Development of Entering Order and Work-Volume Assignment Algorithms for the Management of Piping Components in Offshore Structure Construction

Abstract

In the early 2010s, with rising oil prices and increasing purchase orders for offshore structures for deep-sea resource development, the shipyards that took these orders suffered unexpected losses. Unlike the construction of commercial carrier vessels, the construction of offshore structures necessary to develop deep-sea resources is difficult to manage due to the complexity of the outfitting process of the topside structure, which is a plant for gas and oil production and treatment. Piping components in particular, which comprise most of the design items, are difficult to manage because they involve 2 to 3 times the man-hours and up to 10 times the quantity of items compared to commercial carrier vessels. Due to not only high man-hours and quantity but also large fluctuations caused by design changes and long procurement lead times, process delays that result in delayed compensation frequently occurred. In response, Samsung Heavy Industries developed an integrated management system for piping components. This study describes the entering order optimization algorithm and work-volume assignment optimization algorithm, which are the core algorithms of this system. The entering order optimization algorithm determines the optimal installation order considering the procurement status of the piping components and the installation readiness status of the installation work site, through which it determines the entering order of the piping components. The algorithm seeks to accelerate the completion rate of installation of the piping components. Next, to minimize delivery delays of sub-contractors to the shipyard, this study developed a work-volume assignment optimization algorithm that can equalize the load on multiple sub-contractors considering the raw material readiness status and the production capacity of the sub-contractors, in terms of materials that must be ordered from external sub-contractors among the piping components whose entering order was determined. Finally, applying the algorithm developed using actual shipyard data resulted in an accelerated completion rate of installation and improved balance of load in terms of volume assigned to the sub-contractors.

1. Introduction

With the increasing deep-sea development of energy resources for oil and gas, the role of shipyards in charge of drilling vessel and floating platform construction are becoming more important1. However, compared to previously constructed commercial vessels (oil carrier, container carrier, bulk carrier, etc.), these offshore structures face construction challenges due to the outfitting of the plant (topside structure) that processes gas and oil. According to Back, et al. [1], large shipyards in Korea suffered huge losses due to the offshore structure business. Reports have pointed the complexity of the outfitting process as the key factor affecting these losses [2].

Especially, pipes used to manufacture the plant (topside structure)2 require 2 to 3 times as many man-hours as commercial carrier vessels [1]. For example, compared to the container vessle’s outffiting man-hour of about 15%, the FLNG’s outffiting man-hour is about 30–40%. Also, with respect to the number of piping components, general transportation vessels require approximately 10,000 pipes, whereas mega liquid gas carriers require 20,000 [3]. However, an offshore structure requires over 100,000 pipes, which is 5 times the amount for mega gas carriers [4]. As a result, offshore structures are difficult to assemble owing to the huge amounts of piping components and their complex connection relationships, which unavoidably raises the complexity of procuring and installing piping components. This problem, which severely threatens the profit structure of large shipbuilders that construct offshore structures, arises from insufficient experience in constructing new types of offshore structures [5]. In particular, inadequate support systems and standardization necessary to manage the process of offshore structure construction leads to this problem [6,7].

Studies on outfitting management including piping components are active within the areas of construction and plant engineering as well. However, if the scope is limited to shipbuilding within the shipbuilding industry, then representative prior research includes the following studies.

First of all, the several studies were conducted regarding the order of installation of outfitting items.

In the research of Lee [8], a five-step technique of focusing improvement included the DBR methodology of the theory of constraint (TOC) and established a solution for delivery delays to prevent delays in the delivery of piping components. This study focused on finding the constraint process and argued that a solution to the pharmaceutical process could mitigate the overall supply chain problems.

Dong, et al. [9] proposed a flexible two-step queuing network model for the planning and accurate execution of the outfitting material installation process. The developed model uses the optimal dynamic control policy and the Markov decision process to obtain the optimal cost. The researchers developed a regression model that calculates the threshold policy empirical approach using data from both dynamic and static models. The results demonstrated that the heuristic model’s performance was very close to the optimal value.

