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Time and finance optimization model for multiple construction projects using genetic algorithm

  • Musaab Falih Hasan EMAIL logo and Sawsan Rasheed Mohammed
Published/Copyright: June 8, 2022
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Journal of the Mechanical Behavior of Materials
From the journal Journal of the Mechanical Behavior of Materials Volume 31 Issue 1

Abstract

Construction contractors usually undertake multiple construction projects simultaneously. Such a situation involves sharing different types of resources, including monetary, equipment, and manpower, which may become a major challenge in many cases. In this study, the financial aspects of working on multiple projects at a time are addressed and investigated. The study considers dealing with financial shortages by proposing a multi-project scheduling optimization model for profit maximization, while minimizing the total project duration. Optimization genetic algorithm and finance-based scheduling are used to produce feasible schedules that balance the finance of activities at any time with the available funds. The model has been tested in multi scenarios, and the results are analyzed. The results show that negative cash flow is minimized from −693,784 to −634,514 in enterprise I and from −2,646,408 to −2,529,324 in enterprise II in the first scenario and also results show that negative cash flow is minimized to −612,768 with a profit of +200,116 in enterprise I and to −2,597,290 with a profit of +1,537,632 in enterprise II in the second scenario.

Keywords: optimization; multiple construction projects; cash flow; genetic algorithm

1 Introduction

The most critical resource for any project is cash, as companies fail more often due to lack of cash than due to lack of other resources. Over 60% of contractor failures are attributed to economic factors, according to [1]. In addition to conducting a financial feasibility analysis, there are two primary goals: the first step is to see if the contractor has enough money to complete the project. In the second step, the goal is to show how much of the investment has been used and how the payments have progressed throughout the project. Once the contractor has achieved these two goals, he can begin managing the cash flow of the project, which is referred to as cash flow management [2]. The importance of financial management in construction management has long been recognized. On the other hand, the construction industry has the highest rate of insolvency compared to other sectors of the economy. Due to poor financial management, many construction businesses fail, particularly due to lack of focus on cash flow forecasting. Lack of cash flow control has been a major contributor to the industry’s high rate of insolvencies for years; as a result, it is a topic that all contractors should consider seriously. Contractors go out of business because they run out of cash, not because they do not have enough work. Cash flow is one of the most important tools for regulating an enterprise’s cash flow by determining the cash in and cash out in a project and presenting the possible outcomes with a time effect [3]. Contractors used to face financial shocks when undertaking multiple construction projects concurrently. Despite any reasons behind that, they need to maneuver with their available resources, especially funds, to minimize time or cost overrun. Such optimum solutions are challenging and complicated without a comprehensive view of the whole situation in all the undertaken projects. A computerized system might be of great help in this sense.

2 Research methodology

This study’s methodology is based on the premise that project financing costs and profits are affected by negative cash flow. Because of this, schedulers can use an optimization algorithm by a quantitative system design to devise schedules that maximize project profit, while minimizing negative cash flow to avoid a budget deficit without delaying project completion, allowing contractors to relieve financial pressure on activity execution. Hence, the maximum profit can be attained. This necessitates an appropriate cash flow management strategy; the following steps are performed in this research:

  • Literature review: Investigating the state-of-art for modeling cash flow combination of multi construction projects.

  • Data collection and analysis: Gathering factual data on multi construction projects’ cash flow in some local major contracting enterprises.

  • Building the optimization model: The model should provide for cash flow planning that assures profit maximization, while maintaining the total project duration using the optimization algorithm.

3 Literature review

Time-cost trade-off analysis and financing optimization are proposed as part of an integrated model. The optimization problem is solved using a hybrid GALP algorithm, which combines genetic algorithms (GA) with linear programming (LP). Using small and large networks, the proposed model is evaluated to see if it achieves optimal results in terms of financing costs and profits, to validate the model’s performance and structure, and to confirm its practicality in large networks [4]. A practical method for solving the multi-objective optimization problem in construction project management to reduce the error probability that the optimized project will have in the actual project was proposed in [5]. Payments to subcontractors and suppliers, as well as financial arrangements with banks, are highlighted as the main payment conditions based on portfolio cash flow management. An optimization model that uses a GA is presented to assist construction enterprises in determining the optimum project schedules that minimize the total interest paid by a contractor for a portfolio of projects as well as minimize the maximum negative cash flow while accounting for various payment conditions between multiple parties [6]. A model that minimizes financing cost by integrating a line-of-credit and a long-term loan using a work schedule with normal activity durations is presented. The proposed model provides the optimum schedules of financing inflow (borrowed money) and outflow (repayments of principal and interest). The contractor benefits when the proposed model is used because the contractor: (1) pays less financing cost, (2) obtains higher profit, and (3) has more negotiating power with a lender because the contractor provides an optimal financing schedule when applying for a loan and/or credit line [7]. A model that minimizes financing costs by taking into account various financing options and a work schedule with typical activity durations is presented. There are several advantages in using a new financing model, such as a lower financing cost, avoiding a longer project duration, avoiding liquidated damages, and reducing the risk of a work schedule that includes more critical activities, over previous models [8]. An innovative multi-objective scheduling optimization model for multiple construction projects is developed in this study. Time, cost, profit, and resource fluctuations are among the goals of this project. Multi-objective scheduling optimization model for multiple construction projects was developed using the fast elitist non-dominated sorting genetic algorithm (NSGA-II) [9].

