Column Generation for the Container Relocation Problem

Container terminals offer transfer facilities to move containers from vessels to trucks, trains and barges and vice versa. Within the terminal the container yard serves as a temporary buffer where incoming containers are piled up in stacks. Only the topmost container of each stack can be accessed. If another container has to be retrieved, containers stored above it must be relocated first. Containers need to be transported to a ship or to trucks in a predefined sequence as fast as possible. Generally, this sequence does not match the stacking order within the yard. Therefore, a sequence of retrieval and relocation movements has to be determined that retrieves containers from the bay in the prescribed order with a minimum number of relocations. This problem is known as the container relocation problem. We apply an exact and a heuristic column generation approach to this problem. First results are very promising since both approaches provide very tight lower bounds on the minimum number of relocations

Modified Network Simplex Method to Solve a Sheltering Network Planning and Management Problem

This dissertation considers sheltering network planning and operations for natural disaster preparedness and responses with a two-stage stochastic program. The first phase of the network design decides the locations, capacities and held resources of new permanent shelters. Both fixed costs for building a new permanent shelter and variable costs based on capacity are considered. Under each disaster scenario featured by the evacuee demand and transportation network condition, the flows of evacuees and resources to shelters, including permanent and temporary ones, are determined in the second stage to minimize the transportation and shortage/surplus costs. Typically, a large number of scenarios are involved in the problem and cause a huge computational burden. The L-shaped algorithm is applied to decompose the problem into the scenario level with each sub-problem as a linear program. The Sheltering Network Planning and Operation Problem considered in this dissertation also has a special structure in the second-stage sub-problem that is a minimum cost network flow problem with equal flow side constraints. Therefore, the dissertation also takes advantages of the network simplex method to solve the response part of the problem in order to solve the problem more efficiently. This dissertation investigates the extending application of special minimum cost equal flow problem. A case study for preparedness and response to hurricanes in the Gulf Coast region of the United States is conducted to demonstrate the usage of the model including how to define scenarios and cost structures. The numerical experiment results also verify the fast convergence of the L-shaped algorithm for the model

A decomposition method for finding optimal container stowage plans

In transportation of goods in large container ships, shipping industries need to minimize the time spent at ports to load/unload containers. An optimal stowage of containers on board minimizes unnecessary unloading/reloading movements, while satisfying many operational constraints. We address the basic container stowage planning problem (CSPP). Different heuristics and formulations have been proposed for the CSPP, but finding an optimal stowage plan remains an open problem even for small-sized instances. We introduce a novel formulation that decomposes CSPPs into two sets of decision variables: the first defining how single container stacks evolve over time and the second modeling port-dependent constraints. Its linear relaxation is solved through stabilized column generation and with different heuristic and exact pricing algorithms. The lower bound achieved is then used to find an optimal stowage plan by solving a mixed-integer programming model. The proposed solution method outperforms the methods from the literature and can solve to optimality instances with up to 10 ports and 5,000 containers in a few minutes of computing time

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LIST OF FIGURES -- LIST OF TABLES -- PREFACE -- CHAPTER 1— BACKGROUND & OVERVIEW: Alaska’s Native Lands: Alaska Native Claims Settlement Act Lands: Regional Corporations, Village Corporations, Additional ANCSA Land Entitlements, Former Native Reserve Lands; Other Native Lands: Native Allotments, Annette Island Reservation; Native Land Status; Alaskan Forests; What is a Forest Inventory?; Forest Inventories in Alaska; Forest Inventories on Native Land -- CHAPTER 2 — DETERMINING THE NEED FOR AN INVENTORY: Existing Forest Inventory Information; Agency Inventories: Forest Service Inventories, Bureau of Indian Affairs Inventories, Tanana Chiefs Conference Inventories; Level of Inventory -- CHAPTER 3 — INVENTORY PLANNING: Gathering Information; Planning Considerations: Why is This Inventory Needed?, Where will the Inventory Take Place?, What needs to be Inventoried and What Information is to be Collected?, Who is Going to do the Inventory?, When will the Inventory Take Place?, How is the Inventory going to be Done and How will the Data be Processed?, How Much is the Inventory going to Cost?, Unique Alaskan Constraints: Transportation Logistics, Adverse Weather, Musket, Dangerous Wildlife, Vegetation Barriers, Availability of Supplies and Fuel; Advantages of Planning -- CHAPTER 4 — HOW FOREST INVENTORIES ARE CONDUCTED: Maps and Aerial Photographs: Using Aerial Photographs in Forest Inventories, Using Aerial Photographs for Timber Typing; Statistical Considerations of a Forest Inventory: Variability of the Sample, Number of Samples, Sampling Design; Field Measurements: Tree Height, Tree Diameter and Taper, Tree Defects, Tree Age and Growth, Site Conditions, Forestry Equipment -- CHAPTER 5 — AFTER THE FIELD WORK IS DONE: Compilation of Data; When the Inventory is Complete; Looking Toward the Future -- BIBLIOGRAPHY -- APPENDIX I - ALASKA’S PRINCIPAL TREE SPECIES -- APPENDIX II — USES OF ALASKA'S PRINCIPAL TREE SPECIES -- APPENDIX III — FORESTY CONSULTANTS IN ALASKA -- APPENDIX IV — TECHNICAL ASSISTANCE DIRECTORY -- APPENDIX V — SAMPLE OUTLINE FOR DEVELOPING A FOREST INVENTORY PLAN -- APPENDIX VI — USGS OFFICES IN ALASKA -- APPENDIX VII — NATURAL RESOURCES SCHOOLS IN ALASK

The crane split and sequencing problem with clearance and yard congestion constraints in container terminal ports

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.Includes bibliographical references (p. 93-94).One of the steps in stowage planning is crane split and sequencing, which determines the order of container discharging and loading jobs quay cranes (QCs) perform so that the completion time (or makespan) of ship operation is minimized. The vessel's load profile, number of bays and number of allocated QCs are known to port-planners hours before its arrival, and these are input parameters to the problem. The problem is modeled as a large-scale linear IP where the planning horizon is discretized into time intervals and at most one QC can be assigned to a bay at any period. We introduce clearance constraints, which prevent adjacent QCs from being positioned too close to one another, and yard congestion constraints, which prevent yard storage locations from being overly accessed at any time. This makes the model relevant in an industrial setting. We examine the case only a single ship arrives at port, and the case where multiple ships berth at different times in the planning horizon. The berth time of each ship and number of ships arriving is known. The problem is difficult to solve without any special technique applied. For the single-ship problem, a heuristic approach, which produces high-quality solutions, is developed.(cont.) A branch-and-price method re-formulates the problem into a set-covering form with huge number of variables; standard variable branching provides optimal solutions very efficiently. For the multiple-ship problem, a solution strategy is developed combining Lagrangian relaxation, branch-and-price and heuristics. After relaxing the yard congestion constraints, the problem decomposes into smaller sub-problems, each involving one ship; the sub-problems are then re-formulated into a column generation form and solved using branch-and-price to obtain Lagrangian solutions and lower-bound values. Lagrangian multipliers are iteratively updated using the sub-gradient method. A primal heuristic detects and eliminates infeasibilities in the Lagrangian solutions which then become an upper bound to the optimal objective. Once the duality gap is sufficiently reduced, the sub-gradient routine is terminated. The availability of efficient commercial modeling software such as OPL Studio and CPLEX allows for larger instances of the problem to be tackled than previously possible.by Shawn Choo.S.M