Sequential decision problems can often be modeled as Markov decision processes. Classical solution approaches assume that the parameters of the model are known. However, model parameters are usually estimated and uncertain in practice. As a result, managers are often interested in how estimation errors affect the optimal solution. In this paper we illustrate how sensitivity analysis can be perf...

This paper presents an optimization-based solution approach for the dynamic multi-level capacitated lot sizing problem (MLCLSP) with positive lead times. The key idea is to solve a series of mixed-integer programs in an iterative fix-and-optimize algorithm. Each of these programs is optimized over all real-valued variables, but only a small subset of binary setup variables. The remaining binary...

This paper presents an optimization-based solution approach for the dynamic multi-level capacitated lot sizing problem (MLCLSP) with positive lead times. The key idea is to solve a series of mixed-integer programs in an iterative fix-and-optimize algorithm. Each of these programs is optimized over all real-valued variables, but only a small subset of binary setup variables. The remaining binary...

In this paper, an integrated production and transportation scheduling model is proposed. This model is based on multi-item capacitated lot sizing and facility location type models. The objective of the integrated model is to minimize the total production and transportation cost. The integrated model is solved by Lagrangian decomposition method and the decomposed two sub-problems can be solved b...

We address a multi-item capacitated lot-sizing problem with setup times and shortage costs that arises in real-world production planning problems. Demand cannot be backlogged, but can be totally or partially lost. The problem can be modelled as a mixed integer program and it is NP-hard. In this paper, we propose some classes of valid inequalities based on a generalization of Miller et al. [17] ...

In this chapter, an integrated production and transportation scheduling model is proposed. This model is based on multi-item capacitated lot sizing and facility location type models. The objective of the integrated model is to minimize the total production and transportation cost. The integrated model is solved by Lagrangian decomposition method and the decomposed two sub-problems can be solved...

A new mixed-integer programming (MIP) formulation is presented for the production planning of single-stage multi-product processes. The problem is formulated as a multi-item capacitated lot-sizing problem in which (a) multiple items can be produced in each planning period, (b) sequence-independent set-ups can carry over from previous periods, (c) set-ups can cross over planning period boundarie...

This paper explores a single-item capacitated lot sizing problem with minimum order quantity, which plays the role of minor set-up cost. We work out the necessary and sufficient solvability conditions and apply the general dynamic programming technique to develop an O(T ) exact algorithm that is based on the concept of minimal sub-problems. An investigation of the properties of the optimal solu...