4 Scheduling using critical path method

In order to meet financial goals, a project’s activities are shifted without affecting the project’s deadline [6]. First, the Critical Path Method (CPM) was used to determine the time of the project’s activities in order to schedule them. As an extension of the CPM approach, this study explores the effects of varying the start and end times of activities, as well as the total float and free float that can exist between them. Only the names of the activities, their predecessors, and the start date of the first activity in any project need to be entered into the model proposed in this article. Each activity’s CPM will be calculated by the model. Each project’s first activity must be set to begin on a specific date, even though the projects are being carried out at the same time. Changing the start dates of activities will only be possible within the free float of each activity, as each project has a set deadline. Consequently, each activity will have start and finish dates, along with deferred start and deferred finish dates, determined by the optimization model to meet the financial objectives of the contractor.

(1) Activity delayed start = Activity start date + X ,

where X = shifted days within free float determined by the optimization algorithm.

5 Cash flow in construction project

Cash flow has been extensively researched from the contractor’s perspective. The financial terminology and equations used in [10] will be adapted for this study with some minor changes. In Figure 1, you can see a typical construction project’s cash flow. Financial institutions such as banks, suppliers, and subcontractors all have an effect on a contractor’s cash flow. It is important to keep in mind that how much money a contractor gets from the owner depends on the payment terms he has with that person. Bank financing costs, such as interest rates on loans, will have an impact on the contractor’s cash outflow as a result of these terms. The financing costs that contractors incur while working on a project are sometimes referred to as interest payments, and they reduce their profits [11]. Terms like contractor-owner terms, such as advance payment, retention, and when to repay the retention percentage, have an impact on cash outflow as well. When a contractor has multiple projects going on at the same time, they are more likely to be able to negotiate better terms for subcontractors by offering them the opportunity to work on more projects. Contractual expenses (E t ), excluding interest or financing costs, include weekly payments to subcontractors, portions of activities executed by the contractor’s own resources, and project-related indirect costs.

(2) E t = Construction expenses during time period  ( t )  excluding financing costs .

Figure 1 Typical cash flow profile for a construction project [11].
Figure 1

Typical cash flow profile for a construction project [11].

Cumulative cash flow before receiving the interim payment for t ≥ 1 is [11]:

(3) F t = N t − 1 + E t ,

where (N t–1) the cumulative net cash flow from previous time periods up to time period (t – 1). The cumulative net cash flow after receiving the interim payment is given by ref. [11]:

(4) N t = F t + P t ,

where P t is the interim payment received at the end of time (t). The following equation gives the profit for the project [11]:

(5) G = ∑ t = 0 n ( P t + E t ) ,

where G is the profit represented by a positive number, while the cost E t is represented by a negative number. Because of the fact that N t is negative in the early stages of the project and becomes positive towards the end of the project, contractors typically use bank loans to finance their projects and incur financing costs that are affected by a specific annual interest rate (i). As a result, the net cumulative cash flow before and after the payment (P t ) can be explained by Eqs. (6)–(8) [11]:

(6) I t = i N t − 1 ,

(7) F ˆ t = F t + ∑ k = 1 t I k ( 1 + i ) t − k ,

(8) N ˆ t = F ˆ t + P t .

Net cash flow ( N ˆ t ) during a project is the maximum value that the contractor will need to cover its financing at any given project. Enterprise-level equations will be used in this article instead of project-level formulae.

Many researchers’ financial scheduling goals have been to maximize profits (G) or reduce total interest payments (I). In this article, a GA is used to reduce the portfolio’s maximum cumulative negative net cash flow and maximize the portfolio’s overall profit (G) using finance-based scheduling of multiple projects.

6 GA

This study’s optimization engine uses GAs with heuristics. John Holland invented GAs in 1975. GA, a metaheuristic, simulates Darwin’s theory of evolution and survival of the fittest. Changing organisms are thought to be the result of genetic mutation, reproduction, and gene crossover [12]. The metaheuristic solves combinatorial optimization problems by random search. Using GA, the first generation’s improvement becomes the basis for the next generation’s random search. The first step in solving any combinatorial optimization problem using GAs is to create chromosomes. The parameters encoded are generated at random, and each gene offers a potential solution to the problem. Gene structure is a string of elements that corresponds to the start of each activity. Genes represent a possible timetable. Genes are evaluated based on expected contractor profit and negative cash flow at the end of the project. This study’s goal is to find a project schedule that minimizes negative cash and maximizes project profit. Good chromosome individuals produce high values in maximization problems and low values in minimization problems [13]. The first chromosome generation creates many generations. The rest is discarded. Reproduction, crossover, and mutation from that generation are used to improve it. It is then applied to the next generation. The cycle repeats once the termination condition is met. A generation’s best chromosomes are passed down through reproduction. Their role as parents to the next generation adds to the solution’s bitterness. The least fit chromosomes are discarded to keep the population stable. Crossover is the process of mixing two chromosomes to see what happens. It is the main operation in GAs. Like in marriage, two-parent chromosomes are chosen at random to discuss the issue. The best chromosomes are more likely to be chosen at random. The phenomenon of “mutation” occurs when one or two offspring in a generation suddenly become geniuses. Mutations are used in evolution to ensure the best possible outcome for the next generation. No matter how many recombination and crossovers occur, this data will always be lacking. To compensate, some chromosomes are silenced [14]. The procedure compares each generation’s chromosome values to that of the previous generation, keeping only those that improve. The procedure must be repeated until an endpoint is reached.

7 Model development

Project financing costs and profit are impacted by negative cash flow, as discussed previously. When cash flow is properly managed, schedulers can devise plans that maximize project profitability. By reducing negative cash flow as much as possible, this quantitative system design seeks to avoid a budget shortage without delaying project completion. Because of this, you can make the most money possible and a cash flow management strategy is required. This model’s development is illustrated in Figure 2.

Figure 2 Chart for model development.
Figure 2

Chart for model development.

The main goal of the problem can be stated as maximizing the project profit by:

  • The project is initially scheduled based on input data, such as the relationships and duration of activities.

  • The project’s schedule is used to determine the maximum negative cash flow and profit.