Choi and Woo [10] proposed an algorithm that determines the installation order of outfitting materials by considering the process parameters, weights, and installation constraints. They developed an application program for the algorithm and compared it with the outfitting material installation performance in an actual offshore structure, thus verifying the accuracy of the algorithm. Using this study’s results to define the installation order of the outfitting materials, the plan’s accuracy was improved.

However, these studies are studies that solve the problem of determining the optimal order under the assumption that materials and work conditions are determined, and do not present a plan to cope with the variability of the installation state at the work site.

Next, the following studies were conducted on the procurement between the shipyard and sub-contractor.

Wei and Nienhuis [11] proposed an automatic sequence generation method for planning the manufacture of outfitting materials between a shipyard and a manufacturing sub-contractor of the outfitting materials. Based on the results of a field survey, they proposed a mathematical model with parameters of material type, weight, size, installation location, and minimum working distance. The field survey results were analyzed using an analytical hierarchy process (AHP), and the order was determined using a computer-aided design model. They analyzed the work relationship from production to installation and developed a lead time prediction algorithm.

To reduce rework due to scheduling inconsistencies between the installation yard and the manufacturing supplier of the outfitting materials installed on a ship, Rose, et al. [12] proposed a mathematical model to ensure scheduling suitability. They also posed the problem of outfitting material production scheduling using a heuristic algorithm and evaluated the algorithm’s suitability. The algorithm enables manufacturing suppliers to determine priorities for production and meet constraints that minimize transportation times for installation.

Chen, et al. [13] applied a routing optimization technique to comply with material supply schedules in shipbuilding. By defining the outfitting material supply problem as a complex vehicle routing problem, they considered the constraints on capacity and various manufacturing sites. They optimized material assignment using a multi-population genetic algorithm (MPGA) and improved delivery compliance by 71% in comparison to the existing dispatching rules. This is an example of using a genetic algorithm to improve the dispatching rules for delivery in the outfitting material supply problem. However, since only the capacity of the manufacturing site is used as a constraint, this optimization technique has limited applicability.

To supply outfitting material pallets on time, Zhao, et al. [14] developed a mathematical model using a genetic algorithm that can determine the supply order required to optimize the search order for outfitting material pallets. They proposed a mathematical model for picking and batching outfitting material pallets and applied a genetic algorithm that considers the picking characteristics in minimizing delays in the delivery of outfitting materials. In an example application, their model improved compliance with a delivery date by 68% in comparison to entering the product based on the delivery date.

These studies about procurement between companies can be said to be researches about defining a mathematical model and deriving an optimal solution in consideration of the required quantity and characteristics of the sub-contractor. However, since a more improved method was required in considering the physical properties of materials and urgency rate of the constraints related to the optimization of work-volume assignment in this study, the mathematical model (integer linear program) was selected for the optimization through a review of previous researches.

In terms of the planning and scheduling system, a number of studies can be found outside of the shipbuilding industry. The main trend is the material requirement planning (MRP) methodology developed by Rolls Royce and General Electric in the 1950s, and academically established by Joseph [15]. Since then, it has evolved into MRP II, including master planning, rough-cut capacity planning, and capacity requirement planning [16]. In addition, this planning methodology has been developed into enterprise resource planning (ERP) today and spread to various industries [17]. Moreover, a number of patents related to research using MRP as a core algorithm have also been invented [18,19,20]. Furthermore, based on these backgrounds, various types of planning systems are commercially used today [21,22,23,24,25]. Most of the planning systems with a MRP algorithm as the core are easy to apply to mass production industries where the product structure is standardized in the bill of material (BOM) and procurement or production lead times for items constituting the BOM are determined.

However, it is impossible to apply these existing planning methodologies in the shipbuilding field of the order-taking industry. In particular, in order to establish a planning system in a shipyard, it is necessary to link with the existing design system and reflect the shipbuilding production planning system [26]. However, the previously MRP-cored planning systems could not reflect the design system (e.g., Tribon or Aveva marine) and BOM structure of the shipbuilding sector, and also failed to customize into the shipbuilding production planning system. Therefore, it is very common for the shipbuilding industry of a certain size or larger, where the information system investment is possible, to use their own self-developed planning system.

2. Objective

The target shipyard has been developing an integrated management system for the piping components management system3 as a part of the target shipyard’s planning and scheduling system. The integrated management system for piping components seeks to optimize the installation order and work-volume assignment to sub-contractors considering the material readiness status, installation readiness status, and work-load estimation of sub-contractors. Figure 1 shows a configuration of the target management system.

