MixedBacklogging andOutsourcing Models withInventory Capacity
Jinhong Zhong, Chengbin Chu · 2006
andoutsourcing. We showthatthis problem canbesolved inO(T4logT)timewhere Tisthelength oftheplanning horizon. Finally, theproposed algorithm isimplemented inC++andevaluated ona large variety ofinstances generated randomly. I.INTRODUCTION econsider asingle itemcapacitated lotsize problem. AThis problem canbedescribed asfollows. Inaplant ora warehouse, there isadynamic demand forasingle itemin eachperiod oftheT-period horizon. These demands canbe satisfied byproduction or/and through inventory from previous periods or/and bybacklogging tosubsequent periods orpartially orentirely outsourced. There arelimitations on inventory, backlogging andoutsourcing levels. Fourkinds of costsmustbe takenintoaccount: production cost, holding/backlogging cost oroutsourcing cost. Setup cost can beincluded intheproduction cost. Theproblem consists of determining theamounttobeproduced andoutsourced in eachperiod inorder tominimize thetotal costofproduction, inventory holding andbacklogging oroutsourcing overthe horizon. Intheliterature on lot-sizing problem, thebounded inventory model hasreceived little attention. Love[1]gavean 0(T3) algorithm thatsearched theextremepoints ofthe solution spaceforthebounded inventory modelwith piecewise concave costfunction andbacklogging. Gutierrez etal.[2],[3] proposed necessary conditions ofanoptimal production plan toreduce thecomputational effort ofLove's procedure forthebacklogging andnobacklogging cases respectively, anddeveloped anO(T3) dynamic programming algorithm.