  • Optimization process using GA begins to search for the best possible scenario for a given project.

In this step, the available floats are used to generate multiple scenarios with activities starting at various times, and the resulting cash flow is calculated. GA processes, such as reproduction, crossover, and mutation, are used to create project scenarios. The best starting times are then determined by comparing each scenario to a predetermined objective function. In order to achieve this goal, a comprehensive model of various cash problems was constructed. For this, we will use two scenarios. The first scenario is used to find a solution to the problem of devising schedules that correspond to a minimum negative cash flow without reducing profit. The second scenario extends the time of the project and reduces the problem of negative cash flow while maintaining the maximum profit.

  • The output data from the model are the selected scenario’s optimized schedule, optimized cash flow, and net cash flow diagram. In the following section, a practical construction project is used to demonstrate the model’s applicability.

8 Case study

The proposed model can be demonstrated using a sample of multiple construction projects from two public sector enterprises. Scenario analysis is based on a variety of constraints, such as project profitability and completion dates. Table 1 shows the maintenance and restoration projects for the roads and bridges involved.

Table 1

Projects of public and private enterprises

Projects Enterprises Work sector Year
Bagaq Bridge in Nineveh Governorate AL-Mutasim State Constructional Contracting Company Public 2020–2021
Zghitun Bridge in Kirkuk Governorate AL-Mutasim State Constructional Contracting Company Public 2020–2021
Baladruz Road in Diyala Governorate Ashur State Constructional Contracting Company Public 2019–2020
Khanaqin-Naft Khana Road in Diyala Governorate Ashur State Constructional Contracting Company Public 2019–2020
Al-Fajr Al-Bdeir Road in Thi Qar Governorate Ashur State Constructional Contracting Company Public 2019–2020

The data needed to develop models are obtained from 5 projects completed in the period (2019–2021). Information is extracted from the records of the enterprises in the Ministry of Construction and Housing and Municipalities. The project is assigned to one main contractor and includes the following works: removing damaged items, installing new items, and maintaining some damaged items. Tables 2–6 show each item’s work, duration, and direct cost, representing ten columns of input data. The first column, “Activity name,” is used to identify the activities of the project; Second column, “Duration,” is the activity duration in working days; Third column, “Predecessor,” is used to define the precedence relationships between activities; The Fourth column “Activity cost (materials and labor),” is the cost of each activity multiplied by 1,000 Iraq dinar; The Fifth column is the “Lag time,” between activities; Sixth to Tenth columns are refers to dates not events: “Early start time, Early finish time, Late start time, Late finish time, and Total float.”

Table 2

Items of work and other essential data of project I in enterprise I

Activity Duration (day) Predecessor Cost of activity × 1,000 IQD Lag EST EFT LST LFT TF
A1000 60 — 47,400 0 90 149 90 149 0
A1010 46 — 83,149 0 90 135 139 184 49
A1020 40 A1000 and A1010 324,590 35 185 224 185 224 0
A1030 37 A1020 117,514 7 232 268 232 268 0
A1040 31 A1030 75,375 9 278 308 278 308 0
A1050 16 A1040 142,299 10 319 334 319 334 0
A1060 60 A1050 526,015 0 335 394 335 394 0
A1070 26 A1060 167,892 0 395 420 395 420 0
A1080 24 A1020 276,500 0 225 248 405 428 180
A1090 7 A1080 21,978 0 249 255 429 435 180
A1100 30 A1070 and A1090 533,345 15 436 465 436 465 0
A1120 21 A1100 71,890 0 466 486 466 486 0
A1130 10 A1100 6,162 0 466 475 477 486 11
A1110 10 A1101 52,014 0 466 475 477 486 11
A1140 6 A1120, A1130, and A1110 8,651 0 487 492 487 492 0
Table 3

Items of work and other essential data of project II in enterprise I

Activity Duration (day) Predecessor Cost of activity × 1,000 IQD Lag EST EFT LST LFT TF
A1000 15 — 15,800 0 1 15 1 15 0
A1020 60 A1000 300,299 0 16 75 16 75 0
A1084 35 A1000 24,111 259 275 309 336 370 61
A1085 30 A1084 30,382 0 310 339 371 400 61
A1030 30 A1020 171,825 15 91 120 91 120 0
A1040 60 A1030 82,753 15 136 195 136 195 0
A1050 30 A1040 43,450 15 211 240 211 240 0
A1060 30 A1050 166,848 15 256 285 256 285 0
A1070 60 A1060 83,938 0 286 345 286 345 0
A1080 30 A1070 and A1085 54,053 15 361 390 361 390 0
A1090 20 A1080 and A1085 30,462 10 401 420 401 420 0
A1100 15 A1090 22,003 0 421 435 421 435 0
A1120 20 A1080 38,394 0 391 410 446 465 55
A1130 15 A1080 30,119 0 391 405 451 465 60
A1140 10 A1080 10,270 0 391 400 456 465 65
A1110 30 A1100 22,041 0 436 465 436 465 0
A1150 5 A1110, A1120, A1130, and A1140 8,279 0 466 470 466 470 0
Table 4

Items of work and other essential data of project I in enterprise II

Activity Duration (day) Predecessor Cost of activity × 1,000 IQD Lag EST EFT LST LFT TF
A1000 60 — 171,000 0 1 60 1 60 0
A1005 80 A1000 1,125,000 0 61 140 61 140 0
A1010 60 A1000 300,000 0 61 120 101 160 40
A1015 60 A1000 12,000 0 61 120 81 140 20
A1020 80 A1010 777,150 0 121 200 161 240 40
A1025 90 A1005 and A1015 12,000 0 141 230 141 230 0
A1030 60 A1005 240,000 0 141 200 261 320 120
A1040 60 A1015 48,750 0 121 180 151 210 30
A1045 30 A1040 150,000 0 181 210 211 240 30
A1050 70 A1025, A1020, and A1045 2,250,000 10 241 310 241 310 0
A1060 60 A1050 1,764,000 10 321 380 321 380 0
A1090 50 A1030 120,000 5 206 255 336 385 130
A1095 60 A1030 450,000 5 206 265 326 385 120
A1100 35 A1060, A1090, and A1095 48,000 5 386 420 386 420 0
A1110 30 A1060, A1090, and A1095 240,000 5 386 415 391 420 5
A1120 25 A1100 and A1110 240,000 0 421 445 421 445 0
Table 5