This study aims to develop an entering order4 optimization and work-volume assignment optimization algorithms for the integrated management system for piping components. The scope of this paper is limited to pipes, which have the greatest impact on process delays among the various types of piping components (pipes, supports, flanges, valves, etc.).

For the first algorithm, the entering order optimization, an entering order optimization method is needed that considers the installation readiness status. Since the test process (the last process in the piping component installation) takes the longest amount of time, the higher the installation rate of the continuously connected piping components is, the earlier the testing process can be completed, thereby minimizing process delays. If the entering order is determined without considering the installation readiness status, then piping components that cannot be installed are entered, thus increasing the congestion of the installation site or preventing piping components that can be installed from being entered and delaying the installation of other piping components that have a connection relationship with that item. To accelerate the completion rate of piping components, an entering order optimization algorithm must be developed that considers the installation readiness status.

Next, the work-volume assignment optimization algorithm is required for a balanced procurement between shipyards and sub-contractor manufacturers where piping components are installed. Even though the shipyard determines the optimal entering order, process delays are unavoidable if the sub-contractors cannot meet the delivery time of each piping component [27]. The most important part of the decision process for the timely procurement of piping components is the assignment of work-volumes among the sub-contractors. Due to the inefficiency of the existing assignment methods, which are performed manually, firms require a method for systematically assigning production work-volumes based on actual process data. To optimize the assignment of work-volumes for piping components to sub-contractors, an algorithm must be developed that assigns the work-volumes according to the capacity and work-load constraints of each sub-contractor.

The configuration of this paper is as follows. Section 3 describes the developed algorithm. In detail, Section 3.1 describes the installation readiness status and entering of the order optimization algorithm for optimizing the entering order, and Section 3.2 describes the work-volume assignment and work-volume assignment optimization algorithm. Section 4 describes the results of applying the developed algorithms. In detail, Section 4.1 describes the application results of the entering order optimization algorithm and Section 4.2 describes the application results of the work-volume assignment optimization algorithm.

3. Algorithm Development

3.1. Entering Order Optimization Algorithm

In the shipyard, the installation readiness status of piping components is referred to as the piping installation status. When installing piping components, installation work can be started when at least three consecutive pipes are ready. An algorithm that determines the entering order is required to maximize the number of pipe materials that can be completely installed in order to minimize the waiting materials.

As illustrated by the example in Figure 2, the number of pipes that can be completely installed varies depending on which pipes are selected to be entered among the unentered piping components. Therefore, the number of pipes that can be installed depends on the completion rate of installation, which varies with each pipe’s entering order and can be quantified based on the connection relationships. Suppose, for example, that for the status represented on the top of Figure 2, two pipes remain to be installed as indicated by the empty gray boxes. To increase the installation completion rate, it is necessary to determine which of these two piping components should be installed first and to determine the entering order based on this. In Case 1, the number of piping components that can be completely installed increases to four as the No.1 material is entered, whereas in Case 2, the number of piping components that can be completely installed is three (not considering the end pipe). The number of piping components that can be completely installed is influenced by the number of piping components already installed. Therefore, if the entering order changes, depending on the status of the pipes already installed, the number of piping components to be completely installed will be different. This impacts the planning of the following test process. The test process is a major process that takes a long time; therefore, the higher the initial completion rate is secured, the lower the probability of the process delay is.

Based on this, the algorithm for the entering order can be set up as shown in Figure 3. The installation status of each pipe is checked, and the number of pipes that can be completely installed is calculated, taking into consideration the connection relations among pipes. The number of pipes that can be installed is calculated, and the entering order corresponding to the highest number of pipes that can be installed is determined. The detail algorithm of connection relation identification from CAD is added in Appendix A.

