The objective of this module is to search for and identify optimal construction logistics plans that provide optimal tradeoffs between the two optimization objectives of minimizing logistics costs and minimizing project schedule criticality. Genetic Algorithms (GA) is utilized in the present module because of its unique capabilities in multi-objective optimization, especially in complex nonlinear problems with large search spaces (Deb et al 2001). The GA optimization module generates a set of optimal tradeoff solutions for congested logistics planning problem in three main steps, as shown in Figure 5.4: (1) formulating the chromosome of the optimization decision variables and generating an initial population of solutions; (2) evaluating the fitness (objective functions) of each solution; and (3) generating a new population using genetic operators. Steps 2 and 3 are repeated for G generations, after which a set of Pareto optimal solutions are extracted. Each of these solutions represents a unique tradeoff between the two optimization objectives. The following subsections describe in details each of these steps.
1) Formulate Decision Variables Chromosome and generate an initial set of solutions (g = 1)
2) Evaluate Fitness Objective Functions g = 1
Last Generation
g = G?
3) Create a new population using the calculated fitness and a set of genetic operators such as
selection, crossover, mutation, and elitism
Minimize Total Logistics Cost
Minimize Project Schedule Criticality
Logistics Planning Module
Result: Generate Pareto Optimal tradeoff Solutions
Total Logistics Costs Schedule Criticality
GA Optimization Module
Yes
No
Figure 5.4 Genetic Algorithms Optimization Module
5.4.1 Decision Variables Chromosome and Initial Population Generation
The present C2LP model starts the optimization of congested construction logistics planning with formulating the decision variables chromosome and generating an initial population of solutions. A chromosome of optimization decision variables is formulated based on the input data, to represent four main categories of critical logistics decisions, as shown in Figure 5.5:
(1) material procurement; (2) materials storage plan; (3) layout of temporary facilities; and (4) scheduling of noncritical activities. An initial population of solutions is generated the based on the formulated chromosome to be used the subsequent steps of the GA optimization module.
First, material procurement decision variables include Fixed-Ordering-Periods (FOPm,t) of each material (m) in every construction stage (t), as described earlier in Section 4.2. Based on material procurement decisions, construction materials are delivered to the construction site in fixed intervals (FOPm,t) with sufficient quantities to satisfy the demand of the construction activity scheduled in the succeeding interval period. The lower bound of each material FOP is 1 day, which represents a Just-in-Time (JIT) material procurement that is efficient in minimizing site space demands for material storage areas. Otherwise, the FOP variable can be any value greater than one representing a Just-in-Case (JIC) procurement plan with onsite material storage areas.
Material
Second, materials storage decision variables are designed to specify four decisions for each material (m) in every construction stage (t): (1) material storage type; (2) location of material exterior storage area; (3) orientation of material exterior storage area; and (4) material interior storage priority. Material storage type (STm,t) is a binary decision variable that specifies if the delivered quantity of material m in stage t is stored in interior building rooms or in exterior space on site. If the exterior storage type is selected (STm,t = 0), the second and third decision variables (exterior grid location LSm,t and orientation m,St) are then generated to position the material storage in exterior site space. Otherwise (STm,t = 1), the fourth decision variable (material interior storage priority Pm,t) is used to allocate interior building rooms to each delivery of material m in stage t using a newly developed algorithm that is described later in Section 5.5.
Third, the exterior site layout of temporary facilities is planned based on the decision variables of exterior grid location (Lf,t) and orientation (f ,t) decision variables for: (1) every moveable facility in each stage during which the facility exists on site; and (2) every new stationary facility in each construction stage. The C2LP model also considers site exterior layout constraints and space availability in optimally positioning temporary facilities as well as all material storage areas which are selected to be positioned in exterior space (STm,t = 0).
Fourth, the scheduling of noncritical activities is defined by the number of minimum-shifting-days (Si) of each activity within its total float. Shifting of noncritical activities, beyond their early start times, allows for providing additional interior spaces for material storage areas that can lead to lower project logistics costs. This process, however, increases project schedule criticality and the risks of project delays. The present C2LP model is therefore designed to consider this critical tradeoff between minimizing construction logistics costs and project schedule criticality, as described in the following sections.
