Julia Rieck

Mixed-integer linear programming for resource leveling problems

We consider project scheduling problems subject to general temporal constraints, where the utilization of a set of renewable resources has to be smoothed over a prescribed planning horizon. In particular, we consider the classical resource leveling problem, where the variation in resource utilization during project execution is to be minimized, and the so-called “overload problem”, where costs are incurred if a given resource-utilization threshold is exceeded. For both problems, we present new mixed-integer linear model formulations and domain-reducing preprocessing techniques. In order to strengthen the models, lower and upper bounds for resource requirements at particular points in time, as well as effective cutting planes, are outlined. We use CPLEX 12.1 to solve medium-scale instances, as well as instances of the well-known test set devised by Kolisch et al. (1999). Instances with up to 50 activities and tight project deadlines are solved to optimality for the first time.

Many-to-many location-routing with inter-hub transport and multi-commodity pickup-and-delivery

In this paper, we consider a variant of the many-to-many location-routing problem, where hub facilities have to be located and customers with either pickup or delivery demands have to be combined in vehicle routes. In addition, several commodities and inter-hub transport processes are taken into account. A practical application of the problem can be found in the timber-trade industry, where companies provide their services using hub-and-spoke networks. We present a mixed-integer linear model for the problem and use CPLEX 12.4 to solve small-scale instances. Furthermore, a multi-start procedure based on a fix-and-optimize scheme and a genetic algorithm are introduced that efficiently construct promising solutions for medium- and large-scale instances. A computational performance analysis shows that the presented methods are suitable for practical application.

Simultaneous Vehicle and Crew Routing and Scheduling for Partial- and Full-Load Long-Distance Road Transport

This paper studies a simultaneous vehicle and crew routing and scheduling problem arising in long-distance road transport in Europe: Pickup-and-delivery requests have to be fulfilled over a multi-period planning horizon by a heterogeneous fleet of trucks and drivers. Typically, in the vehicle routing literature, a fixed assignment of a driver to a truck is assumed. In our approach, we abandon this assumption and allow truck/driver changes at geographically dispersed relay stations. This offers greater planning flexibility and allows a better utilization of trucks, but also creates intricate interdependencies between trucks and drivers and requires the synchronization of their routes. A solution heuristic based on a two-stage decomposition of the problem is developed, taking into account European Union social legislation for drivers, and computational experiments using real-world data provided by a major German forwarder are presented and analyzed. The obtained results suggest that for the vehicle and driver cost structure prevalent in Western Europe and for transport requests that are not systematically acquired to complement one another, no cost savings are possible through simultaneous vehicle and crew routing and scheduling, although no formal proof of this fact is possible.

Models and solution procedures for the resource-constrained project scheduling problem with general temporal constraints and calendars

In this paper, the resource-constrained project scheduling problem with general temporal constraints is extended by the concept of break-calendars in order to incorporate the possible absence of renewable resources. Three binary linear model formulations are presented that use either start-based or changeover-based or execution-based binary decision variables. In addition, a priority-rule method as well as three different versions of a scatter search procedure are proposed in order to solve the problem heuristically. All exact and heuristic solution procedures use a new and powerful time planning method, which identifies all time- and calendar-feasible start times for activities as well as all corresponding absolute time lags between activities. In a comprehensive performance analysis, small- and medium-scale instances are solved with CPLEX 12.6. Furthermore, large-scale instances of the problem are tackled with scatter search, where the results of the three versions are compared to each other and to the priority-rule method.

Integrated production and staff planning for heterogeneous, parallel assembly lines: an application in the automotive industry

We consider an integrated production and staff planning problem that occurs in the automotive industry. In particular, we focus on a production environment with heterogeneous, parallel assembly lines and search for a least cost schedule for producing a forecasted demand taking into account the application of volume flexibility instruments. The problem is modelled as a (non-linear) mixed-integer programme and solved by using dynamic programming. We present two case studies that are derived from real-world data in order to show the practical usability of our method. Compared to previous approaches presented in the literature, our dynamic programming method can achieve cost improvements of more than 10%.

