In this thesis we study algorithms for scheduling problems. We investigate semi-online minimum makespan scheduling and generalized bin covering. In online minimum makespan scheduling we are given a set of m machines and n jobs, where each job Jt is specified by a processing time. The jobs arrive one by one and we have to assign them to the machines without any knowledge about future incoming jo...

In this paper we introduce the Generalized Bin Packing Problem under Uncertainty, a new packing problem where, given a set of items characterized by volume and stochastic revenue and a set of bins characterized by volume and cost, we want to select a subset of items to be loaded into a subset of bins which maximizes the total profit, given by the difference between the expected total revenue of...

The Generalized Bin Packing Problem (GBPP) is a novel packing problem arising in many transportation and logistic settings, characterized by multiple item and bin attributes and by the joint presence of both compulsory and non-compulsory items. We introduce a change in the definition of the problem that does not impact either on its feasible solution set or on its optimal solutions, but guarant...

Abstract We deal with a model that is called Bin Covering Delivery. Here we search for “good and fast” covering. This problem has been defined investigated recently. continue significantly augment the preliminary investigations of problem. After studying goodness adapted versions some classical algorithms, propose parametrized algorithm use heuristic parameter optimization method to solve this ...

The Max-Profit Generalized Assignment Problem (Max-GAP) is: given sets J of bins and I of items, where each j ∈ J has capacity c(j) and each i ∈ I has in bin j size `(i, j) and profit p(i, j), find a maximum profit feasible assignment. The problem admits a 1/2-approximation algorithm. Our main result is a (1− 1/e)-approximation algorithm for Max-GAP with fixed profits when each i ∈ I has a fixe...

In this paper, we address the selfish bin covering problem, which is greatly related both to the bin covering problem, and to the weighted majority game. What we are mainly concerned with is howmuch the lack of central coordination harms social welfare. Besides the standard PoA and PoS, which are based on Nash equilibrium, we also take into account the strong Nash equilibrium, and several new e...

In the bin covering problem there is a group L=(a1; : : : ; an) of items with sizes s̃(ai)∈ (0; 1), and the goal is to 6nd a packing of the items into bins to maximize the number of bins that receive items of total size at least 1. This is a dual problem to the classical bin packing problem. In this paper we present the 6rst asymptotic fully polynomial-time approximation scheme for the problem. ...

Bin covering is a dual version of classic bin packing. Thus, the goal is to cover as many bins as possible, where covering a bin means packing items of total size at least one in the bin. For online bin covering, competitive analysis fails to distinguish between most algorithms of interest; all “reasonable” algorithms have a competitive ratio of 1 2 . Thus, in order to get a better understandin...