Initial order quantities in multistage serial production systems

This paper considers the determination of initial order quantities in a multistage production system where items are processed into end products at a finite rate within each stage of production, assuming no backlogging is allowed. Before the end products of a batch are made available, from the initial time period of production or during the downtime because of maintenance due to unexpected machine breakdowns, or when a long manufacturing lead time results in a slower response to the market, the demand occurred cannot be met when there is a shortage of on-hand inventory. The operation procedure of the initial order quantities for a single-product process in a serial multistage system is investigated. Overproduction is allowed at different stages such that the production volume per production run at each stage may be an integer multiple of the quantity processed at its successor. By incorporating the effect of lost sales and transforming the composition of production rates at various stages into a global conversion rate, the inclusion of an initial transient phase followed by the stationary phase can be optimal. The size of a series of transient batches increases until it reaches the stationary size and thereafter the stationary runs start.