Hub Location–Allocation in Intermodal Logistic Networks Hüseyin Utku KIYMAZ

Hub location–allocation in intermodal logistic networks Within the context of intermodal logistics, the design of transportation networks becomes more complex than it is for single mode logistics. In an intermodal network, the respective modes are characterized by the transportation cost structure, modal connectivity, availability of transfer points and service time performance. These characteristics suggest the level of complexity involved in designing intermodal logistics networks.

This research develops a mathematical model using the multiple-allocation p-hub median approach. The model encompasses the dynamics of individual modes of transportation through transportation costs, modal connectivity costs, and fixed location costs under service time requirements. A tabu search meta-heuristic is used to solve large size (100 node) problems.

The solutions obtained using this meta-heuristic are compared with tight lower bounds developed using a Lagrangian relaxation approach. An experimental study evaluates the performance of the intermodal logistics networks and explores the effects and interactions of several factors on the design of intermodal hub networks subject to service time requirements.

Introduction Intermodal transportation refers to the integrated use of two or more modes of transportation for delivering goods from origin to destination in a seamless flow. The increased use of intermodal transportation started out as a direct result of globalization of the marketplace.

Using standardized containers, shipments can seamlessly transfer between modes at transfer points. While packages and other smaller size, high value items are moved through road–air. Looking at the benefits (low cost, high capability and reach, competitive transit times) of intermodal transportation.

The ongoing research in this area relates to the complexity of an intermodal network which transcends the benefits and shortfalls of its respective transportation modes. Given the structure of a hub network, this work extends the multiple-allocation p-Hub median approach to the road–rail intermodal logistics domain.

A modeling framework is presented which accommodates the operational structure of individual modes of transportation, the effect of shipment consolidation at hubs on transportation costs, the interactions between modes, the transit time delays and the service time requirements. It also uses a fixed cost of locating intermodal hubs and modal connectivity costs as a tradeoff between opening new facilities and reducing total transportation costs.

- Comparison of studies. Literature

Modeling Framework In model, all four cities have both road and rail network. Network scenarios have shown above.

Model (IHLA) formulation This section presents a mathematical formulation for a road–rail intermodal transportation network.

Lagrangian lower bounds The Lagrangian relaxation procedure is based on identifying a complicating set of constraints in a model. These constraints are added to the objective function, weighted by associated multipliers, known as Lagrange multipliers. This Lagrangian relaxation problem is solved iteratively while the multipliers are adjusted along the way.

Tabu search meta-heuristic A meta-heuristic solution approach is particularly suitable for solving larger size problem instances. Tabu search is a general iterative meta-heuristic for solving combinatorial problems. It has been shown that tabu search can find very good solutions compared to other meta-heuristics such as simulated annealing.

Tabu search is composed of two phases, known as intensification phase and diversification phase. In the intensification phase, tabu search starts at a randomly generated initial solution. This initial solution is comprised of a set of hub nodes, H. The neighborhood, N(H), of the current solution H is comprised of solutions that can be reached with a pair wise interchange of a non-hub node with a hub node. This exchange is called a move. As a move is made, the move attributes, i.e., entering node and exiting node are recorded in a tabu list.

The search moves from one solution to the next and stops when a local optima is reached. After the intensification phase is completed, tabu search enters into the diversification phase. In this phase the tabu search restarts the search process from a new starting solution.

Computational study The purpose of the computational study is to evaluate the performance of meta-heuristic solution approach by comparing it with optimal solutions (where available) and lower bounds. The performance is evaluated based on the optimality gap, the distance from lower bound and the computation time.

While generating random data for this research, it was important that the generated data conform to the realities of real world logistic networks.

Results: Benchmark with optimal solutions The percent optimal gaps for the four replications of each problem instance are averaged and recorded as the average percent optimality gap. The average percent optimality gaps obtained by solving the problem instances using tabu search. The average of optimality gaps over all test instances is 0.71%.

The minimum average gap for tabu search is 0.00% with 73% of the problem instances solved to within 1% of the optimal solution and 99% of the problem instances are solved to within 3% of the optimal solution. The maximum average optimality gap is 3.19%. The average of percent duality gaps over all test instances is 1.26%.

The minimum average duality gap is 0.19% with 35% of the problem instances solved within 1% of optimal solution and 100% of the problem instances have lower bounds within 3% of optimal solution. The maximum average duality gap is 2.36%.

Results: Benchmark with lower bound To evaluate the performance of the tabu search procedure, larger problem instances (10 6 n 6 100) are tested.

Managerial insights This section presents the results of a study in which the structure of the intermodal hub location–allocation problem was explored. This study used the Civil Aeronautics Board (CAB) data which contains origin–destination flows and air transportation costs for 25 cities in the US air network and can be downloaded from the OR-Library.

This data set was modified to generate data for an intermodal network using the following changes. Each city may be serviced by two modes, thus the size of the potential intermodal network is 50 nodes. The cost in the data set was scaled down by 1000 to reflect appropriate unit road transportation costs

Results

Conclusions This research explored the impact of using intermodal shipments within the context of a hub logistics network. The contributions of this research lies in the development of a modeling framework, a fast and accurate solution approach and a procedure to compute tight lower bounds. This research developed a modeling framework which incorporates the fixed cost of operating a hub, the cost of providing intermodal services and service time requirements in a road–rail intermodal network. This research also presented a meta-heuristic (tabu search) solution approach and developed Lagrangian lower bound.

The computational study demonstrated that the solution approach finds high quality solutions (average optimality gap of 0.71%) in a reasonable length of time. This research also showed that the Lagrangian lower bounds for this problem are very tight (average duality gap of 1.26%). Large size test problems (up to 100 nodes) were used to demonstrate the performance of the tabu search meta heuristic. The solutions obtained by tabu search were compared with the corresponding lower bounds, and the results showed that for a large number (84%) of these problems, the solution approach yielded solutions which were within 5% of the lower bound.

Thank you for listening.