A method for scheduling and constraint programming of cruise ship cabin assembly

Abstract

The application belongs to the technical field of cruise cabin construction scheduling management, and discloses a cruise cabin assembly scheduling constraint programming method, and the specific steps are as follows: a scheduling optimization model is constructed, and constraints, decision variables, storage modes, soft logic and deadline constraints of the model are designed; then a scheduling constraint programming model is constructed, and interval decision variables, sequence decision variables, six types of constraint relationships and optimization objectives of the model are designed, and finally, the two models are compared to realize a scheduling scheme with optimal project duration and cost. Under the premise of fully considering the key resource restrictions such as material storage space and work team, the application allows the parallel execution of processes in different units, applies constraint programming to find the optimal or feasible solution, and through example verification, it is proved that the cruise cabin project plan obtained after optimization can shorten the duration by 27.6%, proving the effectiveness of the model.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of cruise ship cabin construction scheduling management, and particularly relates to a cruise ship cabin assembly scheduling constraint planning method. BACKGROUND

[0002] Building a large cruise ship is a formidable challenge for the shipbuilding industry. Due to the great difficulty in design and construction, large cruise ships, together with large liquefied natural gas carriers and aircraft carriers, are known as the "three pearls" on the crown of the shipbuilding industry. One of the difficulties in manufacturing large cruise ships compared to ordinary ships is the on-board construction management of thousands of cabins. Each deck has a large number of cabins, and the main types of cruise ship cabins are interior rooms and balcony rooms. Due to the single type of large cruise ship cabins, the on-board construction process of most cabins is basically the same, and has the characteristic of repetitive construction projects. Therefore, the cruise ship cabin construction project scheduling can be classified as repetitive project scheduling. A repetitive project refers to a project that can be divided into several similar or identical construction units, and some or all processes need to be repeated on multiple construction units. In a repetitive project, the construction sequence of different processes in the same construction unit is determined by the priority relationship and cannot be changed; while the construction sequence of the same process in different construction units depends on the logical relationship of the process, which has fixed logic and soft logic. Fixed logic means that there is only one feasible construction sequence for the same process in different construction units, for example, the "concrete beam pouring" process in high-rise buildings must be performed layer by layer; in soft logic relationship, the construction sequence of the process can be adjusted between different construction units, and when the project resource conditions are met, the process on multiple construction units can be performed at the same time.

[0003] Cruise ship cabin construction requires construction on the deck. Under normal circumstances, the deck will be divided into six main vertical zones from the bow to the stern, and each main vertical zone can be regarded as a construction unit. Due to the characteristics of project repetition, the work team needs to perform the same process in different construction units. How to arrange the start time of each process and which work team is responsible is the key content of the project scheduling. At the same time, during the construction of the cruise ship, various types of construction are carried out on the deck, the construction space on the ship is limited, and the cabin construction needs to transport materials to the ship first and then perform the construction. The limited storage space restriction is another factor that needs to be considered. While considering the storage space restriction, integrating soft logic into the repetitive scheduling optimization model of the cruise ship cabin can help improve the work efficiency of the work team and the utilization rate of the storage space, thereby making the project progress more competitive in terms of time, space, cost, etc.

[0004] A mathematical optimization model is disclosed in the prior art for optimizing project duration in consideration of work break scheduling, assuming constant activity progress, maintaining work continuity, and allowing planned work breaks. However, the method is often used to schedule typical repetitive projects based on the Line of Balance (LOB) technique, and the cost of the project is not considered in the optimization process. Another prior art discloses a soft logic integrated into a time-cost trade-off and a flexible repetitive scheduling model, which allows the same activity to be performed in different construction units (all activities are performed simultaneously), sequentially (one after another), or partially in parallel and partially sequentially. Due to the combinatorial explosion of feasible solutions, the model applies constraint programming to quickly find the optimal or acceptable approximate solution, but does not consider the impact of storage space on construction planning at the construction site. Therefore, it is necessary to further study the project time-cost scheduling optimization problem considering the storage space and soft logic constraints. SUMMARY

[0005] In view of the existing prior art defects in the background art, the present application proposes a cruise ship cabin assembly scheduling constraint programming method, which considers the cruise ship cabin assembly scheduling problem with storage space constraints and soft logic, aims to determine the storage mode, construction duration and sequence of each process, work team allocation scheme, and construction sequence between construction units, so as to realize the optimal scheduling scheme of project duration and cost under the condition of meeting the storage space constraints, and the step process includes:

[0006] Step S1, constructing a scheduling optimization model of the cruise ship cabin assembly plan;

[0007] Step S1.1, defining the constraints and decision variables of the scheduling optimization model;

[0008] Step S1.2, designing the storage mode of the cruise ship cabin assembly plan, designing the project soft logic, and constructing the deadline constraint;

[0009] Step S2, constructing a scheduling constraint programming model of the cruise ship cabin assembly plan;

[0010] Step S2.1, defining the interval decision variables and sequence decision variables of the scheduling constraint programming model;

[0011] Step S2.2, designing six types of constraint relationships of the scheduling constraint programming model, including priority constraints, uniqueness constraints, storage mode constraints, process logic constraints, work team span constraints, and deadline constraints;

[0012] Step S2.3, defining the optimization objective of the scheduling constraint programming model;

[0013] Step S3, using the CP Optimizer tool in the CPLEX Studio software to solve the scheduling constraint programming model.