Items of work and other essential data of project II in enterprise II

Activity Duration (day) Predecessor Cost of activity × 1,000 IQD Lag EST EFT LST LFT TF
A900 50 — 123,750 0 123 172 123 172 0
A1000 60 A900 585,975 0 173 232 173 232 0
A1010 30 A900 184,500 0 173 202 203 232 30
A1020 80 A1000 and A1010 306,000 0 233 312 248 327 15
A1030 90 A1000 and A1010 181,500 0 233 322 233 322 0
A1040 30 A1000 and A1010 9,000 0 233 262 298 327 65
A1050 80 A1030, A1040, and A1020 1,532,550 5 328 407 328 407 0
A1060 70 A1050 1,217,025 5 413 482 413 482 0
A1070 40 A1060 1,275,375 5 488 527 488 527 0
A1079 90 A1000 and A1010 105,000 0 233 322 443 532 210
A1080 30 A1070 and A1079 184,500 5 533 562 533 562 0
A1100 30 A1080 49,725 0 563 592 563 592 0
A1110 30 A1080 248,625 0 563 592 563 592 0
A1120 19 A1100 and A1110 18,750 0 593 612 593 612 0
Table 6

Items of work and other essential data of project III in enterprise II

Activity Duration (day) Predecessor Cost of activity × 1,000 IQD Lag EST EFT LST LFT TF
A1000 60 — 19,614 0 184 243 184 243 0
A1005 70 A1000 28,133 0 244 313 244 313 0
A1010 30 A1000 16,164 0 244 273 284 313 40
A1020 60 A1005 and A1010 105,000 0 314 373 314 373 0
A1050 40 A1020 37,594 5 379 418 379 418 0
A1070 30 A1050 and A1080 486,000 5 424 453 424 453 0
A1080 30 A1020 222,833 5 379 408 394 423 15

Figures 3–6 illustrate the planned activities and time schedule of the projects. The application of the optimization method was put to use in three stages: setting a time schedule, calculating the cash flow for multiple construction projects, and finally optimizing the cash flow under various constraints. In order to achieve this goal, a complete model of multiple cash issues is used. For this, the previously mentioned two scenarios are used.

Figure 3 Planned activity network for enterprise I.
Figure 3

Planned activity network for enterprise I.

Figure 4 Planned activity network for enterprise II.
Figure 4

Planned activity network for enterprise II.

Figure 5 Time schedule for enterprise I.
Figure 5

Time schedule for enterprise I.

Figure 6 Time schedule for enterprise II.
Figure 6

Time schedule for enterprise II.

9 Calculation of cash flows

Table 7 shows the total cash-in and cash-out values for the first enterprise and the other financial parameters’ values and the total duration of projects. The maximum negative cash flow is −693,784 at the end of the 9th month, and the profit of the projects is +304,451 in enterprise I. On the other hand, Table 8 shows the total cash-in and cash-out values for the second enterprise and values of the other financial parameters along with the total duration of projects. The maximum negative cash flow is −2,646,408 at the end of the 13th month, and the profit of the projects is +1,726,720 in enterprise II. The GA system can then be used to search for optimum schedules that minimize maximum negative cash flow and optimize project profit. Explanation of calculation of cash flows:

  • Bill to owner: The value of progress payment to the contractor without discounts of retention and taxes.

  • Total receipts: Total progress payment to the contractor subtracted from the discounts of retention and taxes.

  • Total cost: The total costs incurred by the contractor in each month (materials, labor, and overhead).

  • Cumulative cash flow (F t ): The cumulative cash flow for each month (–103, 162–166, 938 = –270,100) (net cash flow in month 1+ total cost in month 2).

  • Net cash flow (N t ): The net cash flow for each month (–270, 100 + 105, 255 = −164,875) (cumulative cash flow in month 2+ total receipts in month 2).

Table 7

Cash flow calculation according to time schedule in enterprise I

Month Bill to owner Retention Taxes Total receipts Materials Labor Overhead Total cost Cumulative cash flow F t Net cash flow N t
1 57,042 38,837 7,282 103,162 –103,162 –103,162
2 121,367 12,137 4,005 105,225 92,307 62,847 11,784 166,938 –270,100 –164,875
3 196,398 19,640 6,481 170,277 45,524 30,995 5,812 82,331 –247,206 –76,929
4 96,860 9,686 3,196 83,978 143,317 97,578 18,296 259,191 –336,120 –252,142
5 304,931 30,493 10,063 264,375 44,531 30,319 5,685 80,534 –332,677 –68,302
6 94,746 9,475 3,127 82,145 25,437 17,319 3,247 46,003 –114,305 –32,160
7 54,121 5,412 1,786 46,923 143,684 97,827 18,343 259,854 –292,014 –245,091
8 305,711 30,571 10,088 265,051 228,463 155,549 29,165 413,177 –658,268 –393,217
9 486,091 48,609 16,041 421,441 166,196 113,155 21,217 300,567 –693,784 –272,343
10 353,608 35,361 11,669 306,579 103,563 70,511 13,221 187,295 –459,638 –153,059
11 220,347 25,820 7,271 187,255 139,176 94,758 17,767 251,702 –404,761 –217,506
12 296,120 9,772 286,348 177,781 121,043 22,695 321,519 –539,025 –252,678
13 378,258 12,483 365,775 198,209 134,951 25,303 358,463 –611,141 –245,365
14 421,722 13,917 407,805 145,619 99,145 18,590 263,353 –508,718 –100,913
15 309,827 10,224 299,602 281,020 191,333 35,875 508,227 –609,141 –309,538
16 597,914 19,731 578,183 143,835 97,930 18,362 260,126 –569,665 8,519
17 306,031 10,099 295,932 — — — — 8,519 304,451
Total 4,544,051 227,203 149,954 4,166,894 2,135,704 1,454,096 272,643 3,862,443
Table 8