This sorting algorithm can be set up as shown in Figure 4, where P indicates the connection relationships among pipes as a matrix that can reflect the connection relation information from the CAD program. S represents the current installation status as a matrix. X represents the matrix that assumes the receipt of each installation pipe. The number of items that can be completely installed is found by changing the values in the X matrix. L indicates the final calculated value of the number of pipes that can be completely installed for each pipe type. A pipe is considered to be completely installable if the value of L is 2 or more. For the L matrix to have a value of 2 or more, it must also be possible to install the surrounding connected pipes. The total number of pipes that can be installed when the $j^{th}$ item is received is calculated, and the receipt order is determined by ranking the calculated values in descending order.

The proposed algorithm can be expressed by (1)–(3). The matrix that represents the possibility of connection, depending on the receipt of a pipe, was defined as P*. To calculate the P* matrix, S, which was defined as a vector, was redefined as an N $\times$ N square matrix. Thus, the P* matrix can be calculated as follows:

$$\begin{array}{l}{P}^{*}=\left[\begin{array}{c}{P}_1^{*}\\ \begin{array}{c}{P}_2^{*}\\ ⋮\end{array}\\ P_N^{*}\end{array}\right]=\left[\begin{array}{c}{s}_1·P_1\\ \begin{array}{c}{s}_2·P_2\\ ⋮\end{array}\\ s_N·P_N\end{array}\right]=\left[\begin{array}{ccccc}{s}_1& 0& 0& \dots & 0\\ 0& s_2& 0& \dots & 0\\ 0& 0& s_3& \dots & 0\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ 0& 0& 0& \dots & s_N\end{array}\right]\left[\begin{array}{ccccc}{p}_{11}& p_{12}& p_{13}& \dots & p_{1N}\\ p_{21}& p_{22}& p_{23}& \dots & p_{2N}\\ p_{31}& p_{32}& p_{33}& \dots & p_{3N}\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ p_{N1}& p_{N2}& p_{N3}& \dots & p_{NN}\end{array}\right]\\ =\left[\begin{array}{ccc}{s}_1{p}_{11}& \dots & s_1{p}_{1N}\\ ⋮& \ddots & ⋮\\ s_N{p}_{N1}& \dots & s_N{p}_{NN}\end{array}\right]\end{array}$$

(1)

Matrix P represents the connection among pipes, which is extracted from the CAD model, and matrix P* is the connection among pipes that are installable, determined by considering the incoming status of each pipe. If the value of the S matrix is 0, the corresponding row of the P* matrix has a value of 0. When the current state of the installed pipes is confirmed (represented by $S$), the number of installable pipes can be represented by vector L, as shown in (2). Each element of vector L represents the number of items that are installable.

$$L=\left[\begin{array}{c}{l}_1\\ \begin{array}{c}{l}_2\\ ⋮\end{array}\\ l_N\end{array}\right]=P^{*}·S=\left[\begin{array}{ccc}{s}_1{p}_{11}& \dots & s_1{p}_{1N}\\ ⋮& \ddots & ⋮\\ s_N{p}_{N1}& \dots & s_N{p}_{NN}\end{array}\right]\left[\begin{array}{c}{s}_1\\ \begin{array}{c}{s}_2\\ ⋮\end{array}\\ s_N\end{array}\right]$$

(2)

Vector $S$ is updated as $S_j^{\prime }$ when the $j^{th}$ pipe is received. The number of additional connected pipes ($L_j$) can be expressed as shown in (3) when pipe j is added:

$$L_j=\left[\begin{array}{c}{l}_1\\ \begin{array}{c}{l}_2\\ \begin{array}{c}⋮\\ l_j\\ ⋮\end{array}\end{array}\\ l_N\end{array}\right]=P^{*}·S_j^{\prime }$$

(3)

$L_j$ is the number of pipes that can be connected to the already installed pipes when the $j^{th}$ pipe is installed. Among the elements of this calculated vector $L_j$, the largest value is defined as $M_j$. Accordingly, as $M_j$ increases, more pipes are connected, thereby raising the entering priority. A simple example is described in Appendix B.

3.2. Work-Volume Assignment Optimization Algorithm

After the entering order is determined, the work-volume must be assigned to the sub-contractors (sub-contractors) who manufacture the piping components. Conventionally, work-volumes of piping components are mostly assigned manually or depend on the experience of the operator. However, with consistent delivery delays, it was determined that each sub-contractor’s unbalanced workload had the greatest impact. This highlights the necessity of rationally assigning work-volume.

