Fast movement strategies for a step-and-scan wafer stepper

We describe algorithms for the determination of fast movement strategies for a step-and-scan wafer stepper, a device that is used for the photolithographic processing of integrated circuits. The proposed solution strategy consists of two parts. First, we determine the maximum number of congruent rectangular chips that can be packed on a wafer, subject to the restriction that the chips are placed in a rectangular grid. Second, we find fast movement strategies for scanning all chips of a given packing, given the mechanical restrictions of the wafer stepper. The corresponding combinatorial optimization problem is formulated as a generalized asymmetric traveling salesman problem. We show how feasible scan strategies are determined, and how these strategies are improved by local search techniques, such as iterative improvement based on 2- and 3-exchanges, and simulated annealing based on 2-exchanges.\ud \u

On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems

Let $E_1 ,\cdots,E_m$ be subsets of a set $V$ of size $n$, such that each element of $V$ is in at most $k$ of the $E_i$ and such that each collection of $t$ sets from $E_1 ,\cdots ,E_m$ has a system of distinct representatives (SDR). It is shown that $m/n\leqq (k(k - 1)^r - k)/(2(k - 1)^r - k)$ if $t = 2r - 1$, and $m/n \leqq (k(k - 1)^r - 2)/(2(k - 1)^r - 2)$ if $t = 2r$. Moreover it is shown that these upper bounds are the best possible. From these results the "worst-case ratio" of certain heuristics for the problem of finding a maximum collection of pairwise disjoint sets among a given collection of sets of size $k$ is derived

Models and algorithms for the microdata protection problem

This article focuses on the mathematical modeling and an algorithmic approach to microdata protection based on a strategy of local suppression and global recoding. Protecting sensitive individual information using such an approach must be balanced against the usefulness of the resulting edited datafile. We discuss the two subproblems of suppression and recoding of microdata in light of the information loss that occurs. We combine them into an overall disclosure problem formulated as a combinatorial optimization problem. We describe how to decompose the problem into smaller more tractable parts and how to use local search methods to find good approximations of the optimal solution.Keywords:Mathematical modeling; optimization algorithms. <br/

Attaining stability in multi-skill workforce scheduling

In this paper, we define a set inequalities that are satisfied by stable multi-skill workforce schedules. In our analysis, a schedule is said to be stable if it does not contain a blocking pair, extending the notion of blocking pair in the Marriage Model of Gale-Shapley. Skill efficiency is chosen as the criterion in the preference structure. The proposed algorithm either constructs a stable multi-skill workforce schedule or decides that no stable schedule exists

A combinatorial approach to multi-skill workforce scheduling

This paper deals with scheduling complex tasks with an inhomogeneous set of resources. The problem is to assign technicians to tasks with multi-level skill requirements. Here the requirements are merely the presence of a set of technicians that possess the necessary capabilities. An additional complication is that a set of combined technicians stays together for the duration of a work day. This typically applies to scheduling of maintenance and installation operations. We build schedules by repeated application of a exible matching model that selects tasks to be processed and forms groups of technicians assigned to combinations of tasks. The underlying mixed integer programming (MIP) model is capable of revising technician-task allocations and performs very well, especially in the case of rare skills

A reversible loss system with multi-type customers and multi-type servers

We consider a memoryless loss system with servers S = {1,...,J}, and with customer types C = {1,...I}. Servers are multi-type, so that server j can serve a subset of customer types C(j). We show that the probabilities of assigning arriving customers to idle servers can be chosen in such a way that the Markov process describing the system is reversible, with a simple product form stationary distribution

Stability in multi-skill workforce scheduling

This paper analyzes stability in multi-skill workforce schedules. In our stability analysis, we extend the notion of blocking pairs as stated in the Marriage model of Gale-Shapley. It is shown that finding stable schedules is NP-Hard. In some special cases stable schedules can be constructed in polynomial time. An integer linear programming model is proposed to decrease the instability of schedules