Supply Chain Cost Prediction for Prefabricated Building Construction under Uncertainty

This paper considers the problem of predicting a supply chain cost for prefabricated building construction under an uncertain situation. Based on the Activity-Based Costing (ABC) method, we establish a computational model to estimate the total cost of the prefabricated supply chain. The model can assist in not only finding the critical areas for cost reduction of the whole supply chain but also analyzing other costs of prefabricated construction projects. Furthermore,we provide a numerical example of prefabricated building construction to validate the results.


Introduction
Modern building construction industry always faces significant challenges to incorporate all the building construction activities and reduce the cost of its logistics.Supply Chain Management (SCM) will be a fundamental tool to alleviate the expenses of all the parties [1].SCM is a process to coordinate and distribute all commodities among the stakeholders in a strategic manner.In the building construction industry, the supply chain manages the material flow, the information flow, and the fund flow, which are of importance for owners, designers, manufacturers, suppliers, and contractors.In [2], it is pointed out that a proper planning approach to utilize materials along with an efficient logistics and inventory system will improve the project performance and will consequently reduce the whole construction cost.Since many components and stages have been involved in prefabricated building construction, it is hard to find out which ones lead to the rise of the total cost.The identification of the impact of each action for the cost increase becomes critical for prefabricated building construction [3].
In this paper, we consider the supply chain cost problem of prefabricated building construction under an uncertain environment.We utilize an ABC method to predict the total weekly cost of the prefabricated supply chain of a construction project.It is difficult to estimate "overhead cost" against the direct material cost of the prefabricated supply in a construction project [3].Therefore, the purpose of this article is to develop a cost model to predict those overhead costs in an uncertain situation.The proposed cost model is established by using the unit rate of the resources involved in the prefabrication process, the rate of resource utilization of each activity, and the volume of the cost driver activity.The model ensures better prediction performance by considering every activity of the project and uncertain factors.The cost model will help supply chain decision makers and senior executives for supply chain cost reduction.From the model, the senior management team can find the growing cost sector (it could be a resource, activity, or improper utilization of the resource).
Our main contributions of this paper are twofold.One contribution is that combining existing works on supply chain cost with the activity-based cost model, we propose a new supply chain cost model to predict the corresponding cost for prefabricated building construction industry under uncertainty.Another one is to provide an explementary case to illustrate the application of the model in an Australian prefabricated building construction industry.

Activity-Based Cost Model
The section briefly introduce the ABC model, which has been applied extensively [3][4][5].In construction industry, around 50 percent of a product cost is the overhead cost and 15 percent cost of the product cost is the direct labour cost [6].
The ABC method in Figure 1 is to reformulate the product costing by determining the company's internal and external resource and service consumption on each task that produces the product.For a traditional costing method, the overhead cost is used as the general basis.On the other hand, the ABC method checks the overhead cost more exclusively and now the activity-based cost model is in use to compute the daily cost by many managers [5].

Cost Model to Uncertainty
The proposed cost model aims to predict the total cost of prefabricated supply chain in a week.Each cost of each activity associated with this prefabricated supply chain is summed up for the total cost for the deterministic setting.This cost model includes the overhead cost of wages of the resources, utilities, and land cost, together with workforce cost.The weekly material cost is predicted using the unit material price and weekly material consumption.The cost of uncertainty is then added to obtain the total cost.A mathematical model of the prefabricated supply chain cost can be described by where   ,   ,   , and   denote the weekly total cost, the labor, energy and land leasing cost in a week, the direct material cost of the week, and the cost produced by the uncertainty, respectively.In ABC, a cost driver is a factor that makes the difference in the total cost [7].For example, the number of the purchase order is a cost driver for a company.When the number of the purchase order increases, the total expenditures of a company increase as well.The cost driver and the total cost is linearly proportional [8].As the total work can be subdivided in to many multiple work, optimum selection of the cost driver is critical to find out the total cost [9].In model (1), the creation and revision of the prefabricated component drawing is a cost driver.When more drawings are created, or required, or reviewed, the weekly prefabricated component supply cost would increase.The numerical value of each cost driver indicates the importance or its impact on the total weekly supply chain cost.For details, see [10][11][12][13][14] and the references therein.The relationship of the activities and the cost drivers of total cost of prefabricated supply chain can be found at Figure 2.
In many cases, the total project can be divided into three significant steps: (a) shop drawing, (b) prefabrication, and (c) assembly, delivery, inspection, and installation.To complete every level, some activities are required to finish.Every activity is a cost driver in the entire supply chain cost of the weekly prefabricated supply.As mentioned earlier, to complete the step Shop Drawing, a series of activities are identified in this cost model.For example, generating the drawing of the component is an activity, again revising of that drawing is another activity in the Shop drawing stage.Preparing the material list based on that approved drawing is an activity and placing the order is another activity.Here, the number of the orders is a cost driver in the total supply chain cost of weekly prefabricated supply.
Again, in the prefabrication plant, preparing the fabrication is an activity and number of the production run is the cost driver of that activity.The other activities in prefabrication plant include ordering the raw component, assembling the fabricated component as per drawing, or even moving the component to the assembly site.Then, the corresponded cost drivers are the number of purchased orders of the raw component, the working hours required for assembling the component, and the working hours needed in the movement of the component in the assembly yard.Furthermore, the number of the deliveries is a cost driver, and delivery the fabricated component in the main project location is the activity.Thus, total activities can be identified in the project.Let j denote the activity index, m denote the number of activity, i denote the resource index, l denote the number of resources available for the activity j,   denote the volume of the cost driven activity,   denote the unit cost of the resource, and   denote the rate consumption for the resource i by the activity j.
The cost model is constructed by determining the volume of cost driver (  ), workforce utilization rate as per activity (  ), and unit cost of each workforce (  ).The total weekly work of component fabrication and supply to the construction site is divided into three significant steps including shop drawing, prefabrication, and installation.Each of these three steps consists of several activities, and each activity or each cost driver had a different value in the ABC driven model.The number of the prefabricated construction activity is shown in Table 1.
Therefore, the total weekly cost can be predicted to be