To assign work-volumes, the production capacity of each sub-contractor should be evaluated first. Production capacity was defined as the number of units that can be processed per day. To assign the work-volume that can be processed by each sub-contractor, the slot concept, as shown in Figure 5, was introduced. Each slot represents the production capacity of a sub-contractor and is filled with the work-volume. The daily work status can be monitored based on the status of each slot. The work-volume remaining in the current slot was calculated as the total work-volume of materials, depending on the production site, from the start of production to the final production stage. The work-volume assignment is performed daily with newly created work-volumes from the design stage.

The entire process of work-volume assignment can be explained as follows. First, the system evaluates the production capacities of each sub-contractor. It then calculates the assignable work-volume by subtracting work-in-process (WIP) from the previously calculated production capacity. Then, the assignment of the 1st phase is conducted so that the workload is evenly distributed among the sub-contractors with respect to the assignable work-volume. The additional work-volume is assigned by considering the production capacity of each sub-contractor from the 2nd phase sequentially until the completion of work-volume assignment.

The linear optimization problem was defined to assign the work-volume (the volume unit is defined as the welding length in this study) to the slots of each sub-contractor. Linear programming involves the optimization of linear objective functions while satisfying the given linear constraints. A linear program consists of decision variables, an objective function, and constraints. In an optimization problem, the decision variables represent the quantities to be determined; they should minimize or maximize the objective function, which comprises the linear function of the decision variables. The decision variables must satisfy the constraints, i.e., the constraints or requirements of the system. The constraints must comprise the linear function of the decision variables and be expressed as an equality or inequality [28]. In general, in linear programming, integer linear programming is applied when all of the decision variables are integers, and mixed-integer linear programming when only some of the decision variables are integers. This study applied mixed-integer linear programming because the decision variable is mixed with integer and non-integer value.

The goal of the optimization was to balance the work-volume assigned to each sub-contractor based on their production capacity. To this purpose, a unit workload was defined to determine whether the work-volume assigned to a manufacturing sub-contractor was appropriate. Here, the unit workload5 of a certain pipe is defined as the work-volume per day (m/day). Moreover, the condition whether the given pipe order could be manufactured by the sub-contractor, based on the product material and the detailed process required for the production is considered. Then, the production capacity6 was defined as the same unit with a unit workload. The unit workload defined in this way is reflected in $cum{W}_{i,t}$, which is the sum of workloads allocated to sub-contractor $i$ at time $t$. In addition, the production capacity is allocated as the value of the sub-contractor’s production capacity defined as $OD{C}_i$.

The optimization model was developed as follows with the dicision variables and model parameters those are shown in Box 1:

(1)

Difference in the ratio of work-volume assigned to the production capacity among the sub-contractors was minimized.

(2)

Difference in the ratio of work-volume assigned to the work-volume by urgency level among the sub-contractors was minimized.

(3)

Constraints are applied requiring that any piping component be assigned to only one sub-contractor and that all piping components should be assigned.

Box 1. Decision variables and model parameters.

• Decision variables

• $x_{p,i} \in \left\{0,1\right\}$: Indicates whether a product has been assigned to a manufacturing sub-contractor. One pipe must be assigned to one manufacturing sub-contractor. P refers to the product, and i refers to the manufacturing sub-contractor.
• $LO{D}_{i,j,t}$: Positive difference in the assigned workload required at time t for manufacturing sub-contractors i and j.
• $LU{D}_{i,j,t}$: Negative difference in the assigned workload required at time t for manufacturing sub-contractors i and j.
• $I{D}_{i,t}= LU{D}_{i,j,t}- LO{D}_{i,j,t}$: Maximum difference in the ratio of the assigned workload required at time t for manufacturing sub-contractors i and j.
• $EO{A}_i$, $EO{B}_i$, $EO{C}_i$: Positive difference in the ratio of normal, quasi-urgent, and urgent materials to the total assigned process requirements of the assigned materials for manufacturing sub-contractor i.
• $EU{A}_i$, $EU{B}_i$, $EU{C}_i$: Negative difference in the ratio of normal, quasi-urgent, and urgent materials to the total assigned process requirements of the assigned materials for manufacturing sub-contractor i.

