OR Spektrum (1993) 15:167-172

�9 Springer-Verlag 1993

Routing of straddle carriers at a container terminal with the special aspect of internal moves Dirk Steenken 1, Andreas Henning 1, Stefan Freigang:, and Stefan VoB 2

Hamburger Hafen- und Lagerhaus AG, DC/EDP Department Container, Bei St. Annen 1, D-20457 Hamburg, Germany 2 Technische Hochschule Darmstadt, Institut ftir Betriebswirtschaftslehre, Fachgebiet Operations Research, Hochschulstrasse 1, D-64289 Darmstadt, Germany

Received 11 March 1993/Accepted I1 August 1993

Summary. Besides loading and discharging of ships, trucks and railway internal transportations are performed at a container terminal. Those transports amount to about 100000km a year at the Container Terminal of the Hamburger Hafen- und Lagerhaus AG. Different me- thods for the routing of the vehicles (Straddle Carriers) were tested to minimize no-load ways. Heuristics solving the Multiple Travelling Salesman Problem were applied to the routing problem as well as a method for sequencing insertions in printed circuit board assemblies and rules for machine scheduling. Simulation with real data indicated a total saving of 20-35 % in no-load distances which corre- spond to about 20000 km a year. The routing solution was implemented into a radio data transmission system.

Zusammenfassung. Neben dem Be- und Entladen von Schiffen, LKWs und Bahnwaggons werden interne Trans- porte an einem Containerterminal durchgefiihrt, die sich bei der Hamburger Hafen- und Lagerhaus AG auf ca. 100000km im Jahr summieren. Um die Leerwege zu minimieren, wurden verschiedene Methoden zur L6sung des Touren-Problems getestet. Dies waren sowohl Heuri- stiken zur L6sung des Multiplen Travelling Salesman Pro- blems, wie zur Reihenfolgenbildung bei der Bestiickung yon Platinen mit elektronischen Bauteilen und Verfahren der Maschinenbelegung. Simulationen mit Echtdaten ergaben, dab die Leerwege um 20-35 % reduziert werden k6nnen, was einer j~ihrlichen Einsparung von ca. 20000 km ent- spricht. Das Optimierungsverfahren wurde in eine Daten- funkanwendung zur Steuerung der Fahrzeuge integriert.

Key words: Container operation, radio data transmission, Multiple Travelling Salesman Problem, sequencing circuit board assemblies, scheduling

Schliisselw6rter: Container Operation, Datenfunk, Mul- tiples Travelling Salesman Problem, Platinenbestiickung, Maschinenbelegung

Introduction

The Container Terminal "Burchardkai" of the Ham- burger Hafen- und Lagerhaus AG (HHLA) had a turn- over of 1.1 mio container units in 1992, thus loading and discharging about 3000 ships. The total stock per day is about 15000, 3300 container movements are carried out daily in average. The transportation and stacking of the containers is performed by special equipment, called Straddle or Van Carriers. The information about these jobs are transmitted via a radio data system (rdt) from the host into the drivers cabin. In order to minimize no-load distances of straddle carrier tours, routing and scheduling systems are tested and integrated into the rdt application.

Terminal organisation

The container terminal is structured into different oper- ation areas according to different logistics in the spheres of action. These areas and the flow of containers are illustrated in Fig. 1.

Some details should be added:

. . . . . T r u c k / T r a i n O p e r a t i o n . . . . . . . . . . . . . ~ ~ -

Fig. 1. Operation areas and container flow

168 D. Steenken et al.: Routing of straddle carriers at a container terminal

Ship operation: loading and discharging of vessels. Export and import stack areas are preplanned by graphical computer systems. Detailed preinformation from ship- ping lines is available by electronic data interchange (EDI). Truck operation: loading and discharging of trucks. No preinformation about containers and trucks arriving by EDI. Railway operation: loading and discharging of trains. Detailed preinformation about containers, trains and waggons by EDI. Hinterland: covers all internal movements on the yard: transport of empty containers from empty stock to packing centres, of stuffed containers to export stock, stripped containers from shed to empty stock, prestows for export loading, etc. Empty stock: Special stock for empty containers which are stowed according to different types and ownership (ship- ping line) of containers. Stacking is done by forklifts, the transportation is done by straddle carriers.