[0014] Preferably, in the step S1.1, the process of defining the constraints and the decision variables of the scheduling optimization model comprises:

[0015] ① Define the constraints as follows:

[0016] Based on the actual construction process of the cruise ship cabin construction project, the constraints of defining the scheduling optimization model include the following 7 constraints:

[0017] Constraint 1: Each work team can only execute one work procedure in each construction unit;

[0018] Constraint 2: All alternative work teams for each work procedure have the same size, that is, the activity duration of each work procedure remains unchanged regardless of which work team is selected;

[0019] Constraint 3: A work procedure pauses work after completing a construction unit and continues work from the next construction unit after a period of time;

[0020] Constraint 4: Determine the priority relationship between work procedures in each construction unit, including end-to-start, start-to-start, and start-to-end; wherein the end-to-start means that the next work starts after the previous work is completed; the start-to-start means that the next work starts after the previous work starts; and the start-to-end means that the time period during which the previous work starts and ends determines the progress of the next work;

[0021] Constraint 5: The duration of each work procedure is related to the storage mode and is determined;

[0022] Constraint 6: Determine the storage mode and the corresponding storage space;

[0023] Constraint 7: Do not consider the impact of learning effect in repeated projects;

[0024] Through the above constraints, the problem of cruise ship cabin assembly plan scheduling is converted into a scheduling optimization model of cruise ship cabin assembly plan, and it is ensured that the model can be solved, and the decision variables represent the content of the solution of the model;

[0025] ② Define the decision variables as follows:

[0026] x ijm represents that work procedure i, construction unit j selects the mth storage mode, when the condition is met, then the variable x ijm = 1, when the condition is not met, then the variable x ijm = 0;

[0027] y ijh represents the work order of the same work procedure, that is, first execute work procedure i in construction unit j, and then execute work procedure i in construction unit h, when the condition is met, then the variable yijh = 1, otherwise y ijh = 0.

[0028] x ik denotes that process i employs k teams, when the condition is satisfied, then the variable x ik = 1, otherwise x ik = 0.

[0029] Preferably, the step S1.2 specifically comprises:

[0030] The process of designing the storage mode is as follows:

[0031] The selected storage mode of each process and the number of employed teams are calculated, and the calculation formula is as follows:

[0032]

[0033] Wherein, M i denotes the selectable storage mode of process i, the set of processes I = {1, 2, 3,..., n}; the set of construction units J = {1, 2, 3,..., n}; the set of teams K = {1, 2, 3,..., n};

[0034] Formulas (1) and (2) are used to determine the selected storage mode of each process and the number of employed teams; formula (1) denotes the selection of the storage mode of each process i, which is summed up for all construction units j and all storage modes m, so that it is equal to 1, that is, the storage mode is selected; formula (2) denotes that the result of summing up all team numbers k is equal to 1, that is, the number of teams employed by each process i is calculated;

[0035] The corresponding priority relationship between processes among construction units is calculated, and the calculation formula is as follows:

[0036]

[0037] Wherein, s pj denotes the start time of process p in construction unit j, s ij denotes the start time of process i in construction unit j, M p denotes the selectable storage mode of process p, d pjm denotes the execution period of process p in construction unit j when the storage mode m is selected, K denotes the serial number of the team, x pk denotes that process p employs k teams, when team k is assigned to process p, then x pk = 1, otherwise x pk = 0, E denotes the set of process pairs, and J denotes the serial number of the construction unit;

[0038] Formula (3) shows that there is a priority relationship between the processes in the construction unit. The start time of process p plus its execution time must be less than or equal to the start time of process i, which ensures that the processes are performed in the correct order, i.e., process p is performed first and process i is performed later, so that each process pair (p, i) in set E satisfies the priority relationship;

[0039] The process of designing the soft logic of the project is as follows:

[0040] The start time relationship of the same process in different construction units is calculated, and the calculation formula is as follows:

[0041]

[0042] In the formula, s ij represents the start time of process i in construction unit j, s ih represents the start time of process i in construction unit h, x ik represents that process i employs k work teams, when a work team is assigned to process i, x ik = 1, otherwise x ik = 0, δ represents the scheduled deadline of the project, y ijh represents the work order of the same process, i.e., process i in the jth construction unit is performed first, and then process i in the hth construction unit is performed, when the condition is met, the variable y ijh = 1, otherwise y ijh = 0, M i represents the optional storage mode of process i, i represents the serial number of the process; d ijm represents the execution period of process i in construction unit j under the condition that the storage mode m is selected;

[0043] Formula (4) shows that for the same process i in different construction units j and h, based on whether it is performed by the same work team and the limitation of the deadline, the start time of the same process i in different construction units j and h is coordinated through the formula, the end time of construction unit h must be less than or equal to the start time of construction unit j, which is used to determine the start time relationship of the same process in different construction units;

[0044] The limitation on y ijh is performed, which excludes unreasonable association relationships between the same process in different construction units, and the calculation formula is as follows:

[0045]

[0046] Formula (5) shows that for each process i and construction unit h, the sum of y ijh must be less than or equal to 1, in order to limit unreasonable association relationships between the same process in different construction units;

[0047] For y ijh The restriction is made to ensure the reasonable association between processes in different construction units, and the calculation formula is as follows:

[0048]

[0049] Formula (6) indicates that for each process i and construction unit j, the sum of variables y ijh is less than or equal to 1, so as to ensure the reasonable association between processes in different construction units;

[0050] For x ik and y ijh , based on the case of employing different number of work teams and the association of process i between different construction units, the calculation formula is as follows:

[0051]

[0052] Formula (7) indicates that for each process i, the first term on the left side represents the case of employing different number of work teams, and the total number of all work teams employed by process i is calculated, and the second term represents the association of process i between different construction units;

[0053] The scheduling scheme is ensured to meet the soft logic by means of formulas (4)-(7);

[0054] ③The process of designing the deadline constraint is as follows:

[0055] The total time of the start time of process i in construction unit j plus its execution time is calculated, and the calculation formula is as follows:

[0056]

[0057] In the formula, EA represents the set of ending processes, each of which has no immediate process;

[0058] Formula (8) indicates that for each process i in the set of ending processes and construction unit j, the start time of process i in construction unit j plus its execution time is less than or equal to the total project duration t;

[0059] It is judged whether the total project duration is completed before the project deadline, and the formula is as follows:

[0060] t≤δ(9)

[0061] In the formula, δ represents the project deadline;

[0062] Formula (9) indicates that the total project duration is completed before the given project deadline;

[0063] The minimum cost min F1 and the minimum duration min F2 are calculated, and the calculation formula is as follows:

[0064]

[0065] minF2=T EA (11)

[0066] In the formula, LCR ik represents the daily labor cost when K working teams are employed in the project process i, SCR represents the daily material storage cost of a single storage site, sc m represents the number of storage sites occupied when the mth storage mode is selected, MCR ik represents the material cost rate when K working teams are employed in the project process, Q ij represents the workload of the sub-process i in the construction unit j, T EA represents the completion time of the last process.

