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.
The scheduling of gantry cranes with respect to mutual interference has received considerable attention in recent years. We consider a subproblem which arises when each crane has a sequence of tasks ...to be assigned. The problem is concerned with resolving the interference between two cranes by determining which crane avoids the other in order to let it complete its next task first. We provide a fairly general problem framework accounting for different crane systems and various side constraints. We assume a cost function for each task that determines the cost of completing the task at a specific point in time. We then distinguish between the objectives to minimize both the total cost and the maximum cost among tasks. A general dynamic programming framework is provided which allows us to solve all problem versions in pseudo-polynomial time. Furthermore, we show that while the general problem aiming for minimum total cost is binary NP-hard, the general problem aiming for minimum maximum cost can be solved in polynomial time. Finally, we address two important special cases of the former, and we show that they can be solved in polynomial time as well.
•Scheduling mechanism concerning a Kiva system.•Integrated sequencing of orders and racks visits.•Allows to cut fleet size by 50%.•Investigation of impact of the shared storage policy.
This paper ...treats a special parts-to-picker based order processing system, where mobile robots hoist racks and bring them directly to stationary pickers. This technological innovation – known as the Kiva system – heavily influences all traditional planning problems to be solved when operating a warehouse. We, specifically, tackle the order processing in a picking station, i.e., the batching and sequencing of picking orders and the interdependent sequencing of the racks brought to a station. We formalize the resulting decision problem and provide suited solution procedures. In a comprehensive computational study we show that an optimized order picking allows to more than halve the fleet of robots compared to simple decision rules often applied in real-world warehouses.
Last mile deliveries with unmanned aerial vehicles (also denoted as drones) are seen as one promising idea to reduce excessive road traffic. To overcome the difficulties caused by the comparatively ...short operating ranges of drones, an innovative concept suggests to apply trucks as mobile landing and take‐off platforms. In this context, the paper on hand schedules the delivery to customers by drones for given truck routes. Given a fixed sequence of stops constituting a truck route and a set of customers to be supplied, we aim at a drone schedule (i.e., a set of trips each defining a drone's take‐off and landing stop and the customer serviced), such that all customers are supplied and the total duration of the delivery tour is minimized. We differentiate whether multiple drones or just a single one are placed on a truck and whether or not take‐off and landing stops have to be identical. We provide an analysis of computational complexity for each resulting subproblem, introduce efficient mixed‐integer programs, and compare all cases with regard to their potential of reducing the delivery effort on the last mile.
•We consider distributed scheduling with the central objective to maximize the number of non-tardy jobs.•We determine the (absolute) prices of anarchy for various scheduling environments with selfish ...jobs.•We are the first to consider Moore-Hodgson’s algorithm as a local policy.•We show that simple sorting policies do not suffice to achieve a finite price of anarchy.•We prove that two long established heuristics have an approximation guarantee.
We consider the distributed scheduling problem on parallel machines with the central objective of maximizing the number of on-time jobs. Jobs are self-interested utility-maximizers that can choose the machines they are processed on and are exclusively interested in reducing their own private objective function. Each machine processes the jobs according to a local policy. We discuss Nash equilibria in the resulting schedules and perform a thorough analysis of the resulting (absolute) prices of anarchy for various parallel machine environments, utilities of the agents, and local policies of the machines. We show that local policies that are based on simple sorting-based procedures like shortest processing time first (SPT) and earliest due date first (EDD) lead to big losses in welfare compared to the global optimum. However, when employing Moore-Hodgson’s algorithm as a local policy, we can prove a price of anarchy of (2m−1)/m for identical machines and a price of anarchy of 2 for related and unrelated parallel machines. Moreover, we show how these results can be used to prove approximation ratios for greedy scheduling algorithms. This paper is the first to prove approximation ratios for two greedy scheduling procedures, turning them from simple heuristics into actual approximation ratios with a provable approximation ratio.
In order to increase the productivity of sea port container storage yards, a triple-crossover-stacking-crane setting can be deployed. Although this setting yields promising results, there is ...increasing risk of cranes interfering. Coping with interference is a key factor for exploiting the potential of triple-crossover-stacking-cranes to increase overall productivity. In this paper, we tackle the problem of finding an assignment of transport jobs to cranes, a processing sequence for each crane as well as a conflict-free routing under the objective of minimizing the makespan. We develop several variants of branch-and-bound algorithms differing in the order of assignment and sequencing decisions and in the techniques applied for routing decisions. We compare the performance of our algorithms with regard to solution quality and run times and use standard solver CPLEX as benchmark.
To enable the efficient division of labor in container yards, many large ports apply twin cranes, two identical automated stacking cranes each dedicated to one of the transfer zones on the seaside ...and landside. The use of a handshake area, a bay of containers that separates the dedicated areas of the two cranes, is a simple means to avoid crane interference. Inbound containers arriving in the transfer zone of one crane and dedicated to a stacking position of the other crane's area are placed intermediately in the handshake area by the first crane and then taken over by the second crane, and vice versa for outbound containers. Existing research only evaluates simple heuristics and rule-based approaches for the coordination of twin cranes interconnected by a handshake area. For this setting, accounting for precedence constraints due to stacking containers in the handshake area, we derive exact solution procedures under a makespan minimization objective. In this way, a comprehensive computational evaluation is enabled, which benchmarks heuristics with optimal solutions and additionally compares alternative crane settings (i.e., without workload sharing and cooperation with flexible handover). We further provide insights into where to position the handshake area. Our results reveal that when planning is too simple (i.e., with a rule-based approach), optimality gaps become large, but with sophisticated optimization, the price of a simplified crane coordination via a handshake area is low.
In recent years, more and more disasters occurred. Additionally, the amount of people affected by disasters increased. Because of this, it is of great importance to perform the relief operations ...efficiently in order to alleviate the suffering of the disaster victims. Immediately after the occurrence of a disaster, there is an urgent need for delivering relief goods to demand locations and affected regions, respectively. Due to roads being blocked or damaged by debris, some demand locations may be out of reach and therefore the delivery of relief goods is hampered. This paper investigates the basic problem of simultaneously unblocking roads in order to make demand locations accessible and delivering relief goods in order to satisfy demand. Strict deadlines for the delivery of relief goods are considered at the demand locations. A formal problem statement is provided, and its computational complexity is analyzed. Additionally, a mixed integer programming model is developed and an exact solution method based on a branch and bound approach is proposed. A computational study investigating the performance of the model formulation and the branch and bound algorithm is conducted.
Single machine scheduling with sequence-dependent setup times is one of the classical problems of production planning with widespread applications in many industries. Solving this problem under the ...min-makespan objective is well known to be strongly NP-hard. We consider a special case of the problem arising from products having a modular design. This means that product characteristics, (mass-)customizable by customers, are realized by separate components that can freely be combined. If consecutive products differ by a component, then a setup is necessary. This results in a specially structured setup matrix that depends on the similarities of product characteristics. We differentiate alternative problem cases where, for instance, the setup operations for multiple components either have to be executed sequentially or are allowed to be conducted in parallel. We analyze the computational complexity of various problem settings. Our findings reveal some special cases that are solvable in polynomial time, whereas most problem settings are shown to remain strongly NP-hard.
A Home–Away-Pattern (HAP) set defines each team’s 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.
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