H H L A operates 70 straddle carriers at the Container Terminal Burchardkai. A straddle carrier is able to pick up one container at a time. Each operation area builds a functional unit working with a given number of straddle carriers. The assignment of straddle carriers is done at the beginning of a shift. The number of straddle carriers depends on the quantity of jobs in the operation area. A straddle carrier remains in its assigned area unless it is directed to another one by a "supervisor", who controls the employment of the straddle carriers in all areas.

Transportation and stacking of the containers by straddle carriers and forklifts are directed by a radio data transmission (rdt) system, which is connected to the host computer and integrated into the container terminal application. Transportation jobs are created by the staff of the operation units. The job data are transformed into radio telegrams whose main components are the actual position, identifier and target position of a container. This telegram is sent to the straddle carrier via a radio interface and is displayed on a terminal screen in the driver's cabin. After execution of commission the new coordinates of the container location are sent back to the host to update the data base.

Routing systems

Routing systems using methods of Operations Research were implemented into the radio data application. The first installation was established at the truck operation area. The problem to be solved was to combine export (container from truck area to export stock) with import jobs (container from stock to truck area) in such a way that the no-load drives were minimized. The problem was solved by using a linear assignment algorithm. The no- load drives had been reduced by 13% thus saving about 1400 km per month (Steenken 1992).

This encouraging result initiated the development of a further module optimizing the internal moves in the "hinterland area". In purpose of implementing such a module detailed analysis and tests were carried out.

Radio data transmission

The container terminal operation is supported and con- troled with a dialog computer system, whose main modules are the container terminal system (ship operation, truck and railway operation, stack and container adminis- tration, etc.) and planning systems like ship (or stowage) planning, yard and berthplanning, which are using a graphical display environment with distributed data pro- cessing.

Types of Hinterland activities (see Fig. 2)

The radio data area "Hinterland" has a characteristic organisation differing from the other operation areas. The main characteristics are different types of jobs such as:

- single jobs (EZ): Transportation of a distinct container from one location to another. -job-groups: Collection of single jobs with common features.

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D. Steenken et al.: Routing of straddle carriers at a container terminal 169

m ~ [ ~ tainer tock (Import/Export) Fig. 3. Job sequence for one straddle carrier

during a shift

The job-groups split into distinct types. These types are:

- Delivery of empty containers to a shed (LH) Several containers of specific type and material and undistinct container no. are moved from the empty stock to a packing centre. - Clearing a shed area (HA) A number of containers (undistinct container no.) is transported from a shed to the empty stock or export stack for ship loading. - Export prestow: delivery of empty containers to the export stock (LE) Empty containers are transported from the empty stock to the export ship stack. - Clearing up a yard area (AK) All containers located on different yard positions are shifted to a common stock location (reorganisation of a stock area). - Stow of empty import containers (ZW) Delivery of empty import containers to the empty con- tainer depot.

P r o b l e m d e s c r i p t i o n "Hinterland"

A typical sequence of jobs carried out by one straddle carrier during a shift is shown in Fig. 3. Evidently there are a lot of no-load drives, some resulting from to-and-fro moves ("n-fold"), others resulting from nonoptimal job combinations causing long no-load drives. The "to-and- fro" moves are typical for some of the group jobs like "clearing a shed area" or "delivery of empty containers to a shed". These empty drives are unavoidable as long as "job-groups" are not combined with others to form routes.

Many jobs have a due-date, i.e., they have to be performed until a given date and time which should not be exceeded. For example a container has to be delivered until a fixed time to an export yard position not causing an interruption during ship loading or to a shed for stuffing purposes. Usually several straddle carriers are engaged in the Hinterland area.

