Stochastic programming in production planning: a case with none‐simple recourse

Abstract

In modeling real world planning problems as optimization programs the assumption that all parameters are known with certainty is often more seriously violated than the assumption that the objective function and the constraints can be approximated sufficiently accurate by lineair functions. In this paper we discuss the concrete application of stochastic programming to a multiperiod production planning problem in which the demand for the products during the various periods is assumed stochastic with known probability distribution. Since the resulting stochastic program does not possess the property of “simple” recourse no direct use can be made of existing methods that have been proposed in literature for solving problems of this type.

A metamodel-based Monte Carlo simulation approach for responsive production planning of manufacturing systems

“…These deterministic models have been extended in several ways to incorporate uncertainty in both production and demand. Several authors [20][21][22][23] have proposed scenario-based stochastic programming models. The main difficulty with this approach is the extremely rapid growth in the size of the models as the number of decision epochs and random variables increases.…”

Build-pack planning for hard disk drive assembly with approved vendor matrices and stochastic demands

“…In this case a subset K i is given, and we need to minimize (19) over b v and Q i (we temporally suppress the subscripts h and j for clarity of notation). Substituting the expression for C i (Q i ) from (6) we can re-write (19) as…”

“…A general approach commonly used for modeling stochastic planning problems is the scenario-based stochastic linear-programming (SLP). Applications of SLP in production planning include among examples stochastic product mix planning [21,5], stochastic HPP production planning [14], delayed product differentiation [28] and multi-period production planning [19]. In SLP future uncertainty is modeled as a finite set of possible outcomes or scenarios, each with an associated probability of occurence.…”

A multi-stage stochastic programming approach in master production scheduling

“…Furthermore, Peters et al (1977), Escudero et al (1993), Voss and Woodruff (2006), Karabuk (2008) and Higle and Kempf (2011) apply multi-stage stochastic programming to production planning. Balibek and Koksalan (2010) apply a multi-objective multi-stage stochastic programming approach for the public-debt management problem.…”