Cash flow calculation according to time schedule in enterprise II

Month Bill to owner Retention Taxes Total receipts Materials Labor Overhead Total cost Cumulative cash flow F t Net cash flow N t
1 53,010 35,340 9,424 97,774 –97,774 –97,774
2 117,800 11,780 3,887 102,133 61,148 40,765 10,871 112,783 –210,557 –108,425
3 135,883 13,588 4,484 117,811 358,283 238,855 63,695 660,832 –769,257 –651,446
4 796,183 79,618 26,274 690,291 367,871 245,247 65,399 678,517 –1,329,963 –639,672
5 817,491 81,749 26,977 708,765 411,196 274,131 73,102 758,429 –1,398,101 –689,336
6 913,769 91,377 30,154 792,238 425,542 283,695 75,652 784,888 –1,474,225 –681,987
7 945,649 94,565 31,206 819,877 513,811 342,541 91,344 947,696 –1,629,682 –809,805
8 1,141,802 114,180 37,679 989,942 451,146 300,764 80,204 832,114 –1,641,919 –651,976
9 1,002,547 100,255 33,084 869,208 852,199 568,133 151,502 1,571,834 –2,223,810 –1,354,602
10 1,893,776 189,378 62,495 1,641,904 688,224 458,816 122,351 1,269,390 –2,623,993 –982,089
11 1,529,386 152,939 50,470 1,325,978 556,730 371,153 98,974 1,026,857 –2,008,946 –682,969
12 1,237,177 62,937 40,827 1,133,412 905,524 603,683 160,982 1,670,188 –2,353,157 –1,219,744
13 2,012,275 66,405 1,945,870 773,493 515,662 137,510 1,426,664 –2,646,409 –700,539
14 1,718,873 56,723 1,662,150 516,807 344,538 91,877 953,221 –1,653,760 8,390
15 1,148,460 37,899 1,110,560 679,781 453,187 120,850 1,253,818 –1,245,428 –134,868
16 1,510,624 49,851 1,460,774 288,621 192,414 51,310 532,345 –667,213 793,561
17 641,379 21,166 620,214 573,919 382,613 102,030 1,058,561 –265,000 355,213
18 1,275,375 42,087 1,233,288 219,465 146,310 39,016 404,791 –49,578 1,183,710
19 487,700 16,094 471,606 151,686 101,124 26,966 279,776 903,934 1,375,539
20 337,080 11,124 325,956 82,854 55,236 14,730 152,820 1,222,720 1,548,676
21 184,120 6,076 178,044 1,548,676 1,726,720
Total 19,847,349 992,366 654,963 18,200,020 8,931,307 5,954,205 1,587,788 16,473,300

10 Optimization model

The main objective is developing a tool that will help contractors maximize their profits. In order to achieve this goal, a comprehensive model of various cash problems was constructed. For this, we will use two scenarios. The complete GA procedure is coded in MATLAB and then used to find an optimal time schedule for the problem at hand for the purposes of implementation

Scenario I: Maximizing profits while minimizing negative cash flow using a GA technique, we can find a solution to the problem of creating schedules that have the minimizing negative cash flow. The following are the objective function and constraints for the two enterprises involved in this scenario:

(9) Minimize : F t ,

(10) E st ≤ A st ≤ L st ,

where F t is the maximum cumulative cash flow, E st is the early start time for activity according to time schedule, A st is the activity start data in the project, and L st is the late start time for activity according to time schedule.

To generate schedules, critical path activities are started early and non-critical activities are started at random while maintaining a link between them. These random schedules generate corresponding cash requirement profiles. The GA procedure then looks for a schedule that generates the minimizing negative cumulative cash flow while keeps maximizing profit. Tables 9 and 10 show the optimized cash flow calculation in the scenario I in two enterprises.

Table 9

Cash flow calculation in the scenario I in enterprise I

Month Bill to owner Retention Taxes Total receipts Materials Labor Overhead Total cost Cumulative cash flow F t Net cash flow N t
1 57,042 38,837 7,282 103,162 –103,162 –103,162
2 121,367 12,137 4,005 105,225 92,307 62,847 11,784 166,938 –270,100 –164,875
3 196,398 19,640 6,481 170,277 46,934 31,955 5,992 84,881 –249,756 –79,479
4 99,860 9,986 3,295 86,579 109,980 74,880 14,040 198,900 –278,379 –191,800
5 234,000 23,400 7,722 202,878 59,252 40,342 7,564 107,158 –298,958 –96,080
6 126,068 12,607 4,160 109,301 42,644 29,034 5,444 77,121 –173,202 –63,901
7 90,731 9,073 2,994 78,664 162,995 110,975 20,808 294,778 –358,679 –280,015
8 346,798 34,680 11,444 300,674 115,083 78,354 14,691 208,128 –488,144 –187,470
9 244,857 24,486 8,080 212,291 247,189 168,299 31,556 447,045 –634,514 –422,223
10 525,935 52,594 17,356 455,986 107,212 72,996 13,687 193,894 –616,118 –160,132
11 228,111 22,811 7,528 197,772 132,938 90,511 16,971 240,419 –400,551 –202,779
12 282,846 5,790 9,334 267,722 183,411 124,876 23,414 331,701 –534,480 –266,757
13 390,236 12,878 377,358 190,559 129,742 24,327 344,628 –611,386 –234,028
14 405,445 13,380 392,065 134,352 91,474 17,151 242,978 –477,005 –84,940
15 285,856 9,433 276,423 277,099 188,663 35,374 501,137 –586,077 –309,654
16 589,573 19,456 570,117 176,706 120,310 22,558 319,575 –629,229 –59,111
17 375,970 12,407 363,562 –59,111 304,451
Total 4,544,051 227,203 149,954 4,166,894 2,135,704 1,454,096 272,643 3,862,443
Table 10

