## Time-Cost-Quality Tradeoff Modeling based on Resource Allocation

Read this article. The paper presents an optimization model that enables managers to effectively evaluate trade-offs related to time, cost, and other competing priorities. Pay particular attention to Section 6 as it provides an illustrated example of building a home.

### Example Illustration and Discussion

#### Example Illustration

Here is a typical brick concrete house with a concrete raft slab foundation and three stories as a study example to illustrate application of the PTCQTP model, shown in Figure 2. Construction lot is nearly 300 square meters (m2), and depth of the shallow foundation is one-half meter and earthwork volume needed to be moved is 240 m3. The first floor is 120 m2, the second floor is about 105 m2, and the third floor is 90 m2.

Figure 2

A three-story house as a study example.

The building consists of 20 construction activities, and the construction procedure is shown in an activity-on-node network in Figure 3. Each activity has a number of possible resource options and work options that can be used to construct the activity as shown in Table 1. Construction resources in each activity are labors, materials, equipment, and administration. Normal working shift is eight hours a day and the maximum working overtime is additional four hours a day. During working overtime, construction labors and administrators will be paid doubly ( and ).

 Activity group Activity  ID Quantity ( ) Productivity (LPRDmin–LPRDmax) Overtime factor ( ) Labor Material Equipment Administration Cost rate ( ) ($/d) Labor cost ( ) Labor quality (LQmin–LQmax) Cost (MCmin–MCmax) ($) Quality (MQmin–MQmax) Cost (ECmin–ECmax) ($) Quality (EQmin–EQmax) Productivity factor (DEKmin–DEKmax) Cost rate (ACRmin–ACRmax) ($/d) Quality (AQmin–AQmax) Cost ( ) (\$) Earth work 1 240 m3 100–150 m3/d 1–1.5 700 — 0.8–1.0 3200–4500 0.7–1.0 600–650 0.8–1.0 0.8–1.2 90–150 0.7–1.0 — Foundation 2 110 m2 10–12 m2/d 1–1.5 300 — 0.8–1.0 800–1100 0.7–1.0 110–120 0.8–1.0 0.98–1.02 90–150 0.7–1.0 — 3 1.6 t 0.6–0.8 t/d 1–1.5 600 — 0.7–1.0 5600–7200 0.7–1.0 128–144 0.8–1.0 0.9–1.1 90–150 0.7–1.0 — 4 52 m3 15–20 m3/d 1–1.5 750 — 0.9–1.0 18200–23400 0.7–1.0 150–180 0.9–1.0 0.95–1.05 90–150 0.7–1.0 — 5 75 m3 8–12 m3/d 1–1.5 1700 — 0.8–1.0 16000–20000 0.7–1.0 1500–1800 0.8–1.0 0.98–1.02 90–150 0.7–1.0 — 6 60 m3 20–25 m3/d 1–1.5 430 — 0.8–1.0 6400–8600 0.7–1.0 120–150 0.8–1.0 0.9–1.1 90–150 0.7–1.0 — 1st story 7 120 m2 8–11 m2/d 1–1.5 450 — 0.7–1.0 1200–1700 0.7–1.0 210–230 0.9–1.0 0.98–1.02 90–150 0.7–1.0 — 8 3.2 t 0.8–1.2 t/d 1–1.5 800 — 0.7–1.0 11200–14400 0.7–1.0 256–288 0.8–1.0 0.9–1.1 90–150 0.7–1.0 — 9 48 m3 7–10 m3/d 1–1.5 1000 — 0.7–1.0 16800–21600 0.7–1.0 200–240 0.9–1.0 0.95–1.05 90–150 0.7–1.0 — 10 62 m3 4–6 m3/d 1–1.5 750 — 0.8–1.0 13200–16600 0.7–1.0 1240–1488 0.8–1.0 0.98–1.02 90–150 0.7–1.0 — 2nd story 11 105 m2 8–11 m2/d 1–1.5 460 — 0.7–1.0 1100–1600 0.7–1.0 180–200 0.8–1.0 0.98–1.02 90–150 0.7–1.0 — 12 2.8 t 0.8–1.2 m2/d 1–1.5 800 — 0.7–1.0 9800–12600 0.7–1.0 224–252 0.8–1.0 0.9–1.1 90–150 0.7–1.0 — 13 43 m3 7–10 m3/d 1–1.5 1000 — 0.7–1.0 15050–19350 0.7–1.0 180–210 0.9–1.0 0.95–1.05 90–150 0.7–1.0 — 14 55 m3 4–6 m3/d 1–1.5 750 — 0.8–1.0 11700–14700 0.7–1.0 1100–1320 0.8–1.0 0.95–1.05 90–150 0.7–1.0 — 3rd story 15 95 m2 7–10 m2/d 1–1.5 470 — 0.7–1.0 1100–1600 0.7–1.0 180–210 0.8–1.0 0.95–1.05 90–150 0.7–1.0 — 16 2.2 t 0.8–1.2 t/d 1–1.5 800 — 0.7–1.0 7700–9900 0.7–1.0 176–198 0.8–1.0 0.9–1.1 90–150 0.7–1.0 — 17 38 m3 7–10 m3/d 1–1.5 1000 — 0.7–1.0 13300–17100 0.7–1.0 175–190 0.9–1.0 0.95–1.05 90–150 0.7–1.0 — 18 50 m3 4–6 m3/d 1–1.5 750 — 0.8–1.0 10600–13300 0.7–1.0 1000–1200 0.8–1.0 0.9–1.1 90–150 0.7–1.0 — Roof 19 135 m2 18–24 m2/d 1–1.5 300 — 0.7–1.0 3200–3800 0.7–1.0 40–50 0.8–1.0 0.98–1.02 90–150 0.7–1.0 — 20 160 m2 40–50 m2/d 1–1.5 750 — 0.7–1.0 7000–8500 0.7–1.0 100–120 0.8–1.0 0.98–1.02 90–150 0.7–1.0 —

