Resource-Constrained Project and Multi-Project Scheduling Problems (RCPSPs and RCMPSPs) have been essential topics of study over the last three decades. Both prob-lems consist of activities that must be scheduled subject to precedence and resource constraints. This paper surveys studies of RCPSPs and RCMPSPs under consideration of four categories of project activities, simply recorded as categories A, B, C, and D. Category A refers to activities can be performed using fixed resources along The Y-axis over fixed durations along The X-axis, and cannot be interrupted. Category B applies to activities that can be performed using the same type of resource in category A but can be interrupted. Category C refers to activities that can be performed using flexible resources over flexible durations and cannot be interrupted. Category D refers to activities can be performed using flexible resources over flexible durations and can be interrupted. Many algorithms have been developed to solve the RCPSPs and RCMPSPs when activities are classified individually under category A, B, or C. However, in practice, welding, cutting or assembly activities in a manufacturing projects for an oil cargo can be under a new category so-called D. The project manager can speed up or slow down these activities by allocating or removing more resources, and these activities can be interrupted or can be resumed at any time. From the perspective of activity categories, we intend to review the literature on RCPSPs and RCMPSPs and to obtain the new research directions for solving the problems.

The resource-constrained project scheduling problem (RCPSP) is a well-known and widely studied topic. The underlying problem assumes that non-preemptions and that constant resources are restrictions imposed on project activities, which are to be scheduled, subject to precedence relation and limited resource constraints. Project activities, in RCPSP, are classified under category A. The problem is expanded to include various other activity assumptions categories, such as B and C. In the Preemptive-RCPSP, project activities are classified under category B, which refers to the activity that can be implemented using constant resources and constant durations. In the Flexible-RCPSP, project activities are classified under category C, which refers to the activities that can be executed using flexible resources over flexible durations, and preemptions are not allowed. However, in One-of-a-Kind Production companies (OKP), such as the housing industry, plastic injection moldings, and RV manufacturing, all known as “manufactured-to-order” operations, the activities are classified under category D in addition to A, B, and C, simultaneously. Category D refers to the activities that can be executed using flexible durations and flexible resources, and preemptions are allowed. In this paper, therefore, we present a new effective model in order to deal with the projects that consist of all the previous activity assumptions simultaneously to generate feasible project schedules. Case studies are included, and the results show that the resources usage is increased and the project makespan is reduced.