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International audience; Self-storage is a booming industry. Both private customers and companies can rent temporary space from such facilities. The design of self-storage warehouses differs from other facility designs in its focus on revenue maximization. A major question is how to design self-storage facilities to fit market segments and accommodate volatile demand to maximize revenue. Customers that cannot be accommodated with a space size of their choice can be either rejected or upscaled to a larger space. Based on data of 54 warehouses in America, Europe, and Asia, we propose a new facility design approach with models for three different cases: an overflow customer rejection model and two models with customer upscale possibilities, one with reservation and another without reservation. We solve the models for several real warehouse cases, and our results show that the existing self-storage warehouses can be redesigned to generate larger revenues for all cases. Finally, we show that the upscaling policy without reservation generally outperforms the upscaling policy with reservation.

In this paper we present two algorithms for a machine allocation problem occurring in manufacturing systems. For the two algorithms presented we prove worst-case performance ratios of 2 and 3/2, respectively. The machine allocation problem we consider is a general convex resource allocation problem, which makes the algorithms applicable to a variety of resource allocation problems. Numerical results are presented for two real-life manufacturing systems.

In this chapter, we discuss a modification of the standard path-following scheme that tends to speed up the global convergence. This modification, the central region method, generates iterates that do not really trace the central path, or at least not closely. In this way, it has a relatively large freedom of movement, and consequently the ability to take long steps. This makes it interesting to consider more sophisticated search directions. We propose a search direction that is built up in three phases, viz. 1. Initial centering, 2. Predictor, 3. Second order centrality corrector.

In Chapter 3, we have analyzed the iteration complexity of finding an ϵ-optimal solution, if an interior, sufficiently centered pair of primal and dual solutions is known beforehand. We will see in this chapter how we can adapt the algorithms of Chapter 3 to solve semidefinite programming problems without any pre-knowledge. To this end, we use the self-dual embedding technique. This technique will also be used to tackle semidefinite programming problems that may be unbounded, unsolvable, or infeasible.

Modern solvers for linear and quadratic programming often incorporate some variant of the primal-dual path-following method, which is a class of interior point methods. This method turns out to be suited for solving semidefinite programming problems as well. In this chapter, we propose a framework for analyzing primal-dual path-following algorithms for semidefinite programming. Our framework is a direct extension of the v-space approach, which was developed by Kojima et al. [63] in the context of complementarity problems.