Dirk Briskorn

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts.

Inventory-based dispatching of automated guided vehicles on container terminals

This paper deals with automated guided vehicles (AGVs) which transport containers between the quay and the stack on automated container terminals. The focus is on the assignment of transportation jobs to AGVs within a terminal control system operating in real time. First, we describe a rather common problem formulation based on due times for the jobs and solve this problem both with a greedy priority rule based heuristic and with an exact algorithm. Subsequently, we present an alternative formulation of the assignment problem, which does not include due times. This formulation is based on a rough analogy to inventory management and is solved using an exact algorithm. The idea behind this alternative formulation is to avoid estimates of driving times, completion times, due times, and tardiness because such estimates are often highly unreliable in practice and do not allow for accurate planning. By means of simulation, we then analyze the different approaches. We show that the inventory-based model leads to better productivity on the terminal than the due-time-based formulation.

Complexity of single machine scheduling subject to nonnegative inventory constraints

This paper focuses on single machine scheduling subject to inventory constraints. Jobs either add items to an inventory or remove items from that inventory. Jobs that have to remove items cannot be processed if the required number of items is not available. We consider scheduling problems on a single machine with the minimization of the total weighted completion time, the maximum lateness, and the number of tardy jobs, respectively, as objective and determine their computational complexity. Since the general versions of our problems turn out to be strongly NP-hard, we consider special cases by assuming that different jobs have certain parameter values in common. We determine the computational complexity for all special cases when the objective is either to minimize total completion time or to minimize maximum lateness and for several special cases when the objective is either to minimize total weighted completion time or to minimize the number of tardy jobs.

Truck scheduling in cross-docking terminals with fixed outbound departures

At a cross-docking terminal, inbound shipments are directly transshipped across the terminal to designated outbound trucks, so that delays and inventories are kept as low as possible. We consider an operational truck scheduling problem, where a dock door and a start time have to be assigned to each inbound truck. A set of outbound trucks is scheduled beforehand and, therefore, departure times are fixed. If a shipment is not unloaded, transshipped to the outbound gate and loaded onto the designated outbound truck before its departure, we consider the shipments’s value as lost profit. The objective is to minimize total lost profit. This paper at hand formalizes the resulting truck scheduling problem. We settle its computational complexity and develop heuristics (namely, decomposition procedures and simulated annealing) in order to tackle the problem. We show the efficiency of these heuristics by means of a computational study. Last but not least, a case study is presented.

Exact algorithms for inventory constrained scheduling on a single machine

This paper focuses on single machine scheduling subject to inventory constraints. Jobs add or remove items to or from the inventory, respectively. Jobs that remove items cannot be processed if the required number of items is not available. We consider scheduling problems on a single machine where the objective is to minimize the total weighted completion time. We develop properties of optimal solutions and design a branch and bound algorithm and a dynamic programming algorithm with two extensions. We compare the approaches in our computational study and empirically derive parameter settings leading to instances which are hard to solve.

Feasibility of home-away-pattern sets for round robin tournaments

A Home-Away-Pattern (HAP) set defines each teams venue in each period. We consider the decision problem of whether a round robin tournament can be arranged on the basis of a given HAP set. We give a necessary condition which can be checked in polynomial time and conjecture it to be sufficient.

A generalized classification scheme for crane scheduling with interference

Nowadays, many industries rely on cranes for efficiently executing storage and retrieval operations of goods. Areas of application are, for instance, container logistics in seaports and warehousing operations in automated storage and retrieval systems. Therefore, it is not astounding that plenty scientific papers on crane scheduling in many different yet closely related logistics settings have accumulated. In many of these problems, crane interference occurs. A prominent example is non-crossing constraints where cranes share a common pathway and cannot overtake each other. In order to structure this vast field of research, this paper provides a classification scheme for crane scheduling problems with crane interference. We apply this scheme to classify the existing literature, to determine the status-quo of complexity results, and to identify future research needs.

Aircraft landing problems with aircraft classes

This article focuses on the aircraft landing problem that is to assign landing times to aircraft approaching the airport under consideration. Each aircraft’s landing time must be in a time interval encompassing a target landing time. If the actual landing time deviates from the target landing time additional costs occur which depend on the amount of earliness and lateness, respectively. The objective is to minimize overall cost. We consider the set of aircraft being partitioned into aircraft classes such that two aircraft of the same class are equal with respect to wake turbulence. We develop algorithms to solve the corresponding problem. Analyzing the worst case run-time behavior, we show that our algorithms run in polynomial time for fairly general cases of the problem. Moreover, we present integer programming models. We show by means of a computational study how optimality properties can be used to increase efficiency of standard solvers.

Round robin tournaments and three index assignments

Scheduling a sports league can be seen as a difficult combinatorial optimization problem. We study some variants of round robin tournaments and analyze the relationship with the planar three-index assignment problem. The complexity of scheduling a minimum cost round robin tournament is established by a reduction from the planar three-index assignment problem. Furthermore, we introduce integer programming models. We pick up a popular idea and decompose the overall problem in order to obtain two subproblems which can be solved sequentially. We show that the latter subproblem can be casted as a planar three-index assignment problem. This makes existing solution techniques for the planar three-index assignment problem amenable to sports league scheduling.

Scheduling co-operating stacking cranes with predetermined container sequences

With the proliferation of multi-gantry automated stacking cranes, the already difficult crane scheduling problem in container terminals has become even more challenging. In this paper we present an efficient algorithm that can solve a sub-problem that arises in this context, namely the prioritization of crane gantry movements once transportation tasks have been assigned. We tackle this problem for both, twin crane setting and crossover crane setting, and develop graphical models and strongly polynomial algorithms accordingly. A series of experiments is carried out where it is shown that the method can produce optimum solutions with exceptionally small run times.