[0067] Preferably, in the step S2.1, defining the interval decision variable and the sequence decision variable specifically includes:

[0068] ① The interval decision variable includes:

[0069] A ij , the interval variable related to the process i task in the construction unit j;

[0070] σ ik , the optional interval variable related to the kth group of working teams of the process i;

[0071] x ijk , the optional interval variable, representing the kth group of working teams for the process i in the construction unit j to execute the sub-process A ij ;

[0072] ② The sequence decision variable includes:

[0073] x ik , if x ik equals 1, it means that the process i selects k working teams, otherwise x ik equals 0;

[0074] x ijm , if x ijm equals 1, it means that the process i in the construction unit j executes the mth storage mode, otherwise x ijm equals 0.

[0075] Preferably, in the step S2.2, six types of constraint relationships of the scheduling constraint programming model are designed, specifically including:

[0076] ① The process of designing priority constraints is as follows:

[0077]

[0078] where endBeforeStart represents a constraint function, the end time of the previous process p in the construction unit j must be before the start time of the subsequent process i in the construction unit j, so as to constrain the sequence between processes, that is, to constrain the minimum delay time between the end of one interval variable and the start of another interval; A pj represents an interval variable related to the process p task in the construction unit j, A ij represents an interval variable related to the process i task in the construction unit j;

[0079] ②The process of designing the uniqueness constraint is as follows:

[0080]

[0081] where H ij represents a sub-process A ij assigned to each work team, X ijk represents that the process i in the construction unit j selects k work teams, represents the maximum number of work teams, and alternative represents a function for creating an alternative constraint between an interval variable and a set of interval variables in an array, that is, to constrain the sub-process A ij can only be selected from the set H ij to ensure that each sub-process is assigned to only one work team;

[0082] Formulas (13) and (14) are uniqueness constraints that ensure that each sub-process A ij is assigned to only one work team;

[0083] ③The process of designing the storage mode constraint is as follows:

[0084] According to the actual situation, the storage mode of the process is selected, and the calculation formula is as follows:

[0085]

[0086] where M i represents the storage mode that can be selected for the process i;

[0087] All storage modes that can be selected for the process i in the construction unit j are traversed and calculated, and the duration of the process i in the construction unit j is calculated, so as to ensure that the duration of each process matches the storage mode it performs, and the calculation formula is as follows:

[0088]

[0089] where lengthOf represents a function for returning the length of the specified interval variable;

[0090] (4) The process of designing the process logic constraints is as follows:

[0091] In the presence of soft logic, the process logic constraints require that all sub-processes assigned to the same work team be executed in sequence. The task range of each work team is divided by the formula, which is as follows:

[0092] Q ik = {X i1k ,...,X ijk ,...,X imk}(17)

[0093] where Q ik represents the set of all sub-processes assigned to the kth work team of process i, which is also called the interval sequence variable of the kth work team of process i; X ijk represents the selection of k work teams by process i in construction unit j;

[0094] After a unit time elapses between the execution of two consecutive sub-processes, the work team is moved from the current construction unit to the next construction unit, and the formula is as follows:

[0095]

[0096] where noOverlap represents a function for constraining a group of interval variables so that they do not overlap with each other, ensuring that different sub-process execution intervals related to processes and work teams do not overlap; M represents an m x m unit matrix, which is used to move the work team from the current construction unit to the next construction unit only after a unit time elapses between the execution of two consecutive sub-processes, i.e., to establish the rule of the interval between sub-process execution times using the unit matrix;

[0097] Equation (18) is a logic constraint, which represents that for all processes i and all work teams k, the set of sub-processes Q ik assigned to the kth work team of process i is constrained by the noOverlap function so that it does not overlap, and combined with the unit matrix M, it ensures that there is a unit time interval between the execution of two consecutive sub-processes, ensuring that the work team is moved from the current construction unit to the next construction unit;

[0098] (5) The process of designing the work team span constraint is as follows:

[0099]

[0100] where span represents a function for creating a span constraint between an interval variable interval and a group of interval variables in an array; σ ikdenotes a variable related to the kth work team of the ith process, which is an input of the span function;

[0101] Equation (19) is the work team span constraint, which is used to guarantee the final state of each work team, including whether it is selected, which processes are executed, and the start and end times;

[0102] The process of designing the deadline constraint is as follows:

[0103] T≤δ (20)

[0104]

[0105] where endOf denotes a function that returns an integer expression equal to the end of the interval variable if it exists, i.e., returns the end time of the task of the process in the construction unit; EA denotes the set of ending processes;

[0106] Equations (20) and (21) are deadline constraints, equation (20) guarantees that the total project duration t is less than or equal to the given deadline δ, and equation (21) ensures that the end time of each process in the set of ending processes in construction unit j is less than or equal to the total project duration t, ensuring that the project can be completed on time.

[0107] Preferably, in step S2.3, the process of defining the optimization objective of the scheduling constraint programming model is as follows:

[0108] The optimization objective of the scheduling constraint programming model is to calculate the objective function that minimizes the total cost and duration of the project, and its calculation formula is as follows:

[0109]

[0110] where ICR denotes the daily management cost of the project, |M i denotes the absolute value of the number of storage modes, t denotes the total project duration, I denotes the total number of processes, i denotes the process number, M i denotes the storage mode available for process i, m denotes the storage mode, k denotes the work team, and j denotes the construction unit.

[0111] Preferably, in step S3, the specific process is as follows:

[0112] CP Optimizer tool in CPLEX Studio software is used as its solution; when using CPOptimizer tool to solve the model, the optimal solution is constantly searched, unless the optimal solution is found earlier, otherwise all examples will use the best feasible solution at the end of 3 minutes of CPU time, and all calculation results are obtained using the default search strategy.