The C2LP model is designed to generate optimal decision variables that comply with all relevant constraints that are imposed by interior space availability, exterior space availability, and suppliers’ capacities. First, interior space constraints are imposed the assignment of interior spaces to material storage areas. These constraints include room capacities, creation times of rooms, and permissible periods of interior material storage. Second, four types of geometric constraints are imposed on exterior material storage areas and temporary facilities:
boundary, overlap, distance, and zone constraints. Third, the maximum ordering quantities of
material suppliers are considered in the present model during the generation of material procurement decision variables (Fixed-Ordering-Periods FOP).
5.4.2 Optimization Objective Functions
The present model is designed to optimize the tradeoff between the two important planning objectives of minimizing total construction logistics costs and minimizing project schedule criticality. First, total logistics cost (TLC) is calculated using Equation 5.7 as the summation of: (1) ordering cost; (2) financing cost ; (3) stock-out cost; and (4) site layout cost. Ordering cost (OC) represents the purchase of the needed materials from the supplier and their delivery costs to the construction site. Financing cost (FC) represents the lost interest on the contractor’s capital that is tied up in onsite material inventories that are created based on material procurement decisions. Stock-out cost (SC) includes any project delay costs that occur as a result of late material deliveries. Layout cost (LC) includes the travel cost of contractor’s personnel/equipments moving between site facilities, cost of material handling time from interior and/or exterior storage areas to activities workspaces, and cost of reorganizing the site layout between construction stages, if applicable. Each of these costs is calculated in the logistics planning module considering the generated values of the optimization decision variables, as described later in Section 5.5.
LC SC
FC OC
CLC
(5.7)SRC RTC
MHCE MHCI
LC
(5.8)Where,
CLC = construction logistics costs;
OC = ordering cost;
FC = financing cost;
SC = stock-out cost;
LC = layout cost;
LC = layout cost;
MHCI = material handling cost of interior storage areas:
MHCE = material handling cost of exterior storage areas:
RTC = resource traveling cost; and SRC = site reorganization cost.
The schedule criticality is calculated in the C2LP using a newly developed metric that aggregates the amount of consumed floats of noncritical activities as a result of their scheduling decision variables. As shown in Equation 5.9, a criticality index (CIi) is calculated for each activity i as the ratio between: (1) the number of days that activity i is shifted within its total float, as the difference between its scheduled start (SSi) and early start (ESi) times;
and (2) the total float (TFi) of activity i. The scheduled times of noncritical activities are calculated using a new scheduling algorithm in the logistics planning module, which is described later in Section 5.5. The calculated criticality indexes of all noncritical activities are then averaged to calculate the project schedule criticality index (SCI), as shown in Equation 5.9. The lower bound of the activity criticality index (CIi) is 0, which represents scheduling the activity on its early start time (SSi = ESi); while the upper bound is 1, which represents scheduling the activity on its late start time (SSi = LSi). Accordingly, the schedule criticality index (SCI) of the whole project ranges from 0 (all activities are scheduled on their early times) to 1 (all activities are scheduled on their late times).
SCI = Schedule criticality index;
N’ = number of noncritical activities;
CIi = criticality index of activity i;
SSi = scheduled start time of activity i;
ESi = early start time of activity i; and TFi = Total float of activity i.
5.4.3 Generation of New Populations
A new population of solutions is created in every generation based on the calculated fitness values (objective functions) using a set of genetic operators such as selection, crossover, mutation and elitism. The present optimization module utilizes a multi-objective optimization algorithm named Non-dominated Sorted Genetic Algorithm II (NSGAII) (Deb et al. 2001) due to its unique capabilities in: (1) generating, in a single run, a set of optimal pareto solutions with different tradeoffs between the conflicting optimization objectives; and (2) utilizing novel metrics, such as elitism and pareto front crowding, in order generate a wide and uniform spectrum of high quality tradeoff solutions (Deb et al. 2001, El-Rayes and Kandil 2005). The set of optimal tradeoff solutions of congested construction logistics plans are extracted after the last generation and planners can select a single solution that fits the specific needs and priorities of each project.