## 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

#### Discussion

(1) If $Q=0.8$ or above and $C=\ 350000$ or below.

If the overall quality objective is $0.8$ or above and the overall cost objective is $\ 350000$ or below, the optimal overall time is 64 days suggested by the PTCQTP model.

All optimized construction arrangements and resource utilizations suggested by this model are available; for example, the optimal working hours of each activity are shown in Figure 4. The optimal working arrangement reveals that nearly all activities are carried out in overtime working hours since the construction time is limited. Although overtime working demands higher labor cost, overtime working shortens construction time and secures construction quality.

Figure 4

Optimized working hours a day in twenty activities.

The optimized material quality performances in 20 construction activities vary much, as shown in Figure 5. For example, materials in the activity (6) "-Refill foundation earth" are required to maintain the highest quality level $(=0.95)$, while the activity (10) "Build block in 1st story" and (12) "-Install reinforcing for 2nd story" only need to be the lowest quality level $(=0.7)$. Obviously the lowest quality requirement would save cost.

Figure 5

Optimized material quality performances in twenty activities.

(2) Optimized overall time-cost-quality.

A part of optimized results (shown in Table 3) are excerpted from numerous calculations when construction cost and quality are confined within potential solution boundaries. A visual tradeoff among construction time, cost, and quality is presented in Figure 6.

 Quality Time (days) Cost ( dollars) 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 0.74 109 101 84 78 72 65 — — — — — — — 0.76 — 105 88 80 75 68 66 — — — — — — 0.78 — — 94 81 77 73 67 60 — — — — — 0.80 — — 97 83 80 76 67 64 61 — — — — 0.82 — — — 85 82 76 72 66 62 57 — — — 0.84 — — — 97 85 82 76 67 64 59 — — — 0.86 — — — — 90 83 79 73 67 61 58 54 — 0.88 — — — — 97 84 79 75 67 64 60 57 54 0.90 — — — — 98 89 84 77 68 65 62 57 56 0.92 — — — — 103 89 84 79 74 66 63 59 56 0.94 — — — — — 90 86 80 75 68 64 61 56 0.96 — — — — — 91 91 80 75 69 65 62 56 0.98 — — — — — — — — 76 69 65 62 57 1.00 — — — — — — — — — — — — —
Note: — means not available.

Table 3

The minimum time of a building project while project cost and general quality are bounded.

Figure 6

A visual three-dimensional tradeoff pattern among project time, cost, and quality.

When a moderate quality performance, for example, 0.86, is set and the overall cost is $320,000, the overall time is about 90 days by the tradeoff model. The overall cost will climb to$390,000 if the overall time is shortened to 54 days and the quality objective is unchanged.

Tradeoff curves between the overall cost and time under different quality objectives are shown in Figure 7, which proves that traditional linear assumptions between project cost and time are reasonable somehow.

Figure 7

Tradeoff relationship between construction cost and time when the quality sets 0.80, 0.86, and 0.92.