Lower Bound Solutions to Multi-Stage Production Scheduling Problems with Startup Delays

A methodology for determination of lower bound solutions for multi-stage production scheduling problems is treated here. The startup delays are expressed as analytical functions of demand, production rate, and cycle times for the appropriate stages. A theorem is proved which states that the lower bound solution is achievable if and only if adjacent stage cycle times differ by proportionality constants which are positive integers, or the reciprocal of positive integers. Computer algorithms for the solution of the lower bound problem are discussed.