Civil engineering systems Analysis
Materi 02: Mathematical Modeling and application
Civil Engineering System
Decision Elemen dalam Sistem Rekayasa Sipil
• Civil engineers deal with three main tasks during their career:
• analysis, design and construction.
• When analysing, engineers are commonly required:
• to verify and suggest means to comply with regulations
• to improve the performance of a system,
• to achieve performance goals.
• In designing, engineers face the need:
• to create built environment, and this typically results in conflicting objectives of professionalism, developer’s interests and resources.”
Decision Elemen dalam Sistem Rekayasa Sipil
• during construction, an engineer faces the need:
• to allocate labour, equipment and materials to reach given milestones on time.
• However, timely achievement of such deadlines requires more intensive use of the resources mentioned which triggers project cost.
• Hence, the engineer is faced with two common conflicting goals:
• minimization of resource utilization
• achievement of a certain level of quality and/or performance.”
Objective and Constraints
• Seeking the largest amount of utility or profits is called maximization,
• and seeking the usage of the smallest amount of resources is called minimization.
• The amount to be minimized or maximized is called an objective.
• Restricting yourself to a given amount of some resource gives you a constraint.
• The amount of resources you will use is called decision variable or control variable.
• How effective you use your time, your machines, etc., gives you parameters which are typically related to productivity. Let us look at some examples.?
Bagaimana Mengidentifikasi Objective dan Constraints ?
• an objective is nothing but a constraint without limitation, so objectives and constraints can be interchangeably used, but duplication should be avoided.
• Typically, we define only one objective and many constraints.
• In more advanced problems, one can have many objectives and even define a problem only in terms of multiple (conflicting) objectives.
Creating Decision Models
(1) an identification of the very nature of the problem, (2) writing a mathematical formulation
(3) solving it
Contoh Masalah Pembangunan Jalan Rel
Contoh Masalah Pembangunan Jalan Rel
Masalah Supply Air
Bagaimana mengidentifikasi masalah
• Masalah tanki atau pipa?
• Berapa tangka yang dibutuhkan utk meminimalkan deficit?