Multidimensional scheduling

The first n — 3 rows of the transformation matrix are called the multidimensional scheduling vectors. 

Multidimensional scheduling can be interpreted as follows the first scheduling vector Hi partitions the index space D into subdomains Di by using the relation Ui X I = i. Each of these subdomains can be further partitioned by the other multidimensional scheduling vectors. This results in a set of three-dimensional subdomains Each of these can be executed in parallel on a 2-D... 

In addition to their ability to capture the multidimensionality of batch operations, another advantage of mathematical programming techniques is the flexibility and adaptability of the performance index, i.e. the objective function. In a design problem, the objective function can take a form of a capital cost investment function. In a scheduling problem it can be minimization of makespan, maximization of throughput, maximization of revenue, etc. In this chapter, the objective function will either... 

An array is a multidimensional (not linear) data structure. An appointment schedule for the business week, hour by hour and day by day, is an example of an array. A mathematical function can generate data for an array structure. For example, the four-dimensional array shown in Table I (with entries in exponential notation) was obtained by substituting numeric values for x, y, w, and z in the expression ... 

Clearly, this class of problems requires a triple optimisation, so-called integrated optimisation, at the same time allocating available resources to each production line, production line sequencing and production line scheduling. It is a multidimensional, precedence-constrained, knapsack problem. The knapsack problem is a classical NP-hard problem, and it has been thoroughly studied in the last few decades [2]. 

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