[0113] Compared with the prior art, the cruise ship cabin assembly scheduling constraint programming method has the following beneficial effects:

[0114] The cruise ship cabin assembly scheduling constraint programming method is proposed, a cruise ship cabin assembly scheduling constraint programming model is constructed, and the model is solved by using interval variables and constraint programming expressions; unlike existing research, the cruise ship cabin assembly scheduling constraint programming model can consider key resource conditions such as storage space and work teams while allowing process parallelism and sequential execution, and can consider the influence of storage space limitation on the construction period; then, the practicability and flexibility of the cruise ship cabin assembly scheduling constraint programming model are verified through a case study; the results show that the cruise ship cabin assembly scheduling constraint programming model is far superior to the cruise ship cabin assembly scheduling optimization model in providing a project schedule table, especially when dealing with more complex projects. BRIEF DESCRIPTION OF DRAWINGS

[0115] Figure 1 The method flowchart of the present application is shown in the figure;

[0116] Figure 2 The project schedule comparison chart of the constraint programming model and the scheduling optimization model is shown in the figure, wherein (a) is the project schedule chart of the constraint programming model, and (b) is the project schedule chart of the scheduling optimization model;

[0117] Figure 3 The project storage space occupation condition comparison chart of the constraint programming model and the scheduling optimization model is shown in the figure, wherein (a) is the project storage space occupation condition chart of the constraint programming model, and (b) is the project storage space occupation condition chart of the scheduling optimization model. DETAILED DESCRIPTION

[0118] The technical solutions in the embodiments of the present application will be further described in detail below with reference to the accompanying drawings of the embodiments of the present application. It should be noted that the described embodiments are only some of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of the present application.

[0119] In order to make the purposes, technical solutions and advantages of the present application clearer, the embodiments of the present application will be further described in detail below with reference to the accompanying drawings of the present application. In order to more clearly understand the above purposes, features and advantages of the present application, the advantages of the present application will be further described through the comparison of embodiments with reference to the accompanying drawings and specific embodiments.

[0120] The application provides a cruise ship cabin assembly scheduling constraint programming method, and a flowchart of the method is shown in the figure Figure 1 The steps of the method are described in detail as follows:

[0121] Step S1, constructing a scheduling optimization model of the cruise ship cabin assembly plan;

[0122] The scheduling optimization model of the cruise ship cabin assembly scheduling plan is constructed to solve the problem in a small scale, and the solving result is compared with the solving result of the subsequent constraint programming model, and the specific comparison includes:

[0123] Step S1.1, defining the constraints and decision variables of the scheduling optimization model;

[0124] Step S1.2, designing the storage mode of the cruise ship cabin assembly plan, designing the project soft logic and constructing the deadline constraint;

[0125] Specifically, the step S1.1 specifically includes:

[0126] ①The process of defining the constraints and decision variables of the scheduling optimization model is as follows:

[0127] Based on the actual construction process of the cruise ship cabin construction project, the scheduling optimization model is defined to be constrained, and the following seven constraints are set:

[0128] Constraint 1: Each work procedure in each construction unit can only be executed by one work team;

[0129] Constraint 2: All alternative work teams of each work procedure have the same size, that is, the activity duration of each work procedure remains unchanged regardless of the selected work team;

[0130] Constraint 3: Work interruption is allowed, that is, a work procedure is suspended after the completion of a construction unit, and continues to work from the next construction unit after a period of time;

[0131] Constraint 4: The priority relationship type between the work procedures in each construction unit includes end-to-start, start-to-start and start-to-end, wherein the end-to-start means that the next work starts after the previous work is completed, the start-to-start means that the next work starts after the previous work starts, and the start-to-end means that the time period of the start and end of the previous work determines the progress of the next work;

[0132] Constraint 5: The duration of each work procedure is related to the storage mode and is known;

[0133] Constraint 6: The storage mode and the corresponding storage space are known;

[0134] Constraint 7: The learning effect in repeated projects and the like is not considered.

[0135] The cruise ship cabin assembly scheduling problem is converted into a cruise ship cabin assembly scheduling optimization model by the above constraints, and the model can be solved, and the decision variables represent the content of the model solution.

[0136] ② Define the decision variables as follows:

[0137] x ijm indicates that the mth storage mode is selected for process i, construction unit j, when the condition is met, then the variable x ijm = 1, when the condition is not met, then the variable x ijm = 0;

[0138] y ijh indicates the order of the same process, i.e. first execute process i of the jth construction unit, then execute process i of the hth construction unit, when the condition is met, then the variable y ijh = 1, otherwise y ijh = 0;

[0139] x ik indicates that k working teams are hired for process i, when the condition is met, then the variable x ik = 1, otherwise x ik = 0.

[0140] Specifically, the step S1.2 specifically comprises:

[0141] ① The process of designing the cruise ship cabin assembly plan storage mode is as follows:

[0142] Calculate the selected storage mode for each process and the number of hired working teams, and the calculation formula is as follows:

[0143]

[0144] Where M i indicates the storage mode available for process i, the set of processes I = {1, 2, 3,..., n}; the set of construction units J = {1, 2, 3,..., n}; the set of working teams K = {1, 2, 3,..., n};

[0145] Formulas (1) and (2) are used to determine the selected storage mode for each process and the number of hired working teams; formula (1) indicates that the storage mode for each process i is selected, and only one storage mode can be selected. The formula is summed over all construction units j and all storage modes m, and the result is equal to 1, indicating that a storage mode is determined; formula (2) indicates that the result of summing all working team quantities k is equal to 1, i.e. the number of working teams hired for each process i is calculated;

[0146] The priority relationship between the processes in different construction units is calculated by the following formula:

[0147]

[0148] where s pj represents the start time of process p in construction unit j, s ij represents the start time of process i in construction unit j, M p represents the optional storage mode of process p, d pjm represents the execution duration of process p in construction unit j when the storage mode m is selected, K represents the serial number of a work team, x pk represents that process p employs k work teams, when work team k is assigned to process p, x pk = 1, otherwise x pk = 0, E represents a set of process pairs, and J represents the serial number of a construction unit.

[0149] The formula (3) represents the priority relationship between the processes in different construction units, and the start time of process p plus its execution time must be less than or equal to the start time of process i, which ensures that the processes are performed in the correct order, i.e., process p is performed first and process i is performed second, so that each process pair (p, i) in the set E satisfies the priority relationship.

