Heuristic algorithms for payment models in project scheduling

Abstract

Imagine that the city council of Ghent has approved the construction of a new bridge across the Leie. The bridge will serve as a means to reduce traffic congestion in the city center, and the city council imposes a deadline to ensure the bridge is completed in time. Based on the specifications, a contractor subsequently determines the required resources (e.g. manpower, machines) and constructs a project schedule. This schedule holds the start and finish times of each activity (e.g. pouring concrete for the bridge foundations), and respects the imposed resource restrictions and the order in which the activities have to be executed (e.g. excavate the river banks before pouring concrete for the foundations). Whereas the objective of the client (i.e. the city council) is clear, they want the bridge to be constructed within the specified deadline, the objective for the contractor is less obvious. Is the goal to minimize the project duration, minimize total costs, maximize net present value (NPV), etc.? Assume that the contractor can construct two schedules. The first schedule minimizes the project duration, obtains a duration of 6 weeks less than the deadline and has a NPV of € 1 mio. The second schedule, on the contrary, maximizes the project NPV, which results in a duration equal to the deadline and a NPV of € 1.2 mio. The latter schedule is obtained by delaying certain activities within the imposed restrictions, starting from the first schedule. If we assume that sufficient margins are included in the proposed schedules to compensate for any delays, the contractor would obviously prefer the second schedule, since the financial return is larger. The crucial question here is, however, how the second schedule can be obtained in an effective and efficient manner starting from the first schedule. This dissertation aims to develop algorithms, which optimize the project NPV under different restrictions, by means of five studies. The first paper chapter focuses on NPV optimization subject to precedence and resource restrictions. It is furthermore assumed that both cash inflows (payments received from the client) and cash outflows (payments to subcontractors) occur at the end of each activity. This way, the size of payments is set in advance by the client and corresponds with each activity’s cash flows, whereas the timing depends on the project schedule by means of the selected activity finish times, and is controlled by the contractor. The second and third studies consider other payment models, in which the client determines the payment times in advance, rather than the size of payments. As an example, the client may stipulate that the contractor is paid every month, whereas the size of the payments depends on the work performed by the contractor in each month. Both studies furthermore include several alternatives or modes for each activity. These modes constitute different duration-resource combinations for an activity, out of which one has to be selected by the contractor, and allow for a greater degree of flexibility. The fourth paper chapter introduces capital management on the side of the contractor, by imposing that the total funds available should not become negative during the project. The total funds or cash balance consider the initial capital available and respectively add or subtract cash in- and outflows. A general model is constructed which affects the capital availability throughout the project. The fifth and final study integrates the resource availability in the scheduling process, and as such optimizes the NPV of the project including the resource usage cost, rather than decide on the amount of a resource made available first and schedule the activities second