Table 1

Construction activities with resource and work options.

Figure 3

Construction procedure of the building example. 1: clear lot and excavate for foundation; 2: erect formwork for foundation concrete; 3: install foundation reinforcing; 4: pour footings; 5: build foundation block; 6: refill foundation earth; 7: erect formwork for 1st story; 8: install reinforcing for 1st story; 9: pour columns, beam, and slabs for 1st story; 10: build block in 1st story; 11: erect formwork for 2nd story; 12: install reinforcing for 2nd story; 13: pour columns, beam, and slabs for 2nd story; 14: build block in 2nd story; 15: erect formwork for 3rd story; 16: install reinforcing for 3rd story; 17: pour columns, beam, and slabs for 3rd story; 18: build block in 3rd story; 19: install heat insulation in the roof; 20: install waterproof layers for the roof.

Since construction materials weigh heavily on the overall quality of a construction project, the quality weight indicators of construction materials are bigger than any other indicators. In this case the quality weight indicators of administration are the least important when comparing with other indicators.

After deliberating on all construction activities, 20 activities are grouped as 7 works: earth work, foundation work, 1st story work, 2nd story work, 3rd story work, and roof work. The quality weight indicators of group works  are suggested first and then the quality weight indicators of all 20 construction activities  are assigned from the quality weight indicators of their groups. All quality weight indicators applied in this building case are shown in Table 2.

 Group works Quality weight indicators of group works ( ) Activity (i) (ID) Quality weights indicators of activity (i)( ) Quality weight indicators of labors (i)( ) Quality weight indicators of materials (i)( ) Quality weight indicators of equipment (i)( ) Quality weight indicators of administration (i)( ) Earth work 0.05 1 0.05 0.1 0.7 0.15 0.05 Foundation work 0.25 2 0.05 0.1 0.7 0.15 0.05 3 0.06 0.1 0.7 0.15 0.05 4 0.06 0.1 0.7 0.15 0.05 5 0.06 0.1 0.7 0.15 0.05 6 0.02 0.1 0.7 0.15 0.05 1st story work 0.2 7 0.05 0.1 0.7 0.15 0.05 8 0.05 0.1 0.7 0.15 0.05 9 0.05 0.1 0.7 0.15 0.05 10 0.05 0.1 0.7 0.15 0.05 2nd story work 0.2 11 0.05 0.1 0.7 0.15 0.05 12 0.05 0.1 0.7 0.15 0.05 13 0.05 0.1 0.7 0.15 0.05 14 0.05 0.1 0.7 0.15 0.05 3rd story work 0.15 15 0.03 0.1 0.7 0.15 0.05 16 0.04 0.1 0.7 0.15 0.05 17 0.04 0.1 0.7 0.15 0.05 18 0.04 0.1 0.7 0.15 0.05 Roof work 0.15 19 0.07 0.1 0.7 0.15 0.05 20 0.08 0.1 0.7 0.15 0.05 ∑ 1.0 — 1.0 — — — —

Table 2

The quality weight indicators.