The semiconductor manufacturing process usually consists of four main production stages: wafer fabrication, probe, assembly, and final test. This paper considers the lot-sizing and scheduling problem in the assembly stages. A hierarchical solution approach is outlined with focus on the first of three suggested phases, namely the bottleneck lot-sizing and scheduling phase. The approach integrate...

We present a fully polynomial time approximation scheme (FPTAS) for a capacitated economic lot-sizing problem with a monotone cost structure. An FPTAS delivers a solution with a given relative error ε in time polynomial in the problem size and in 1/ε. Such a scheme was developed by van Hoesel and Wagelmans [8] for a capacitated economic lot-sizing problem with monotone concave (convex) producti...

We consider mixed-integer linear programming (MIP) models of production planning problems known as the small bucket lot-sizing and scheduling problems. We present an application of a class of valid inequalities to the case with lost demand (stock-out) costs. Presented results of numerical experiments made for the the Proportional Lot-sizing and Scheduling Problem (PLSP) confirm benefits of such...

In this paper we study sensitivity analysis of the uncapacitated single level economic lot-sizing problem, which was introduced by Wagner and Whitin about thirty years ago. In particular we are concerned with the computation of the maximal ranges in which the numerical problem parameters may vary individually, such that a solution already obtained remains optimal. Only recently it was discovere...

In this paper, we present a fast algorithm for continuous wire-sizing under the distributed Elmore delay model. Our algorithm GWSA-C is an extension of the GWSA algorithm (for discrete wire-sizing) in CL93a]. GWSA-C is an iterative algorithm with guaranteed convergence to optimal wire-sizing solutions. When specialized to discrete wire-sizing problems, GWSA-C is an improved implementation of GW...

  This paper proposes two relax and fix heuristics for the simultaneous lot sizing and sequencing problem in permutation flow shops involving sequence-dependent setups and capacity constraints. To evaluate the effectiveness of mentioned heuristics, two lower bounds are developed and compared against the optimal solution. The results of heuristics are compared with the selected lower bound .

Lot sizing and scheduling in flow shop has been considered in this paper. Our study includes a multi-level and multi-period capacitated lot sizing and scheduling problem (CLSP) with sequence-dependent setups, setups carry over in flow shop. In manufacturing environments backlogging is unavoidable. If the production capacity is infinite, any demand can be satisfied

For the problem of lot-sizing on a tree with constant capacities, or stochastic lot-sizing with a scenario tree, we present various reformulations based on mixing sets. We also show how earlier results for uncapacitated problems involving (Q,SQ) inequalities can be simplified and extended. Finally some limited computational results are presented.

This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under uncertainty. We show that the classical (`, S) inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend the (`, S) inequalities to a general class of valid inequalities, called the (Q, SQ) inequalities, an...

The new strategy for non-uniform initial FE mesh generation is presented in this paper. The main focus is set to a priori procedures that define the sizing function independent on the mesh generation algorithm. The sizing function used by the mesh generation algorithm is established by control sphere and control space concepts and fully controls mesh gradation in the complex 2D problem domains.