[0150] The process of designing the soft logic of the project is as follows:

[0151] The start time relationship of the same process in different construction units is calculated by the following formula:

[0152]

[0153] where s ij represents the start time of process i in construction unit j, s ih represents the start time of process i in construction unit h, x ik represents that process i employs k work teams, when work team k is assigned to process i, x ik = 1, otherwise x ik = 0, δ represents the deadline of the project, y ijh represents the work order of the same process, i.e., process i in the jth construction unit is performed first, and then process i in the hth construction unit is performed, when the condition is met, the variable y ijh = 1, otherwise y ijh = 0, M i represents the optional storage mode of process i, i represents the serial number of a process; d ijm represents the execution duration of process i in construction unit j when the storage mode m is selected.

[0154] Formula (4) represents that for the same procedure i in different construction units j and h, based on whether it is executed by the same work team and the deadline constraint, the start time of them is coordinated by the formula, the end time of construction unit h must be less than or equal to the start time of construction unit j, for determining the start time relationship of the same procedure in different construction units;

[0155] For y ijh , the restriction is carried out to exclude unreasonable certain association relationship of the same procedure between different construction units, and the calculation formula is as follows:

[0156]

[0157] Formula (5) represents that for each procedure i and construction unit h, the sum of y ijh must be less than or equal to 1, to limit unreasonable certain association relationship of the same procedure between different construction units;

[0158] For y ijh , the restriction is carried out to ensure reasonable association relationship of procedures between different construction units, and the calculation formula is as follows:

[0159]

[0160] Formula (6) represents that for each procedure i and construction unit j, the sum of variables y ijh must be less than or equal to 1, to ensure reasonable association relationship of procedures between different construction units;

[0161] For x ik and y ijh , based on the case of employing different number of work teams and the association case of procedure i between different construction units, the calculation formula is as follows:

[0162]

[0163] Formula (7) represents that for each procedure i, the first term on the left side represents the case of employing different number of work teams, the total number of all work teams employed by procedure i is calculated, the second term represents the association case of procedure i between different construction units;

[0164] The scheduling scheme is ensured to meet the soft logic by means of formulas (4)-(7);

[0165] ③The process of designing the deadline constraint is as follows:

[0166] The total time of the start time of procedure i in construction unit j plus its execution time is calculated, and the calculation formula is as follows:

[0167]

[0168] where EA represents the set of ending activities, each of which has no successor activity;

[0169] Equation (8) represents that for each activity i in the set of ending activities and construction unit j, the start time of activity i in construction unit j plus its execution time is less than or equal to the total project duration t;

[0170] Equation (9) represents that the total project duration is completed before the project deadline;

[0171] t < δ (9)

[0172] where δ represents the project deadline;

[0173] Equation (9) represents that the total project duration is completed before the given project deadline;

[0174] Equation (10) represents that the minimum cost min F1 and the minimum duration min F2 are calculated as follows:

[0175]

[0176] min F2 = T EA (11)

[0177] where LCR ik represents the labor cost per day when K teams are employed for project activity i, SCR represents the material storage cost per day for a single storage site, sc m represents the number of storage sites occupied when the mth storage mode is selected, MCR ik represents the material cost rate when K teams are employed for project activity, Q ij represents the workload of sub-activity i, construction unit j, T EA represents the completion time of the last activity.

[0178] Step S2, a scheduling constraint programming model of the cruise ship cabin assembly plan is constructed;

[0179] The scheduling constraint programming model for solving the scheduling problem of the cruise ship cabin assembly plan is constructed, which can filter the definition domain of each variable through constraint propagation, eliminate values that may lead to infeasible or non-optimal solutions from the definition domain, and thus narrow the search range, specifically including:

[0180] Step S2.1, interval decision variables and sequence decision variables of the scheduling constraint programming model are defined;

[0181] Step S2.2, six types of constraint relationships of the scheduling constraint programming model are designed, including priority constraint, uniqueness constraint, storage mode constraint, process logic constraint, work team span constraint, and deadline constraint;

[0182] Step S2.3, the optimization objective of the scheduling constraint programming model is defined.

[0183] Specifically, the interval decision variable and the sequence decision variable of the step S2.1 specifically include:

[0184] ① The interval decision variable includes:

[0185] A ij An interval variable related to the task of process i in construction unit j;

[0186] σ ik An optional interval variable related to the kth group of work teams of process i;

[0187] x ijk An optional interval variable representing the kth group of work teams of process i in construction unit j performing sub-process A ij ;

[0188] ② The sequence decision variable includes:

[0189] x ik If x ik equals 1, it indicates that process i selects k work teams, otherwise x ik equals 0;

[0190] x ijm If x ijm equals 1, it indicates that process i in construction unit j performs the mth storage mode, otherwise x ijm equals 0.

[0191] Specifically, the step S2.2, the six types of constraint relationships of the scheduling programming model specifically include:

[0192] ① The process of designing the priority constraint is as follows:

[0193]

[0194] In the formula, endBeforeStart represents a constraint function, the end time of the previous process p in the task of construction unit j must be before the start time of the subsequent process i in the task of construction unit j, so as to constrain the order between processes, that is, to constrain the minimum delay time between the end of one interval variable and the start of another interval; A pj represents an interval variable related to the task of process p in construction unit j, A ijdenotes the interval variable related to the task of process i in construction unit j;

[0195] Equation (12) is a precedence relationship constraint. The precedence constraint refers to a time constraint, i.e., a process sequence constraint, which ensures that processes are constructed in a specified order;

[0196] ②The process of designing the uniqueness constraint is as follows:

[0197]

[0198] In the formula, H ij denotes the sub-process A ij assigned to each work team, X ijk denotes the set of work teams selected by process i in construction unit j, denotes the maximum number of work teams, and alternative denotes a function for creating an alternative constraint between the interval variable set in the interval variable (A ij ) and the array (H ij ), i.e., the constraint that sub-process A ij can only select one work team from the set H ij , ensuring that each sub-process is assigned to only one work team;

[0199] Equations (13) and (14) are uniqueness constraints that ensure that each sub-process A ij is assigned to only one work team;

[0200] ③The process of designing the storage mode constraint is as follows:

