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In this paper, we analyze the complexity of the gear placement problem (GPP). In the GPP, we are given a rectangular plane, called a gearbox, on which a torque generator source and a set of gears, called target gears, are placed. The task is to find a placement of a set of gears called sub-gears, to connect every target gear to the torque generator source so that every target gear rotates in a given direction. The objective is to minimize the number of sub-gears to be used. We prove that the GPP is NP-hard by giving a reduction from the Hamiltonian path problem on 3-regular planar graphs, which is known to be NP-complete, to the GPP. We also present an upper bound for the number of sub-gears to be placed.

We address the selective pickup and delivery problem with time-window constraints, which is a problem of finding vehicle routes that pick up commodities at stores and deliver them to customers so as to minimize the total distance of the routes under capacity and time-window constraints. In this paper, to design a local search method for this problem, we consider the following: Given the order of customers in a route, we determine the pickup stores and optimal times of visiting at customers so that the total distance is minimized. This is called the optimal pickup point problem and is a subproblem of the selective pickup and delivery problem with time-window constraints. We show that the optimal pickup point problem is NP-hard in general, and then we propose dynamic programmingmethods, which can obtain upper and lower bounds in linear time, and optimal solution in pseudo-polynomial time.

The rectilinear block packing problem is a problem of packing a set of rectilinear blocks into a larger rectangular container with fixed width and unrestricted height. A rectilinear block is a polygonal block whose interior angles are either 90◦ or 270◦. The objective is to pack all the blocks into the container so as to minimize the height of the container. This problem is among classical combinatorial optimization problems and is known to be NP-hard. In this paper, we propose two exact algorithms for the rectilinear block packing problem: one is based on two IP problems and the other is based on a new solution representation. The basic idea of our algorithms is that we iteratively compute lower and upper bounds on the optimal value until the lower bound on the value of an optimal solution for the current search space becomes larger than or equal to the best upper bound found during the search by then, or the search space becomes empty, which means that an optimal solution of this problem has been found. The computational results show that both algorithms obtain five exact and one heuristic solutions for six instances. The algorithm based on a new solution representation improves the running time of the algorithm based on two IP problems.

The management of the automobile industry has changed recently because of the influence of the financial crisis and the industrial boom in developing countries such as Brazil, Russia, India, and China (BRICs). In this paper, we consider a global automobile-production optimization problem (GAPOP), which we model as a mixed integer programming (MIP) problem. The GAPOP determines global production bases and transportation plans to minimize the total cost of production, transportation, and facilities. It is a unified model that contains the facility location, production planning and transportation problems. We analyze the model for instances generated from real-world data with up to 20 production bases and 133 importing countries for the 18 years from 1997 to 2014. The computational results show that near-optimal solutions to our model are close to the present real-world situation. We also analyze our model with various parameter settings and observe from the results that, at each production base, changes in the number of production lines are affected mainly by labor and material costs. In addition, the proportion of each automobile type when allocating production is influenced by the material costs of all automobile types and the demands of nearby importing countries. Our model is expected to be of use to the automobile industry for making forecasts.

In this paper, we consider the crew pairing problem in airline scheduling that calls for assigning crew members in order to cover all flights with the minimum total person-days under the constraints that the schedule of each crew member does not violate given constraints on the total working time, flying time, and the number of landings. In practical applications, it is difficult to create an efficient schedule satisfying all the constraints. We formulate the problem as a set covering problem and apply an LP-based column generation approach to generate a candidate set of schedules. We propose a branch-and-bound method based upon a resource constrained dynamic programming for the column generation procedure. Computational results are given for a number of large-scale instances with up to 10,000 flights.

In this paper, we propose a heuristic algorithm for a container loading problem for logistic platforms, which is the problem for the Challenge Renault/ESICUP 2015. The three-dimensional container loading problem involves packing a set of cuboid items into bins so as to minimize the total volume used. In this paper, we propose an effective approach to solve this problem based on a greedy strategy. We first generate high-quality stacks that consist of some items and then pack these stacks on the floor of bins, considering the resulting problem as a two-dimensional bin packing problem. The proposed algorithm is tested on a series of instances provided for the challenge. The computational results show that the proposed algorithm performs well on these instances.