• Model parameters

• $pos{s}_{p,i}$: Whether manufacturing sub-contractor i can produce material p; set to 0 or 1, depending on the material type.
• $a_p$, $b_p$, $c_p$: Whether the urgency of the delivery request for material p is normal, quasi-urgent, or urgent, expressed as a normal, b quasi-urgent, or c urgent.
• $r_a$, $r_b$, $r_c$: Ratio of normal, quasi-urgent, and urgent workloads among the workloads required for the entire assigned process.
• $s{d}_p$, $e{d}_p$: Start and end dates of the manufacturing process of material p.
• $w_p$: Required process workload of material p.
• $cum{W}_{i,t}$: Total workload already assigned due to the previous assignment result on date t for manufacturing sub-contractor i.
• $w_1$,$w_2$,$w_3$, $w_4$: Weights expressing the importance of each term in the objective function.
• $OD{C}_i$: Production capacity of manufacturing sub-contractor i.

Using the decision variables and parameters defined above, the objective function was expressed as shown in (4). The objective function minimizes the difference in the workload between each sub-contractor, as well as the difference in work-volume for each urgency level.

$$\begin{array}{c}min\{w_1{\displaystyle {\displaystyle \sum }_i}{\displaystyle {\displaystyle \sum }_t}I{D}_{i,t}+ w_2{\displaystyle {\displaystyle \sum }_i}\frac{EO{A}_i- EU{A}_i }{r_a{{\displaystyle \sum }}_p{w}_p}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ w_3{\displaystyle {\displaystyle \sum }_i}\frac{EO{B}_i- EU{B}_i }{r_b{{\displaystyle \sum }}_p{w}_p}+ w_4{\displaystyle {\displaystyle \sum }_i}\frac{EO{C}_i- EU{C}_i }{r_c{{\displaystyle \sum }}_p{w}_p}\}\end{array}$$

(4)

The following conditional functions were developed to express the constraints on the objective function defined above. First, there must be at least one sub-contractor who can produce each pipe; this constraint is expressed by (5). Next, one pipe must be assigned to only one sub-contractor; this constraint is expressed by (6). (7) expresses the difference in the workload assigned to the sub-contractors, which must be a positive value. (8) expresses the difference in the ratio assigned for each production urgency level, which must also be a positive value.

$$x_{p,i} \le pos{s}_{p,i}$$

(5)

$${\displaystyle \sum }_i{x}_{p,i}=1$$

(6)

$$\begin{array}{l}\frac{\left(OD{C}_i-cum{W}_{i,t}-{{\displaystyle \sum }}_p\frac{1}{e{d}_p-s{d}_p }\times w_p\times x_{p,i} \right)}{OD{C}_i}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} - \frac{\left(OD{C}_j-cum{W}_{j,t}-{{\displaystyle \sum }}_p\frac{1}{e{d}_p-s{d}_p }\times w_p\times x_{p,j} \right)}{OD{C}_j}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} = LU{D}_{i,j,t}- LO{D}_{i,j,t} \le I{D}_{k,t}\end{array}$$

(7)

$$\begin{array}{c}{r}_a{\displaystyle {\displaystyle \sum }_p}\left(w_p\times x_{p,i}\right)- {\displaystyle {\displaystyle \sum }_p}\left(a_p\times w_p\times x_{p,i}\right)= EO{A}_i- EU{A}_i\\ r_b{\displaystyle {\displaystyle \sum }_p}\left(w_p\times x_{p,i}\right)- {\displaystyle {\displaystyle \sum }_p}\left(b_p\times w_p\times x_{p,i}\right)= EO{B}_i- EU{B}_i\\ r_c{\displaystyle {\displaystyle \sum }_p}\left(w_p\times x_{p,i}\right)- {\displaystyle {\displaystyle \sum }_p}\left(c_p\times w_p\times x_{p,i}\right)= EO{C}_i- EU{C}_i\end{array}$$

(8)

4. Results

To verify the effectiveness of the entering order optimization algorithm and work-volume assignment optimization algorithm presented above, the algorithms were applied to a case study using actual shipyard data.

4.1. Result of the Entering Order Optimization Algorithm

To verify the entering order optimization algorithm, this study analyzed a zone containing about 400 pipes.