[0201] The storage mode constraint has two functions. One is to ensure that each process can only select one storage mode, i.e., equation (15); the other is to ensure that the duration of each process matches the storage mode it performs, i.e., equation (16);

[0202] According to the actual problem situation, the storage mode of the process is selected, and the calculation formula is as follows:

[0203]

[0204] In the formula, M i denotes the storage mode that can be selected by process i;

[0205] All storage modes that can be selected by process i in construction unit j are traversed and calculated, and the duration of process i in construction unit j is calculated to ensure that the duration of each process matches the matching degree of the storage mode it performs, and the calculation formula is as follows:

[0206]

[0207] where lengthOf represents a function for returning the length of the specified interval variable;

[0208] (4) The process of constructing the process logic constraints is as follows:

[0209] In the presence of soft logic, the process logic constraints require that all sub-processes assigned to the same work team be executed in sequence. The task range of each work team is divided by the formula as follows:

[0210] Q ik = {X i1k ,...,X ijk ,...,X imk}(17)

[0211] where Q ik represents the set of all sub-processes assigned to the kth work team of process i, which is also called the interval sequence variable of the kth work team of process i; X ijk represents the selection of k work teams by process i in construction unit j;

[0212] After a unit time elapses between the execution of two consecutive sub-processes, the work team is moved from the current construction unit to the next construction unit, and the formula is as follows:

[0213]

[0214] where noOverlap represents a function that constrains a set of interval variables to not overlap with each other, ensuring that different sub-process execution intervals related to processes and work teams do not overlap; M represents an m x m unit matrix, which is used to move the work team from the current construction unit to the next construction unit only after a unit time elapses between the execution of two consecutive sub-processes, that is, to establish the rule of sub-process execution time interval with the unit matrix;

[0215] Equation (18) is a logic constraint, which represents that for all processes i and all work teams k, the set of sub-processes Q ik assigned to the kth work team of process i is constrained by the noOverlap function to not overlap, and combined with the unit matrix M, to ensure that there is a unit time interval between the execution of two consecutive sub-processes, ensuring that the work team is moved from the current construction unit to the next construction unit;

[0216] (5) The process of designing the work team span constraint is as follows:

[0217]

[0218] where span represents a function that creates a span constraint between an interval variable interval and a set of interval variables in an array; σ ikdenotes a variable related to the k-th work team of the i-th operation, which is an input of the span function;

[0219] Equation (19) is a work team span constraint, which is used to guarantee the final state of each work team, including whether it is selected, which operations are performed, and the start and end times;

[0220] The process of defining the design deadline constraint is as follows:

[0221] T≤δ (20)

[0222]

[0223] where endOf denotes a function that returns an integer expression equal to the end of the interval variable if it exists, i.e., returns the end time of the task of the operation in the construction unit; EA denotes the set of end operations;

[0224] Equations (20) and (21) are deadline constraints, equation (20) guarantees that the total project duration t is less than or equal to the given deadline δ, and equation (21) ensures that the end time of each operation in the set of end operations in construction unit j is less than or equal to the total project duration t, ensuring that the project can be completed on time.

[0225] Specifically, the specific process of step S2.3 includes:

[0226] The process of defining the optimization objective of the scheduling constraint programming model is as follows:

[0227] The optimization objective of the scheduling constraint programming model is to minimize the total cost of the project consisting of the direct cost of the project and the storage cost of the project, and the duration of the project, mainly including the labor cost, material cost and storage cost of the project, while also considering the project duration; To comprehensively consider the two objectives of total cost and duration, an additional daily management cost is added to the project, converting the double-objective optimization problem into a single-objective optimization problem, which is beneficial to the solution of constraint programming, and the specific objective function is as follows:

[0228]

[0229] where ICR denotes the daily management cost of the project, |M i denotes the absolute value of the number of storage modes, t denotes the total project duration, I denotes the total number of operations, i denotes the operation number, M i denotes the storage mode available for operation i, m denotes the storage mode, k denotes the work team, and j denotes the construction unit.

[0230] Step S3, using CP Optimizer tool in CPLEX Studio software provided by IBM to solve the constraint programming model.

[0231] Specifically, the specific process of S3 is:

[0232] IBM provides CP Optimizer tool in CPLEX Studio software as its solution; when using CP Optimizer tool to solve the model, the optimal solution is searched constantly, unless the optimal solution is found earlier, otherwise all examples will use the best feasible solution at the end of 3 minutes of CPU time, and all calculation results are obtained using the default search strategy.

[0233] The specific case analysis of the application is described in detail in combination with the technical solutions and the drawings:

[0234] Figure 1 The method is a whole flowchart, and the project is divided into six construction units according to the deck main vertical division of the cruise ship. The construction of each unit cabin involves seven main processes, namely, marking (A), positioning of sanitary units (B), ceiling installation (C), wallboard installation (D), furniture installation (E), debugging (F) and inspection (G). Since the construction sequence of each process is variable among different main vertical divisions (units), the soft logic is suitable; assuming that the number of cabins in each unit is the same and the sub-process duration is fixed, the process sequence is 5 days, 7 days, 8 days, 10 days, 8 days, 2 days and 1 day respectively; increase the storage space and solve the problem by limiting the soft logic; the construction sequence of each unit is A-B-C / D-E-F-G, and the processes C and D have no sequence restriction, as long as the process B is completed, the construction can be started; and a total of 5 work teams can be selected;

[0235] According to the method of the application, a cruise ship cabin assembly scheduling constraint programming model is constructed, and six types of constraints are integrated into the solver of CP Optimizer tool in CPLEX Studio software provided by IBM for solving;

[0236] To illustrate the beneficial effects of the method of the application, the method of the application is compared with the cruise ship cabin assembly scheduling optimization model for testing. The results show that the plan obtained by the cruise ship cabin assembly scheduling constraint programming model provides a project duration of 92 days and a project cost of 2587300 RMB; the plan obtained by the cruise ship cabin assembly scheduling optimization model provides a project duration of 127 days and a project cost of 2866500 RMB;