The hinterland activities have low priority compared with other operation areas. Loading and discharging vessels, trains and trucks are more important than the internal moves. Therefore the number of straddle carriers engaged in the hinterland depends on the amount of jobs in other operation areas. It often changes during a shift. It can occur that many jobs are not performed during the main shift but in the late one, the number of jobs thus can accumulate up to 150-200 (Fig. 4 shows two different situations). Such a large number of jobs cannot be combined manually to form an optimal route.

Modelling and testing a p r o t o t y p e

Before formulating the straddle carrier routing problem with respect to all details and restrictions a test study was performed to get a quantitative idea of possible savings.

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Fig. 4. Straddle carrier employment and jobs during one day

170 D. Steenken et al.: Routing of straddle carriers at a container terminal

The distance between the pick up and the delivery position of a container transport is not relevant for an optimal tour. The shortest path between two points at the terminal is known - it is filed in a distance matrix - and has to be followed in any case during a fulMoad drive (see Fig. 3). Thus the problem is reduced to a sequencing problem minimizing the sum of the cost elements in- volved. The elements of the cost matrix are the distances between the delivery and pick up points of the transpor- tation jobs (no-load ways).

A possible model describing the routing problem is the Travelling Salesman Problem (TSP) with Time Window constraints. Because usually more than one straddle carrier is engaged it has to be defined as a Multiple Travelling Salesman Problem. For a survey on these problems with respect to routing problems see e.g. Bodin et al. (1983).

To develop a test prototype the problem was reduced to a simple TSP with the assumptions that only one straddle carrier is engaged and that time windows are neglected. According to these assumptions different heu- ristics were investigated to solve the TSP like the Nearest Neighbour heuristic (NN), the Successive or Cheapest Insertion (SUC) and a 2-optimal exchange method (2OP). For these tests data of real transportation jobs were taken and "reoptimised" by using the above methods. The resulting sum of no-load distances was compared with the no-load sum of real tours which were created manually by assigning jobs to straddle carriers.

Best results were found using the cheapest insertion method: the total savings in no-load distances were about 20-40% depending on the number of jobs (Fig. 5). Such a reduction would result in an annual saving of about 20000 kin. Equivalent results were found with the 2-opt method. However the processing time of this method was 3-times longer than that of the successive insertion method. The 2-opt method therefore was excluded for a real-time application.

Detailed modelling of the routing problem

Solutions of the routing problem regarding all details and restrictions were modelled as follows (Freigang, 1992). The fundamental idea of the first model refers to a heuristic which was applied by Ball and Magazine (1988) to a problem of sequencing insertions in printed circuit board assemblies.

To insert components into a circuit board they have to be picked up at feeders and placed at given positions on the board. The insertion and feeder positions are the nodes, the movements of the head of the drive are the arcs of a directed network. The analogy between the board insertion and the straddle carrier routing problem is evident: the required movements from the feeders to the insertion positions correspond to the load moves of the straddle carriers and the nonrequired moves from an insertion position to a feeder correspond to the no-load moves. Each arc of the directed network can be traversed exactly once. The objective is to minimize the sum of distances of non-required or respective no-load moves.

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Fig. 5. Savings of no-load paths by different heuristics

This analogy is clearly illustrated by comparing Figs. 3 and 6.

A valid solution of the circuit board insertion problem, which can be interpreted as a Rural Postman Problem, is illustrated in Fig. 6b. Each possible solution has two important properties:

1. it is balanced, i.e. the in-degree (number of arcs pointing into the node) equals the out-degree (number of arcs pointing out) 2. it is connected, i.e. a pa th exists from each node to every other node.

The problem thus can be described as follows: given a directed network with a disjoint set of required and non- required arcs and costs associated with each arc, find a subset of arcs with minimum costs such that the resulting network is balanced and connected.

The heuristic applied by Ball and Magazine to this problem is called Balance & Connect: the first step balances the network by solving a transportation prob- lem, the second connects the network by solving a minimum spanning tree problem.