Table 1. Comparison of the rate of installation-completed pipes.

Installation No.	0	50	100	200	300	400
Existing Method	0.0%	10.8%	15.5%	33.3%	62.9%	100%
Proposed Algorithm	0.0%	28.2%	49.3%	70.5%	93.5%	100%
Difference	0.0%	17.4%	33.8%	37.2%	30.6%	0.0%

shows the number of installation-completed pipes when applying the existing manual method and the proposed entering order optimization algorithm to a problem of determining the entering order for 400 pipes (there are 528 pipes in total, and 400 pipes to be installed). Expressed as a graph in Figure 6, the number of installation-completed pipes increases as the pipe installation proceeds. Compared to the existing method, the increase rate of installation-completed pipes sharply rises when applying the proposed entering order algorithm. This signifies that even if the installation of all pipes is completed at the same time, the more pipes that complete the installation early, the earlier the test process can be conducted, thus minimizing process delays. Hence, the test process, a major bottleneck process in offshore plant construction, can be started earlier and proceed more smoothly by securing more connection relationships early.

Figure 7, Figure 8 and Figure 9 show the results of the entering order algorithm for additional blocks. Figure 7 shows determining the entering order for 310 pipes (there are 482 pipes in total, and 172 pipes already installed), Figure 8 shows determining the entering order for 506 pipes (there are 761 pipes in total, and 255 pipes already installed), and Figure 9 shows determining the entering order for 620 pipes (there are 818 pipes in total, and 198 pipes already installed). As can be seen from each graph, it can be concluded that the outfitting delay of the corresponding block can be prevented by providing a sufficient time buffer for the late installation process such as a test by showing a high completion rate in all cases.

4.2. Result of the Work-Volume Assignment Optimization Algorithm

Next, to verify the effectiveness of the optimization algorithm of assigning work-volumes for which the entering order was determined, the algorithm was applied to an actual offshore structure. For the work-volumes of 11 sub-contractors, the work-volume instructions issued during a specific period were assigned and compared. The number of target pipes is 3254 and the total workload is 350,782 m. In addition, the urgent ratios are 0.7, 0.2, and 0.1 as normal, quasi-urgent, and urgent, respectively. The initial workload of each sub-contractor is assumed as 0. Moreover, the planned start and finish date of each pipe are also considered.

To compare the process loads of the sub-contractors after assigning work-volumes, the production capacity of each sub-contractor and the process state at the start of the comparison were set to the same value. If the work-volume assignment target was a special material type that could be allocated only to a specific sub-contractor, then no difference between the assignment methods could be identified. Therefore, only products with material types capable of production by at least two sub-contractors were considered in the comparison of assignment methods.

Table 2. Comparison of manual and optimization work-volume assignment results.

Sub-Contractor	Capacity (m)	Manual Assignment		Optimization Assignment
		Allocation	Workload	Allocation	Workload
A	53,000	39,270	74%	38,176	72%
B	25,000	22,950	92%	20,643	83%
C	105,000	89,474	85%	79,569	76%
D	10,500	1599	15%	7131	68%
E	33,200	23,201	70%	21,325	64%
F	45,000	18,886	42%	31,921	71%
G	22,500	15,950	71%	12,755	57%
H	63,500	24,773	39%	48,317	76%
I	18,500	10,586	57%	16,312	88%
J	78,000	73,562	94%	49,484	63%
K	35,000	30,531	87%	25,149	72%
AVG	-	-	66%	-	72%
STDV	-	-	0.25	-	0.089

compares the results of the operator’s assignment and that of the assignment algorithm. The 11 sub-contractors were classified from A to K, and the production capacity of each sub-contractor was evaluated in the same unit. As the difficulty of applying subjective judgment may increase with the increasing problem complexity for the manual assignment method, it was assumed that there were no WIP or inventory. Based on the production capacity of the sub-contractors, the algorithm was tested with the goal of equalizing the process load with respect to the production capacity.

For sub-contractors A, B, C, and E, the manual and algorithm work-volume assignment results were very similar. This was attributed to the fact that only two sub-contractors can manufacture most of the material types to be produced; therefore, there can be no large differences between the automatic and manual assignments. Overall, the average load factor of the sub-contractor companies increased by approximately 6% from 0.66 for the manual assignment to 0.72 for the algorithm assignment. The standard deviation of the process load factor decreased from 0.25 for the manual assignment to 0.089 for the algorithm assignment, indicating an increase in load leveling.

