Planning productionusingmathematicalprogramming:Thecaseofa woodturning company

Herein wepresentacaseofproductionplanninginawoodturningcompany.Thecompanywishestoplan the turningofvarioustypesofproductsofdifferentradiiinasetofparallelmachines(lathes)andwith the followingprincipalconditions:foreachtypeofproductthereisaminimumproductionlotsize;some lathes cannotmanufactureeverytypeofproduct;theproductioncapacityofalathedependsonthelathe itself andthetypeofproducttobemanufactured;theproductsareclassifiedintofamiliesaccordingto radius; andthereisanintra-familysetuptime(formanufacturingdifferentproductsthathavethesame radius) andaninter-familysetuptime(forconsecutivelymanufacturingproductsthathavedifferentradii), which islonger;partoftheproductioncanbesubcontracted;eachtypeofproductcanbemanufactured on differentlathesand/orsubcontracted;andtheoperatorscanworkovertime,duringwhichadditional time theycansimultaneouslyoperatemultiplelathes.Thegoalistomeetthedemandatminimumcost, which includesthecostofanyovertimeplusthatofanysubcontracting.Theproblemwasmodelledand solved bymixed-integerlinearprogramming(MILP).Thecompanyconsiderstheresultstobesatisfactory.