Several expansions had to be applied to the Balance & Connect heuristic to solve the straddle carrier routing problem. As more than one straddle carrier usually is employed the RuralPostman Problem has to be expanded to a multiple one (MRPP). This can be achieved by introducing fictitious vehicle depots as additional nodes with arcs leading to the original depot. In addition the due dates of straddle carrier jobs have to be considered which in a first step was done by enhancing the objective function. The underlying idea is based on the reflection that two jobs should not succeed each other within the same tour if there is a great difference in their due dates. With this assumption the cost element between node i and j can be written as

d U = a*lbi - bj[ + (1 - a)*cij where bi and bj are the due dates of the jobs i and j , a a weight factor and cij the cost elements.

The simulations showed that this enhancement was not adequate in reducing the delays sufficiently. Therefore an

D. Steenken et al.: Routing of straddle carriers at a container terminal 171

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additional procedure was applied to exchange those jobs which were delayed after the first step of optimisation. With these enhancements better results were found but in some cases the tours of straddle carriers differed very much in length. To avoid this effect an additional term was added to minimize the difference of tour lengths by inserting jobs of overstrained tours into shorter ones. All enhancements together produced very good results in several simulations.

Another model matching the straddle carrier routing problem was developed based on an analogy to machine scheduling (MAS) mentioned by Maas and Vo13 (1991). Such scheduling problems can be solved (heuristically) by using "dispatching rules". The rules can be realized by a respective sorting of the jobs such as:

- Shortest processing t ime (SPT): Jobs are selected ac- cording to increasing processing time - Longest processing t ime (LPT): Jobs are selected ac- cording to decreasing processing time - Earliest due date (EDD): Jobs are selected according to increasing due date/time.

With these rules a first (starting) sequence is obtained analoguously to the Balance & Connect part of the previous heuristic. An insertion procedure can be added which improves the result of the first step: a job i is removed from its actual position and inserted to another one. If CS is the cost savings of removing i and CA are the additional costs of the insertion such positions are candi- dates for the insertion which fulfill CS > CA. Methods to select insertion positions are:

- First f i t (FF): first position which fulfills CS > CA is selected

- B e s t f i t (BF): position which fulfills the condition max(CS - CA) is selected - Bes t -bes t f i t (BB): that position is selected which fulfills the BF condition for all jobs and insertion positions.

Results

Using these two models simulations were run with real data of straddle carrier jobs occurred during operation. The simulations were performed for three different peri- ods: the first two periods used the job volume of two different days (Short I, Short I I ) , the third one used the complete job volume of one week (Long). As the number of straddle carriers often changed during these periods the optimisation procedure was restarted whenever the num- ber of straddle carriers changed.

Within the simulations based on the balance & con- nect heuristic (MRPP) the weight factors influencing the delays were varied. Within the second model using dispatching rules of machine scheduling (MAS) the EDD rule together with the First Fit Me thod was found to give the best results. The results of both heuristics concerning the reduction of no-load distances and job delays are illustrated in Fig. 7.

It has to be mentioned that the complete enhancements to reduce delays had been implemented only in the MRPP solution. Analogue enhancements could be implemented into the MAS procedure.

The computation times for both algorithms were found to be quite acceptable under the constraints of the real time rdt system. An implementation into the real operation environment is in preparation.

172 D. Steenken et al.: Routing of straddle carriers at a container terminal

References

Ball MO, Magazine MJ (1988) Sequencing of insertions in printed circuit board assembly. Oper Res 36(2): 192-201

Bodin L, Golden B, Assad A, Ball M (1983) Routing and scheduling of vehicles and crews. Computers Oper Res 10(2):63-211

Freigang S (1992) Entwicklung eines heuristischen Verfahrens zur Tourenplanung auf einem Containerterminal. Studienarbeit,

Institut far Betriebswirtschaftslehre, Fachgebiet Operations Re- search, TH Darmstadt

Maas C, VoB S (1991) Anwendungen des Rundreiseproblems in der Ablauforganisation. Mitt Math Ges Hamb 12:723-740

Steenken D (1992) Fahrwegoptimierung am Containerterminal unter Echtzeitbedingungen. OR Spektrum 14:161-168