Cash flow calculation in the scenario I in enterprise II

Month Bill to owner Retention Taxes Total receipts Materials Labor Overhead Total cost Cumulative cash flow F t Net cash flow N t
1 53,010 35,340 9,424 97,774 –97,774 –97,774
2 117,800 11,780 3,887 102,133 58,028 38,685 10,316 107,029 –204,803 –102,670
3 128,950 12,895 4,255 111,800 336,443 224,295 59,812 620,550 –723,219 –611,420
4 747,650 74,765 24,672 648,213 358,282 238,855 63,695 660,832 –1,272,252 –624,039
5 796,183 79,618 26,274 690,291 307,635 205,090 54,691 567,416 –1,191,455 –501,165
6 683,634 68,363 22,560 592,711 363,417 242,278 64,608 670,303 –1,171,468 –578,757
7 807,594 80,759 26,651 700,184 663,143 442,095 117,892 1,223,130 –1,801,887 –1,101,703
8 1,473,651 147,365 48,630 1,277,655 401,075 267,383 71,302 739,761 –1,841,464 –563,809
9 891,278 89,128 29,412 772,738 797,103 531,402 141,707 1,470,211 –2,034,020 –1,261,282
10 1,771,339 177,134 58,454 1,535,751 687,492 458,328 122,221 1,268,042 –2,529,324 –993,573
11 1,527,761 152,776 50,416 1,324,569 622,146 414,764 110,604 1,147,514 –2,141,087 –816,518
12 1,382,547 97,782 45,624 1,239,141 921,364 614,243 163,798 1,699,404 –2,515,922 –1,276,781
13 2,047,475 67,567 1,979,908 678,672 452,448 120,653 1,251,774 –2,528,555 –548,647
14 1,508,161 49,769 1,458,392 622,220 414,813 110,617 1,147,650 –1,696,297 –237,905
15 1,382,711 45,629 1,337,082 711,201 474,134 126,436 1,311,771 –1,549,676 –212,594
16 1,580,447 52,155 1,528,292 301,622 201,081 53,622 556,324 –768,919 759,374
17 670,270 22,119 648,151 575,319 383,546 102,279 1,061,143 –301,770 346,381
18 1,278,486 42,190 1,236,296 234,906 156,604 41,761 433,271 –86,889 1,149,407
19 522,013 17,226 504,787 149,409 99,606 26,562 275,577 873,830 1,378,617
20 332,020 10,957 321,063 88,821 59,214 15,790 163,825 1,214,792 1,535,855
21 197,379 6,514 190,866 1,535,855 1,726,721
Total 19,847,349 992,366 654,963 18,200,021 8,931,307 5,954,205 1,587,788 16,473,300

Scenario II: Maximizing profit by extending the project and reducing the problem of negative cash flow while maintaining maximum profit.

(11) Maximize : G .

Random activity start times are used to generate new time schedules while maintaining dependency between activities. It is possible to see how much cash each of these random schedules requires. Afterwards, the GA procedure looks for a schedule that generates the maximum profit, while also generating the minimum of cumulatively negative cash flow possible. Tables 11 and 12 show the optimized cash flow calculation in the scenario II in two enterprises.

Table 11

Cash flow calculation in the scenario II in enterprise I

Month Bill to owner Retention Taxes Total receipts Materials Labor Overhead Total cost Cumulative cash flow F t Net cash flow N t
1 27,266 18,564 3,481 49,311 –49,311 –49,311
2 58,013 5,801 1,914 50,297 92,307 62,847 11,784 166,938 –216,249 –165,952
3 196,398 19,640 6,481 170,277 69,896 47,589 8,923 126,408 –292,360 –122,083
4 148,715 14,872 4,908 128,936 34,108 23,223 4,354 61,685 –183,768 –54,832
5 72,571 7,257 2,395 62,919 143,300 97,566 18,294 259,159 –313,991 –251,072
6 304,893 30,489 10,061 264,342 14,204 9,671 1,813 25,689 –276,761 –12,419
7 30,222 3,022 997 26,202 160,615 109,355 20,504 290,473 –302,892 –276,689
8 341,733 34,173 11,277 296,283 74,269 50,566 9,481 134,316 –411,005 –114,723
9 158,019 15,802 5,215 137,002 74,948 51,028 9,568 135,544 –250,266 –113,264
10 159,463 15,946 5,262 138,254 199,426 135,779 25,459 360,664 –473,927 –335,673
11 424,310 42,431 14,002 367,877 136,624 93,020 17,441 247,086 –582,759 –214,882
12 290,689 29,069 9,593 252,027 111,677 76,036 14,257 201,969 –416,851 –164,824
13 237,611 8,700 7,841 221,070 184,059 125,316 23,497 332,872 –497,696 –276,626
14 391,614 12,923 378,691 185,867 126,548 23,728 336,142 –612,768 –234,077
15 395,461 13,050 382,411 114,106 77,689 14,567 206,362 –440,439 –58,028
16 242,779 8,012 234,767 74,273 50,569 9,482 134,324 –192,352 42,415
17 158,028 5,215 152,813 329,776 224,528 42,099 596,403 –553,988 –401,175
18 701,651 23,154 678,497 102,747 69,956 13,117 185,819 –586,995 91,502
218,611 7,214 211,397 6,237 4,246 796 11,280 80,222 200,116
Total 4,544,041 227,203 149,953 3,807,172 2,135,699 1,454,093 272,642 3,862,435
Table 12

