Models and solution approaches for complex production planning and scheduling
04 / 2008 - 04 / 2012
In industry, one encounters many complex production planning and schedulingproblems. This has inspired many academic researchers to look deeperinto this topic. The fruits of their efforts are both theoretical contributionsto methodological issues and practical applications of these methods to reallifeproblems. We shall look at production planning and scheduling problemsfrom an operational research point of view. The research will focus on modellingsuch problems and solving them using advanced mathematical techniques.Particular interest will be paid to lot sizing problems.In the classical lot sizing problem, we are dealing with demand for a productby customers over a discrete time horizon. In each time period, we arefaced with the decision whether or not to produce and if so, how many unitsare to be produced. If we decide to produce in a period, fixed set-up costs needto be paid. Customer demand can also be fulfilled from inventory. In that casewe incur holding costs per unit per time period. Consequently, there is theclassical trade-off found in lot sizing problems, between fixed set-up costs andvariable holding costs. The goal is to minimise these costs while fulfilling customerdemand.Over the years this (classical) lot sizing problem has been studied thoroughly.Many solution methods were developed, the most well-known ofthem being the famousWagner-Whitin (1958) dynamic programming method.Furthermore, the problem has been extended in many directions to suitmore and more problems that have arisen in practice. One could think of forinstance: production capacities, multiple items, negative inventories (backlogging),set-up times, etc.These extensions usually result in complex mathematical models, whichare traditionally formulated as mixed integer programming problems. Someof those are easy to solve, such as the inclusion of constant capacities and backloggingin the classical problem. Others are much harder, such as the multiitemproblem with production capacities and many more. For these hard problemsit is considered unlikely that a polynomial time algorithm exists.This research aims to contribute to the rich research history by building onthe results that have been obtained with respect to both methodological ad-2vancements as well as by developing challenging new extensions of the classicalproblem.