Since only sub-contractor A, C, E, and F can produce urgent orders, an additional analysis with urgency consideration is conducted with cases of A, C, E, and F.

Table 3. Comparison of manual allocation and automatic allocation results with respect to the urgency rate.

Sub-Contractor	Manual Allocation			Automatic Allocation
	U	Q	N	U	Q	N
A	41%	12%	47%	10%	20%	70%
C	4%	13%	82%	4%	14%	82%
E	50%	-	50%	5%	13%	82%
F	-	-	100%	7%	8%	85%
STDV	0.25	0.07	0.26	0.03	0.05	0.07

U: Urgent; Q: Quasi-urgent; N: Normal.

compares the work-volume assignment results with the urgency level for the four sub-contractors with urgent and quasi-urgent assignments. As the objective was to achieve a workload evening for each sub-contractor according to the urgency level, the standard deviations for each urgency level were compared. As shown in Table 3, the standard deviations were significantly reduced by assignment with optimization in comparison to the manual assignment.

Figure 10 compares the daily workload of manual and optimization algorithm application for emergency volume distribution during 10 days, that is the emergency planning period. In addition, Figure 11 shows the standard deviation of daily workloads among sub-contractors. On the first day of work, for example, the standard deviation of workload of each sub-contractor was 0.16 in the manual plan, but when the optimization algorithm was applied, the workload evening level was reduced to 0.05, increasing the level of load leveling. It can be seen that the overall workload deviation is improved even in the 2–10 day interval. This means that the work-volume has been assigned in a reasonable manner, and this means that the process at each sub-contractor is stabilized and the probability of supplying the product to the yard in a timely manner increases.

Using the entering order algorithm developed through this study, the order of pipe installation was determined according to the priority of installation. In addition, the order to be supplied by the sub-contractors was decided according to the order of installation determined in this way. While optimally assigning the work-volume to be produced through assignment optimization, the actual sub-contractors can maintain a uniform workload.

As a result, the integrated management system for piping components (Figure 1) was developed and it was possible to stably supply pipes without delaying the production period. By applying the developed system to the actual offshore structure construction, it was possible to obtain a result that the timely procurement rate, that was less than 50% before the system development, was improved to more than 90% after the system is developed.

5. Conclusions

Compared to commercial carrier vessels, offshore structures are more likely to suffer losses from process delays due to the complexity of the outfitting process in terms of construction. The piping components needed to manufacture the topside structure of offshore structures require 2 to 3 times the man-hours and 5 to 10 times the quantity of items compared to commercial carrier vessels, thus creating limitations in existing management methods.

To solve this problem, Samsung Heavy Industries developed an integrated management system for the procurement and installation of piping components. The integrated management system for piping components was developed to minimize process delays by monitoring the status of shipyards and sub-contractors and linking the design and management systems.

This study described the development of two key algorithms among the modules that constitute the integrated management system for piping components, that is, an algorithm that optimizes the entering order considering the installation readiness status, and an algorithm that optimizes the sub-contractors’ work-volume assignment of sub-contractors considering the workload estimation of the sub-contractors.

Furthermore, this study confirmed that applying the entering order optimization algorithm to actual piping components increased the completion rate of installation more than the existing manual method (the section with the largest difference showed a 30% completion rate). This accelerated installation completion rate increases the rate at which the test process (the greatest factor in process delays) can be started early, thereby helping minimize process delays.

Next, applying the work-volume assignment optimization algorithm to the work-volume assignment of sub-contractors improved the workload between sub-contractors by approximately 6% compared to the existing method (Table 2). In addition, it was confirmed that the workload balancing level was improved even for frequently occurring emergency orders. As a result, through the development of an integrated management system for piping components with optimization algorithms, the timely procurement rate could be achieved from less than 50% to more than 90%.

Future research will enhance the performance of the integrated management system for piping components by improving the accuracy of the procurement lead time prediction module to over 90% based on machine learning, which is in the testing stage, and applying it to the current fixed lead time-based systems.