Cash flow calculation in the scenario II in enterprise II

Month Bill to owner Retention Taxes Total receipts Materials Labor Overhead Total cost Cumulative cash flow F t Net cash flow N t
1 53,010 35,340 9,424 97,774 –97,774 –97,774
2 117,800 11,780 3,887 102,133 58,148 38,765 10,337 107,250 –205,024 ––102,892
3 129,217 12,922 4,264 112,031 319,283 212,855 56,761 588,899 –691,791 –579,759
4 709,517 70,952 23,414 615,151 359,385 239,590 63,891 662,865 –1,242,625 –627,474
5 798,633 79,863 26,355 692,415 331,967 221,312 59,016 612,295 –1,239,769 –547,354
6 737,705 73,771 24,344 639,590 405,477 270,318 72,085 747,880 –1,295,234 –655,644
7 901,060 90,106 29,735 781,219 567,945 378,630 100,968 1,047,544 –1,703,187 –921,968
8 1,262,101 126,210 41,649 1,094,242 473,681 315,788 84,210 873,679 –1,795,647 –701,406
9 1,052,625 105,263 34,737 912,626 813,362 542,242 144,598 1,500,202 –2,201,607 –1,288,981
10 1,807,472 180,747 59,647 1,567,078 709,324 472,883 126,102 1,308,308 –2,597,290 –1,030,211
11 1,576,275 157,628 52,017 1,366,630 572,032 381,355 101,695 1,055,081 –2,085,293 –718,662
12 1,271,182 83,125 41,949 1,146,108 905,524 603,683 160,982 1,670,188 –2,388,850 –1,242,742
13 2,012,275 66,405 1,945,870 707,503 471,668 125,778 1,304,949 –2,547,692 –601,822
14 1,572,228 51,884 1,520,344 446,864 297,909 79,442 824,215 –1,426,037 94,308
15 993,030 32,770 960,260 566,968 377,978 100,794 1,045,740 –951,432 8,828
16 1,259,928 41,578 1,218,350 593,782 395,855 105,561 1,095,197 –1,086,370 131,981
17 1,319,515 43,544 1,275,971 573,919 382,613 102,030 1,058,561 –926,581 349,390
18 1,275,375 42,087 1,233,288 234,905 156,603 41,761 433,269 –83,879 1,149,409
19 522,011 17,226 504,785 149,409 99,606 26,562 275,577 873,832 1,378,617
20 332,020 10,957 321,063 77,571 51,714 13,790 143,075 1,235,542 1,556,605
21 172,380 5,689 166,691 11,250 7,500 2,000 20,750 1,535,855 1,702,546
22 25,000 825 24,175 1,702,546 1,537,632
Total 19,847,349 992,366 654,963 18,200,021 8,931,307 5,954,205 1,587,788 16,473,300

Tables 13 and 14 show comparison between the initial schedule and the optimized schedule with activities’ new start dates in enterprises. The first scenario is to minimize negative cash flow and keep or maximize the profit. The results show that negative cash flow minimized from −693,784 to −634,514 in enterprise I and from −2,646,408 to −2,529,324 in enterprise II with keeping the profit. On the other hand, the optimized schedule of the project in noncritical activities’ start times have changed to reach the optimum schedule with the minimum negative cash flow and optimum profit. As well as the second scenario is maximizing profit by extending the project and reducing the problem of negative cash flow. The results show that negative cash flow is minimized to −612,768 with a profit of +200,116 in enterprise I and to −2,597,290 with a profit of +1,537,632 in enterprise II. On the other hand, the optimized schedule of the project in critical and non-critical activities start times have changed to reach the optimum schedule with the minimum negative cash flow and optimum profit.

Table 13

Initial schedule and optimized schedule for scenarios in enterprise I

Activity Original schedule start time Optimized schedule start time for scenario I Optimized schedule start time for scenario II
Project I
A1000 90 90 90
A1010 90 124 109
A1020 185 185 188
A1030 232 232 241
A1040 278 278 291
A1050 319 319 342
A1060 335 335 368
A1070 395 395 438
A1080 225 240 283
A1090 249 292 438
A1100 436 436 491
A1120 466 466 521
A1130 466 472 532
A1110 466 466 530
A1140 487 487 542
Project II
A1000 1 1 1
A1020 16 16 26
A1084 275 298 306
A1085 310 344 382
A1030 91 91 123
A1040 136 136 169
A1050 211 211 256
A1060 256 256 301
A1070 286 286 336
A1080 361 361 415
A1090 401 401 464
A1100 421 421 498
A1120 391 439 517
A1130 391 402 453
A1140 391 440 507
A1110 436 436 515
A1150 466 466 545
Max negative cash flow –693,784 –634,514 –612,768
Profit 304,451 304,451 200,116
Table 14

