Operational efficiency frontier [electronic resource] : visualizing, manipulating, and navigating the construction scheduling state space with precedence, discrete, and disjunctive constraints
Keywords: Civil and Environmental Engineering.

Space and time are two fundamental dimensions of human comprehension (Akhundov 1986). The guiding principle of this dissertation is discovering the relationship between these two dimensions within the construction management field. This guiding principle led to three layers of research, each layer each layer uncovering, and subsequently enabling investigation of the next. The first layer of this research formalizes the spatial constraint for construction scheduling and is motivated by my observations of construction sites across three continents. Almost all of the construction sites I witnessed evoke images of vast empty spaces punctuated with pockets of intense work. Construction site space, it seems, is under-utilized. So much empty space on construction sites suggests a significant potential to schedule more construction processes concurrently to reduce construction duration. However, simply increasing space utilization by scheduling more construction processes concurrently leads to spatial congestion (Thomas et al. 2006), which is detrimental to productivity, safety, and quality (Riley and Sanvido 1995). Thus, for every construction project there is a balanced level of construction site space utilization, that achieves short construction durations while still ensuring no spatial congestion. Attaining this ideal level of space utilization requires a systematic approach to construction space allocation. However, current construction management theory cannot achieve these balanced levels of space utilization because the constraint for resolving spatial requirements has not been sufficiently formalized for doing so. Hence, the first layer of this research formalizes the construction scheduling spatial constraint. The spatial constraint is formalized as a disjunctive constraint, which ensures that processes don't occur in the same space at the same time. The second layer of this dissertation's research formalizes and operationalizes three types of construction constraints to form an automated construction scheduler, the Tri-Constraint Method (TCM). The spatial constraint is combined with precedence and discrete resource capacity constraints. Precedence constraints ensure that the laws of physics are not violated while discrete resource capacity constraints ensure that discrete resources, such as labor, are not over-allocated. The mechanisms for resolving these three constraint types are combined with a mechanism for varying sequence, which enables TCM to generate multiple construction sequencing alternatives. To validate TCM, three construction project case studies are used to compare 10,000 TCM schedules to schedules created with the Critical Path Method (CPM) and the Line of Balance (LOB) scheduling methods. The CPM construction durations for the three case studies are on average 49% shorter than the fastest TCM schedules because CPM does not model spatial requirements and thus schedules crews to work in the same space. The fastest TCM construction durations are on average 45% shorter than the fastest LOB construction durations because the LOB scheduling method cannot schedule more than one process in a zone while guaranteeing no spatial congestion. The third layer of this dissertation's research presents a mathematically derived Pareto efficiency frontier for construction and is motivated by observing that there are millions of ways to schedule a typical construction project if all possibilities are considered (Taghaddos et al. 2012). This dissertation refers to the set of all possible scheduling alternatives for a project as the construction scheduling state space or state space. The state space is governed by complex interactions of variables that affect which schedules are feasible for a project. For example, assigning a different number of crews to a project or changing the construction sequence changes which schedules are feasible for construction teams to execute; thus varying the schedule metric values available for a given project. Understanding how these variables affect the state space is desirable because construction managers can use this knowledge to select better values for these variables, thus generating schedules with better performance. Currently to understand how such variables affect the state space, construction managers generate construction schedules one schedule at a time leading to a low number of schedule alternatives. Such a low number of schedules represents a tiny portion of the schedules in the state space and does not give schedulers a clear idea of how this state space is affected by various variables such as construction sequence and labor capacity. Other fields understand the interaction of complex variables by using efficiency frontiers (Kavousian and Rajagopal 2014, Kontodimopoulos and Niakas 2005, Markowitz 1952). The third layer of this research presents the Operational Efficiency Frontier (OEF) by mathematically correlating the schedule metrics of Construction Duration (CD) and a new space utilization metric: the Average Space Utilization Factor (ASUF). Unlike previous space utilization metrics, ASUF measures how an entire construction project uses the space available to it as opposed to how one or several construction processes use the space available to them. Measuring how an entire construction project uses the space available to it allows a more systematic method for formalizing the space constraint and for managing and coordinating the resource of space on site. The Operational Efficiency Frontier (OEF) is dependent on the variables of construction scheduling method (e.g., TCM or CPM) and schedule execution (e.g., delays) and independent of construction sequence and discrete resource capacity. The OEF is used in conjunction with the Tri-Constraint Method (TCM) to present an approach to construction scheduling based on visualizing, manipulating, and navigating the state space. The state space is visualized by plotting the OEF for a construction project, which shows the tradeoff between space utilization and construction duration for the project's efficient schedule executions. The state space is manipulated by changing variables that shift the OEF's location. The state space is navigated by using the TCM to quickly generate thousands of new schedules with different schedule metric values. The Operational Efficiency Frontier, the Average Space Utilization Factor, and the proposed approach to construction scheduling are validated by calculating the OEFs and generating schedules for three case studies and demonstrating which variables affect the location of the OEF. The work in this dissertation has five implications. (1) The TCM formalizes and combines the resolution mechanisms for three constraint types. These resolution mechanisms are clearly and separately defined which could allow future construction researchers to improve these mechanisms. (2) To find shorter feasible schedules, TCM can generate thousands of feasible schedules in minutes compared to the hours required to produce a single schedule with today's construction scheduling methods. For the three case study projects, TCM produced schedules without spatial conflicts with construction durations that are 45% shorter than those produced with the LOB methods, today's best scheduling method that consider spatial requirements of construction processes to some extent. Quickly generating large numbers of feasible schedules can enable construction managers to select schedule alternatives with better schedule metric values. (3) The ASUF metric mathematically conceptualizes construction as throughput via the capacity of a construction site's area: The higher the "throughput" of construction via the construction site's area the shorter the construction duration. This conceptualization emphasizes the importance of managing the often-neglected resource of space on construction sites. (4) The OEF visualizes the relationship between space utilization and construction duration, thus showing the shortest duration for a construction project with the selected construction methods. The OEF can be calculated without generating a single schedule and its dependence on certain variables mean that rapid feedback can be gained on the effect of such variables on the state space, even on schedule alternatives that have not yet been generated. The OEF's independence of construction sequence and discrete resource capacity means that construction managers have a tool that can grasp thousands of sequencing and discrete resource capacity schedule alternatives at a time. (5) The approach to construction scheduling of visualizing, manipulating, and navigating the state space at the very least acknowledges the scheduling state space which is not commonly done in industry today. This approach to construction scheduling offers a more accurate representation of the construction scheduling problem than that offered by creating and analyzing single schedules.