Cost Analysis
Similar to the ABC driven method [12], the model ( 2) can predict actual cost accurately and stipulate a clear understanding of the cost occurring factor associated with the stakeholders.Senior management executives can get a distinct instruction, in which task consumes most of the financial figure in the total supply chain cost and activity should be adjusted to reduce the overall cost.
Company decision-makers will also know about the resource utilization in the weekly supply chain cost.Managers can figure out if any resources are underutilized or overutilized.Task sharing technique can also be applied to reduce the overall cost.On the other hand, from the rate consumption of the resources table, managers can also look at how much time it may need to complete any activity by a resource.Our model provides an opportunity to work on working hours to minimize the total cost by implementing any process improvement or reducing any additional work time in a changing environment.Many optimization methods such as those in [15][16][17][18] can be implemented to obtain the optimal cost.
One of the main hurdles of implementing the supply chain cost model ( 2) is the information sharing in between the cross-functional stakeholders.Sometimes, many industries are unwilling to share their resource data with other company.Similarly, the General Contractor may not share their Labour wages to the Speciality Contractor.But the success and effectiveness of this cost model depend upon information transparency between stakeholders.As more information is shared, the top management can enhance the planning capabilities as well as revealed cost reduction scopes.In this regards, any trade agreement or contract may be used in the shake of the overall performance of the project.

Numerical Example
In this example, we consider a counterpart of the example in [4].In our scenario, we assume that we also have a 19story residential building and 16 story office building in Perth, Australia.Prefabricated components used in this project are manufactured in a plant located 27 miles apart from the project site.The prefabricated components are assembled in an assembly site located near the plant.We also use 20-ton heavy duty trucks to transport the prefabricated component to the project site.Table 2 is the list of activity and its correspondence weights on the total weekly cost, adopted from [4].
To perform those activities or tasks, several resources personnel are involved.In this model, that manpower is represented by five stakeholders: Architect/Structural firm, General Contractor (GC), Specialty Contractor (SC), and Prefabrication Plant and Mill (Driver).These stakeholders executed the total work of this projects such as (1) design, review, and approval of the component drawing, (2) manufacturing and assembling of raw component, (3) transportation, and (4) site installation.The general contractor who is responsible for the total construction of the project assigned a specialty contractor and a component fabricator.The component fabricator prepared the component from the raw component by cutting and bending technology.The specialty contractor ties up those cut pieces of raw components in the assembly yard as per the approved drawing of the general contractor.Then the prefabricated component is transported to the site.If any error is identified in the supplied component by the general contractor, the specialty contractor had to reorder the fabricator to rectify the mistake.Table 3 shows the list of manpower, their functional responsibilities, and respective salaries (on an hourly basis).
The utilities and the prices consumed in the component fabrication are listed in Table 4.
Besides, the weekly direct material cost as per their consumption and unit price will be shown in Table 5.
These Australian data are collected from different local sources to crosscheck the weekly component supply chain cost in Australia.Information is collected on sample basis for research only.We choose local salary rates for structural engineers, project managers, construction civil engineers, construction workers, construction managers, structural drafter, truck drivers, manufacturing engineers, and so on.The unit rates for utilities are $0.1965KWH (electricity), $6.03 / ft 2per week (assembly yard rent) $1.499 per litre (diesel), and $0.312 per litre (propane).The raw material prices are $1450 per ton for raw component and $160 per ton for scrap component.In this scenario, we consider that the uncertain cost is the 5% of the weekly deterministic cost.Using (2), we can predict that the weekly cost of the prefabricated supply chain is 140,490 AUD.

Conclusion
In this paper, a new model is established to predict the supply chain cost of a prefabricated building construction project under an uncertain environment.A virtual Australian

Figure 2 :
Figure 2: The Relationship of the activities and the cost drivers.

Table 1 :
Number of prefabricated construction.

Table 4 :
Utility rate for consumables.

Table 5 :
Raw material price.Ton project case is provided to verify the cost model.All data are collected from the different source of the internet on a random sample basis.The proposed model can be used in the future to estimate the weekly prefabricated component supply chain cost.More detailed analysis of cost calculation can be in the further scope of the study.The model can also allow to analysis the other cost of any prefabricated construction project.