[0237] Figure 2 The figure shows the project progress comparison of the project solved by the constraint programming model and the scheduling optimization model under the same experimental environment; Figure 2The abscissa of the figure represents the project duration, and the unit is day; the ordinate represents the construction process of different units, for example, [1, A] is the process A of the first construction unit; the project duration solved by the constraint programming model is 92 days, the project duration solved by the planning and scheduling optimization model is 127, and the project duration is shortened by 27.6%, which directly reflects the effect of the planning and scheduling optimization model on the project duration optimization;

[0238] Figure 3 The figure shows the comparison of the storage space occupation of the project solved by the constraint programming model and the planning and scheduling optimization model under the same experimental environment; Figure 3 The abscissa of the figure represents the project duration, and the unit is day; the ordinate represents the storage area usage quantity, and the unit is piece;

[0239] In summary, the cruise ship cabin assembly scheduling constraint programming method can process the project assembly scheduling problem in a limited space, can save the construction time of the cruise ship cabin, and can improve the utilization rate of the site resources; the method is also applicable to traditional construction engineering projects, and as long as there is a need for temporary material storage in the project, the method can be used to output a plan.

[0240] Although the preferred embodiments of the present application have been described, those skilled in the art can make further changes and modifications to the embodiments once they know the basic inventive concept. Therefore, the appended claims are intended to be interpreted as including all changes and modifications falling within the scope of the present application.

[0241] Obviously, those skilled in the art can make various modifications and variations to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalent technologies, the present application also intends to include these modifications and variations.

Claims

1. A method of cruise ship cabin assembly scheduling constraint programming, characterized in that, The method comprises the following steps: Step S1, constructing a scheduling optimization model of a cruise ship cabin assembly plan; Step S1.1, defining constraints and decision variables of the scheduling optimization model; Step S1.2, designing a storage mode of the cruise ship cabin assembly plan, designing project soft logic, and constructing a deadline constraint; Step S2, constructing a scheduling constraint programming model of the cruise ship cabin assembly plan; Step S2.1, defining interval decision variables and sequence decision variables of the scheduling constraint programming model; Step S2.2, designing six types of constraint relationships of the scheduling constraint programming model, including priority constraints, uniqueness constraints, storage mode constraints, process logic constraints, work team span constraints, and deadline constraints; The six types of constraint relationships of the scheduling constraint programming model specifically include: ①The process of the priority constraints is as follows: ； In the formula Represents the constraint function, the previous process In the construction unit The task completion time must be in the subsequent process In the construction unit Before the task starts, this constrains the order of operations, that is, it constrains the minimum delay time between the end of one interval variable and the start of another interval. Indication and construction unit intermediate process Task-related interval variables, Indication and construction unit intermediate process Task-related range variables; ②The process of the uniqueness constraints is as follows: ； wherein sub-procedures assigned to each work team, construction unit in the construction unit select work teams, maximum number of work teams, a function for creating a substitution constraint between an interval variable and a set of interval variables in an array, i.e. a sub-procedure only one work team can be selected from the set of work teams, ensuring that each sub-procedure is assigned to only one work team; Equations (13) and (14) are uniqueness constraints that ensure each sub-process assigned to only one work team; ③The process of the storage mode constraints is as follows: According to actual conditions, the storage mode of the process is selected, and the calculation formula is as follows: ； In the formula indicates a process Optional storage mode; The process In construction unit All optional storage mode traversal calculation, calculation process In construction unit The duration of each process to ensure that the duration of the storage mode it performs the matching degree, the calculation formula is as follows: ； In the formula represents a function for returning the length of the specified interval variable; ④The process of the process logic constraints is as follows: In the case of soft logic, the process logic constraint requires that all sub-processes assigned to the same work team be executed in sequence. The task range of each work team is divided by the formula, which is as follows: ； In the formula This indicates all processes assigned to a single step. The A set of sub-processes of a work team, also known as a process. The The interval sequence variables of each work team; Indicates construction unit The process in choose One work team; After a unit of time passes between the execution of two consecutive sub-processes, the work team moves from the current construction unit to the next construction unit, and the formula is as follows: ； wherein represents a function that constrains a set of interval variables so that they do not overlap each other, ensuring that different sub-process execution intervals related to processes and work teams do not overlap; represents a represents an identity matrix that is used to move the work team from the current construction unit to the next construction unit only after the unit time has elapsed between the execution of two consecutive sub-processes, i.e. the rule of establishing the sub-process execution time interval with the identity matrix; Formula (18) is a logical constraint, representing the constraints for all processes i and all work teams. ,pass Functions are used to constrain the assignment of processes. The Sub-processes of each work team This prevents overlap and is combined with the identity matrix. This ensures that there is a unit time interval between the execution of two consecutive sub-processes, and ensures that the work team can move from the current construction unit to the next construction unit. ⑤The process of the work team span constraints is as follows: ； In the formula This function creates a span constraint between a range of interval variables and a set of interval variables in an array. Indication and process The One variable related to each work team is... An input to the function; Formula (19) is the work team span constraint, which is used to ensure the final state of each work team, including whether it is selected, which processes are executed, and the start and end times; ⑥The process of the deadline constraints is as follows: ； wherein denotes a function that returns an integer expression that, if present, is equal to the end of the interval variable, i.e. the end time of the task in the construction unit of the operation; denotes the set of end operations; Formulas (20) and (21) are deadline constraints, with the constraint in formula (20) guaranteeing the total project duration. Less than or equal to the given deadline Formula (21) ensures that each process in the set of completed processes is completed within the construction unit. The task completion time is less than or equal to the total project duration t, ensuring that the project can be completed on time; Step S2.3, defining the optimization objective of the scheduling constraint programming model; Step S3, using the CP Optimizer tool in the CPLEX Studio software to solve the scheduling constraint programming model.