A Hybrid Algorithm for Vehicle Routing of Less-Than-Truckload Carriers

In this paper we address a variant of the vehicle routing problem faced by less-than-truckload carriers in Europe. As a consequence of globalization and increasing customer expectations, medium-sized less-than truckload carriers operate together in cooperations. Each cooperative member faces a multitude of requirements when constructing a low-cost, feasible set of routes. Among other aspects heterogeneous vehicles, time windows, simultaneous delivery and pick-up at customer locations, and multiple use of vehicles have to be considered. After the determination of an adequate set of routes, the vehicles must be assigned to loading bays at the depot at which the loading and unloading activities can occur.We present a vehicle routing model which integrates the real-life vehicle routing problem and the assignment problem of vehicles to loading bays at the depot. The proposed solution heuristic combines a multi-start and a local search procedure. Using a set of suitable benchmark instances, we assess the performance of the proposed method.

Exact Methods for Resource Leveling Problems

Resource leveling problems arise whenever it is expedient to reduce the fluctuations in resource utilization over time, while maintaining a prescribed project completion deadline. Several resource leveling objective functions may be defined, whose consideration results in resource profiles with desired properties, e.g., well-balanced resource profiles or profiles with a minimum number of jump discontinuities. In this chapter, we concentrate on three resource leveling problems that are known from the literature. In order to solve medium-scale instances of the considered problems, an enumeration scheme that uses problem structures is presented. Furthermore, mixed-integer (linear) programming models are introduced, and resource leveling instances are solved using CPLEX 12. In a comprehensive computational study, the performance of the described methods is analyzed.

Exact Solutions to the Symmetric and Asymmetric Vehicle Routing Problem with Simultaneous Delivery and Pick-Up

In reverse logistics networks, products (e.g., bottles or containers) have to be transported from a depot to customer locations and, after use, from customer locations back to the depot. In order to operate economically beneficial, companies prefer a simultaneous delivery and pick-up service. The resulting Vehicle Routing Problem with Simultaneous Delivery and Pick-up (VRPSDP) is an operational problem, which has to be solved daily by many companies. We present two mixed-integer linear model formulations for the VRPSDP, namely a vehicle-flow and a commodity-flow model. In order to strengthen the models, domain-reducing preprocessing techniques, and effective cutting planes are outlined. Symmetric benchmark instances known from the literature as well as new asymmetric instances derived from real-world problems are solved to optimality using CPLEX 12.1.

Machine scheduling in underground mining: an application in the potash industry

In this paper, a scheduling problem that occurs in potash mining is introduced, where a block excavation sequence has to be found taking into account a limited number of underground machines as well as safety-related restrictions. The aim is to minimize the maximum completion time of excavations, i.e., the makespan. The resulting problem can be transformed into a hybrid flow shop scheduling problem with reentry, unrelated machines, and job-precedences. A mixed-integer linear model is presented and small-scale instances are solved with CPLEX. In order to tackle medium- and large-scale instances heuristically, a basic and an advanced multi-start algorithm are developed, based on a specific priority rule-based construction procedure. In addition, a modified version of the Giffler and Thompson procedure is applied. Computational experiments are conducted on problem instances derived from real-world data in order to evaluate the performances of the proposed solution procedures.

A Branch-and-Cut Approach to the Vehicle Routing Problem with Simultaneous Delivery and Pick-up

The vehicle routing problem with simultaneous delivery and pickup (VRPSDP) is an extension of the capacitated vehicle routing problem in which products have to be transported from the depot to customer locations and other products have to be trucked from customer locations to the depot. Each customer requires a simultaneous delivery and pick-up of goods by the same vehicle. The VRPSDP is a basic problem in reverse logistics: In addition to the distribution process to the customers, re-usable goods have to be transported in the reverse direction. We implement a branch-and-cut approach and study how it can be applied to the solution of the VRPSDP. The computational tests have been performed on known benchmark instances. Some benchmark problems are solved to optimality for the first time