. The ratio of the two signifies the production of construction created by the unit resource input during the construction of the project. The larger the ratio, the more efficient utilization of the resources and hence, there is a higher economic effect of the construction. Therefore, the evaluation standard of optimized resource allocation in a construction project could be described as follows: Max EEI ¼ PVðoutputÞ PVðinputÞ The optimized resource allocation in a construction project is defined as the proper determination of the amounts and time input of human resources, capital resources and material resources required by the construction Optimized Resource Allocation from Systems Perspectives 295

8 RESEARCH PAPER of the project, or to maximize EEI through choosing the performing mode and scheduling mode of the activities. Among the feasible modes of resource allocation in a construction project, the mode that maximizes EEI is called the optimal resource allocation mode in a construction project. Compared with the evaluation standard of maximization of the net present value in project scheduling problems in literature, the evaluation standard of maximizing EEI has many benefits. First, its economic meaning is more definite than the net present value. Secondly, it is an indicator of economic effect, while the net present value reflects the economic benefits. Maximization of EEI will lead the construction enterprises to take a more intensive production and place more emphasis on the output of unit resource input, which could not be achieved by the maximization of the net present value. Thirdly, it is in accordance with the statistical data of the economic indicators of the construction enterprises. Fourth, it could be used to make a horizontal comparison between different construction enterprises and a vertical comparison inside a construction enterprise. Finally, it builds a connecting bridge between macro evaluation and micro evaluation. When we use the shadow price of resources instead of the market price, the social discounted ratio instead of the industrial ratio of revenue to adjust the economic efficiency index, the evaluation standard proposed in this paper could be applied to the macro evaluation of optimized resource allocation in a construction project. REFERENCES Syst. Res. Herroelen W, Reyck BD, Demeulemeester E Resource-constrained project scheduling: a survey of recent developments. Computers and Operations Research 25(4): Kastor A, Sirakoulis K The effectiveness of resource levelling tools for resource constraint project scheduling problem. International Journal of Project Management DOI: /j.ijproman Kolisch R, Hartmann S Experimental investigation of heuristics for resource-constrained project scheduling: an update. European Journal of Operational Research 174(1): Shtub A, Bard JF, Globerson S Project Management: Processes, Methodologies, and Economics. Pearson Education, Upper Saddle River, NJ. Tseng LY, Chen SC A hybrid metaheuristic for the resource-constrained project scheduling problem. European Journal of Operational Research 175(2): Xu SB Technological Economics, (3rd edn) People s Press of Jiangsu: Nanjing; Xu SB Theory of six forces of the factors of production. Journal of Beijing Jiaotong University (Edition of Philosophy and Social Science), 5(3): Xu SB How to Assess the Transition of Economic Growth Types? (1st edn) People s Press of Jiangsu: Nanjing. Yang T, Huang H, Chaudhry S Enterprise resource planning for large-scale engineering projects from systems engineering perspectives. Systems Research and Behavioral Science 23(2): Ying Xiong and Sohail Chaudhry