2. The method of claim 1, wherein, In the step S1.1, the process of defining the constraints and decision variables of the scheduling optimization model comprises: ①The constraints are defined as follows: Based on the actual construction process of the cruise ship cabin construction project, the scheduling optimization model is defined to be constrained, including the following 7 constraints: Constraint 1: Each process in each construction unit can only be executed by one work team; Constraint 2: All alternative work teams for each process have the same size, that is, the activity duration of each process remains unchanged regardless of which work team is selected; Constraint 3: A process pauses after completing a construction unit and continues working from the next construction unit after a period of time; Constraint 4: The priority relationship between processes in each construction unit is determined, including end-to-start, start-to-start, and start-to-end; wherein the end-to-start means that the next work starts after the previous work is completed; the start-to-start means that the next work starts after the previous work starts; and the start-to-end means that the time period during which the previous work starts and ends determines the progress of the next work; Constraint 5: The duration of each process is related to the storage mode and is determined; Constraint 6: The storage mode and the corresponding storage space are determined; Constraint 7: Learning effect in repetitive items is not considered; The cruise cabin assembly scheduling problem is converted into a scheduling optimization model of cruise cabin assembly by the above constraints, and the model can be solved, and the decision variables represent the content of the model solution; The decision variables are defined as follows: representing procedure , construction unit selecting a first storage mode, when the condition is satisfied, then the variable , when the condition is not satisfied, then the variable ; the work order of the same procedure, i.e., the procedure of the first construction unit is executed first and then the procedure of the second construction unit is executed when the condition is satisfied, the variable , otherwise ;​​ representing procedure hiring a team of workers, when the condition is met, then the variable , otherwise .

3. The method of claim 1, wherein, The step S1.2 specifically includes: The process of the storage mode is as follows: The selected storage mode of each process and the number of hired work teams are calculated, and the calculation formula is as follows: ； wherein, representing a procedure optional storage mode, set of procedures ; set of construction units ; set of work teams ; Equations (1) and (2) are used to determine the storage mode selected for each process and the number of teams employed; equation (1) indicates the selection of the storage mode for each process , which is summed for all construction units and for all storage modes , so that it equals 1, i.e. the storage mode is selected; equation (2) indicates that the result of the sum of all team numbers equals 1, i.e. the number of teams employed for each process is calculated; There is a corresponding priority relationship between the processes of the construction units, and the calculation formula is as follows: ； wherein denotes a process at construction unit , denotes a process at construction unit , denotes a process optional storage mode, denotes a process in construction unit select storage mode execution duration in case of, denotes the sequence number of a work team, denotes a process hiring a work team, when the work team is assigned to a process , otherwise , denotes a set of process pairs, denotes the sequence number of a construction unit; Formula (3) indicates that there is a corresponding priority relationship between the processes of the construction units, and the start time of the process plus its execution time must be less than or equal to the start time of the process , which ensures that the processes are performed in the correct order, i.e., the process is performed first, and the process is performed later, so that each process pair in the set E satisfies the priority relationship; The process of designing the soft logic of the project is as follows: The start time relationship of the same process in different construction units is calculated, and the calculation formula is as follows: ； In the formula Indicate process In the construction unit The start time, Indicate process In the construction unit The start time, Indicate process employment A work team, when the work team is assigned to a process ,but ,otherwise , Indicates the project deadline This indicates the work sequence of the same process, that is, the first step is performed. Work procedures of each construction unit Then execute the first Work procedures of each construction unit When the condition is met, the variable... ,otherwise , Indicate process Optional storage modes Indicates the sequence number of the process; Indicates construction unit The process in Select storage mode Execution timeline under different circumstances; Formula (4) represents the same process In different construction units and Based on whether the work is carried out by the same work team and the deadline constraints, this formula is used to coordinate the start times of the construction units. The end time must be less than or equal to the construction unit's end time. The start time is used to determine the relationship between the start times of the same process in different construction units; For The restriction is made to exclude unreasonable association between the same process in different construction units, and the calculation formula is as follows: ； Formula (5) represents the process for each step. and construction unit ,make The sum must be less than or equal to 1 in order to limit unreasonable relationships between different construction units of the same process; For The restriction is made to ensure the reasonable correlation between the different construction units in the process, and the calculation formula is as follows: ； Formula (6) represents the process for each step. and construction unit , make the variable The sum must be less than or equal to 1 to ensure a reasonable correlation between different construction units; For and , based on the case of employing different number of work teams and the process of association between different construction units, the calculation formula is: ； Equation (7) indicates that for each process , the first term on the left-hand side represents the case where different numbers of work teams are employed, and the total number of work teams employed is calculated , the second term represents the case where the process is associated between different construction units; The scheduling scheme is guaranteed to meet the soft logic by means of formulas (4)-(7); The process of the deadline constraint is as follows: Computing procedure The total time of the start time of the construction unit plus its execution time is calculated as follows: ； In the formula, EA represents the set of ending processes, each of which has no immediate process; Formula (8) represents the expression for each process in the set of final processes. and construction unit , making the process and construction unit The start time plus its execution time is less than or equal to the total project duration. ; It is judged whether the total project duration is completed before the project deadline, and the formula is as follows: ； In the formulae Indicates the project deadline; Formula (9) indicates that the total project duration is completed before the given project deadline; minimizing cost and minimizing duration whose formula is as follows: ； wherein denotes the project step hiring the labor cost per day for one work team, denotes the material storage cost per day for one storage site, denotes the number of storage sites occupied when choosing the storage mode, denotes the material cost rate for hiring one work team for the project step, denotes the work volume of the sub-step , construction unit , denotes the completion time of the last step.

4. The method of claim 1, wherein, In the step S2.1, the definition of interval decision variables and sequence decision variables specifically includes: The interval decision variables include: with the construction unit in the process task-related interval variable; Optional interval variables related to the first group of work teams of the process of the first group of work teams of the process Optional interval variable indicating the first group of work teams to execute the sub-process in the construction unit ;​ ii. the sequence decision variable includes: if is equal to 1, it means that the process selects a work team, otherwise is equal to 0; , if is equal to 1, it indicates that the construction unit performs a process of the first storage mode, otherwise is equal to 0.

5. The method of claim 1, wherein, In the step S2.3, the process of defining the optimization objective of the scheduling constraint programming model is as follows: The optimization objective of the scheduling constraint programming model is to calculate the objective function of minimizing the total cost and duration of the project, and the calculation formula is as follows: ； wherein represents the management cost of the project per day, represents the absolute value of the number of storage modes, represents the total duration of the project, represents the total number of processes, represents the process number, represents the process optional storage mode, represents the storage mode, represents the work team, represents the construction unit.

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