In this paper the flow shop scheduling problem with minimizing two criteria simultaneously is consider. Selected criteria are: makespan and the sum of tardiness of jobs. For each separate criteria the problem is strongly NP-hard, which makes it NP-hard as well. There is a number of heuristic algorithms to solve the flow shop problem with various single objectives, but heuristics for multi-crite...

We study the algorithmic properties of quantified linear-time temporal logic QLTL in languages with restrictions on number individual variables as well and arity predicate letters. prove that satisfiability problem for two one monadic letter Σ 11 -hard. Thus, is Π -hard, so not recursively enumerable, such languages. The resultholds both increasing domain constant semantics obtained by reductio...

Proper arrangement of facility layout is a key issue in management that influences efficiency and the profitability of the manufacturing systems. Parallel Row Ordering Problem (PROP) is a special case of facility layout problem and consists of looking for the best location of n facilities while similar facilities (facilities which has some characteristics in common) should be arranged in a row ...

We study the maximum differential coloring problem, where the vertices of an n-vertex graph must be labeled with distinct numbers ranging from 1 to n, so that the minimum absolute difference between two labels of any two adjacent vertices is maximized. As the problem is NP-hard for general graphs [16], we consider planar graphs and subclasses thereof. We prove that the maximum differential colo...

Mixed model two-sided assembly lines (MM2SAL) are applied to assemble large product models, which is produced in high-volume. So, the sequence planning of products to reduce cost and increase productivity in this kind of lines is imperative. The presented problem is tackled in two steps. In step 1, a framework is developed to select and prioritize customer orders under the finite capacity of th...