Lot Sizing and Scheduling in Flow Shop with SequenceDependent Setups and Backlogging

Abstract

sizing and scheduling in flow shop has been considered in this paper. Our study includes a multilevel and mu ltiperiod capacitated lot sizing and scheduling problem (CLSP) with sequencedependent setups, setups carry over in flo w shop. In manufacturing environments backlogging is unavoidable. If the production capacity is infinite, any demand can be satisfied on time. But in the real world, production capacity is not infinite so some demand may not be satisfied on time. In this condition backlogging arises naturally. CLSP problems with considering backlogging has been studied fewer by researchers. Also, the sequencedependent setups and setups carry over are two important events that occur occasionally in factories. In this study an exact mixed integer problem (MIP) in a flow shop CLSP problem with considering sequencedependent se tups, setups carry over and backlogging has been formulated. Our formulation is presented to optimize objective function (including, inventory costs, product costs and setup cost). Since the CLSP problems are extremely NPhard a lower boun d is developed and compared against the optimal solution.