Initial schedule and optimized schedule for scenarios in enterprise II

Activity Original schedule start time Optimized schedule start time for scenario I Optimized schedule start time for scenario II
Project I
A1000 1 1 1
A1005 61 61 61
A1010 61 69 75
A1015 61 69 61
A1020 121 138 143
A1025 141 141 141
A1030 141 161 141
A1040 121 134 121
A1045 181 183 195
A1050 241 241 241
A1060 321 321 321
A1090 206 298 280
A1095 206 206 206
A1100 386 386 386
A1110 386 391 386
A1120 421 421 451
Project II
A900 123 123 123
A1000 173 173 173
A1010 173 182 173
A1020 233 248 233
A1030 233 233 233
A1040 233 298 283
A1050 328 328 328
A1060 413 413 413
A1070 488 488 488
A1079 233 401 371
A1080 533 533 533
A1100 563 563 563
A1110 563 563 563
A1120 593 593 620
Project III
A1000 184 184 184
A1005 244 244 244
A1010 244 284 244
A1020 314 314 314
A1050 379 379 379
A1070 424 424 450
A1080 379 394 419
Max negative cash flow –2,646,408 –2,529,324 –2,597,290
Profit 1,726,721 1,726,721 1,537,632

11 Conclusion

This study uses GA to develop a new profit optimization model for enterprise project scheduling problems and conducts periodic financial auditing on behalf of the contractor. To assess the financial feasibility of a project, this work establishes a time schedule and incorporates cash flow and financial data into the model. The analysis employs an example of five projects in two public sector enterprises, and the optimal schedule is developed to minimize negative cash flow, while maximizing profit. Additionally, the scenario includes practical constraints such as a due date and initial negative cash and profit. The model can smooth financial pressure by shifting activities’ schedules without delaying or extending the time of the project (delaying completion time). The results show that negative cash flow is minimized from −693,784 to −634,514 in enterprise I and −2,646,408 to −2,529,324 in enterprise II in the first scenario and also results show that negative cash flow is minimized to −612,768 with a profit of +200,116 in enterprise I and to −2,597,290 with a profit of +1,537,632 in enterprise II in the second scenario. Because of this, the model’s proposed solution helps contractors meet their financial obligations when faced with scheduling problems.

Acknowledgments

This project is supported by the Ministry of Planning, Iraq, and the University of Baghdad in testing and supplying raw materials needed to achieve this work. The author gratefully acknowledges the support received.

  1. Funding information: The authors state no funding involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

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Received: 2022-03-10
Revised: 2022-04-08
Accepted: 2022-04-12
Published Online: 2022-06-08

© 2022 Musaab Falih Hasan and Sawsan Rasheed Mohammed, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/jmbm-2022-0032
Keywords for this article
optimization; multiple construction projects; cash flow; genetic algorithm
Creative Commons
BY 4.0

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  47. Time and finance optimization model for multiple construction projects using genetic algorithm
  48. Identification of the main causes of risks in engineering procurement construction projects
  49. Identifying the selection criteria of design consultant for Iraqi construction projects
  50. Calibration and analysis of the potable water network in the Al-Yarmouk region employing WaterGEMS and GIS
  51. Enhancing gypseous soil behavior using casein from milk wastes
  52. Structural behavior of tree-like steel columns subjected to combined axial and lateral loads
  53. Prospect of using geotextile reinforcement within flexible pavement layers to reduce the effects of rutting in the middle and southern parts of Iraq
  54. Ultimate bearing capacity of eccentrically loaded square footing over geogrid-reinforced cohesive soil
  55. Influence of water-absorbent polymer balls on the structural performance of reinforced concrete beam: An experimental investigation
  56. A spherical fuzzy AHP model for contractor assessment during project life cycle
  57. Performance of reinforced concrete non-prismatic beams having multiple openings configurations
  58. Finite element analysis of the soil and foundations of the Al-Kufa Mosque
  59. Flexural behavior of concrete beams with horizontal and vertical openings reinforced by glass-fiber-reinforced polymer (GFRP) bars
  60. Studying the effect of shear stud distribution on the behavior of steel–reactive powder concrete composite beams using ABAQUS software
  61. The behavior of piled rafts in soft clay: Numerical investigation
  62. The impact of evaluation and qualification criteria on Iraqi electromechanical power plants in construction contracts
  63. Performance of concrete thrust block at several burial conditions under the influence of thrust forces generated in the water distribution networks
  64. Geotechnical characterization of sustainable geopolymer improved soil
  65. Effect of the covariance matrix type on the CPT based soil stratification utilizing the Gaussian mixture model
  66. Impact of eccentricity and depth-to-breadth ratio on the behavior of skirt foundation rested on dry gypseous soil
  67. Concrete strength development by using magnetized water in normal and self-compacted concrete
  68. The effect of dosage nanosilica and the particle size of porcelanite aggregate concrete on mechanical and microstructure properties
  69. Comparison of time extension provisions between the Joint Contracts Tribunal and Iraqi Standard Bidding Document
  70. Numerical modeling of single closed and open-ended pipe pile embedded in dry soil layers under coupled static and dynamic loadings
  71. Mechanical properties of sustainable reactive powder concrete made with low cement content and high amount of fly ash and silica fume
  72. Deformation of unsaturated collapsible soils under suction control
  73. Mitigation of collapse characteristics of gypseous soils by activated carbon, sodium metasilicate, and cement dust: An experimental study
  74. Behavior of group piles under combined loadings after improvement of liquefiable soil with nanomaterials
  75. Using papyrus fiber ash as a sustainable filler modifier in preparing low moisture sensitivity HMA mixtures
  76. Study of some properties of colored geopolymer concrete consisting of slag
  77. GIS implementation and statistical analysis for significant characteristics of Kirkuk soil
  78. Improving the flexural behavior of RC beams strengthening by near-surface mounting
  79. The effect of materials and curing system on the behavior of self-compacting geopolymer concrete
  80. The temporal rhythm of scenes and the safety in educational space
  81. Numerical simulation to the effect of applying rationing system on the stability of the Earth canal: Birmana canal in Iraq as a case study
  82. Assessing the vibration response of foundation embedment in gypseous soil
  83. Analysis of concrete beams reinforced by GFRP bars with varying parameters
  84. One dimensional normal consolidation line equation
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