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We consider the problem of scheduling parallel machines that process service requests from various customers who are entitled to many diierent grade of service (GoS) levels. We propose and analyze one simple way to ensure such diierentiated service. In particular, we investigate how the longest processing time ÿrst algorithm (LPT) would perform in the worst… (More)

In this paper we consider the nonsimultaneous multiprocessor scheduling problem, or NMSP for short. The NMSP is a makespan minimization scheduling problem which involves the nonpre-emptive assignment of independent jobs on m parallel machines with diierent starting times. It is well known that the longest processing time (LPT) algorithm and the modiÿed… (More)

We consider the problem of eeciently packing steel products, known as coils, into special containers, called cassettes for shipping. The objective is to minimize the number of cassettes used for packing all the given coils where each cassette has capacity limits on both total payload weight and size. We model this problem as a two-dimensional vector packing… (More)

We consider the makespan minimization parallel machine scheduling problem where each machine may be unavailable for a known time interval. For this problem, we investigate how the worst-case behavior of the longest processing time first algorithm (LPT) is affected by the availability of machines. In particular, for given m machines, we analyze the cases… (More)

In a recent paper Gutiérrez et al. (2008) show that the lot-sizing problem with inventory bounds can be solved in O(T log T) time. In this note we show that their algorithm does not lead to an optimal solution in general.

We consider the multilevel lot-sizing problem with production capacities (MLSP-PC), in which production and transportation decisions are made for a serial supply chain with capacitated production and concave cost functions. Existing approaches to the multistage version of this problem are limited to nonspeculative cost functions—up to now, no algorithm for… (More)