Dynamic Programming Algorithms with Data Rounding for Combinatorial Food Packing Problems

Combinatorial algorithms for packing and scheduling problems

Bi-criteria Food Packing by Dynamic Programming

In this paper, we deal with a certain type of automated food packing system with n hoppers. The system repeats throwing some amount of foods into empty hoppers to make all hoppers full of foods, and collecting the foods from several hoppers to pack them into a single package. We treat foods thrown into each hopper as an item i with an integer weight wi. Given a set I of n items in the hoppers, ...

Rounding algorithms for covering problems

In the last 25 years approximation algorithms for discrete optimization problems have been in the center of research in the fields of mathematical programming and computer science. Recent results from computer science have identified barriers to the degree of approximability of discrete optimization problems unless P -NP. As a result, as far as negative results are concerned a unifying picture ...

Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation

We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm —for staged pat...

Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problems