On an Economic Lot Sizing Model Subject to Two Imperfect Key Production Subsystems

摘要

This paper considers an Economic Production Quantity (EPQ) model where a product is to be manufactured in batches on an imperfect production system over an infinite planning horizon. During a production run of the product, the production system is dictated by two unreliable key production subsystems (KPS) that may shift from an in-control to an out-of-control state. Suppose the production system is subject to three independent sources of shocks. A shock from source 1 causes the first KPS to shift. As a result, a fixed α percentage of defective items will be produced after the KPS has shifted. It occurs at a random time U1 following an exponential distribution with a mean 1/ λ1. A shock from source 2 causes the second KPS to shift. This leads to a fixed β percentage of defective items to be produced after the KPS has shifted into the out-of-control state. It occurs at a random time U2 following an exponential distribution with a mean 1/λ2 ? Finally, a shock from source 3 will result in both KPS's to shift into the out-of-control state. Consequently, a fixed 8 percentage of defective items will be produced. It occurs at a random time U12 following an exponential distribution with a mean 1/λ12- Hence, we can define a random variable X representing the time-to-shift of the first key component satisfies X = min(U1, U12) while another random variable Y representing the time-to-shift of the second key component satisfies Y = min(U2, U12). The objective is to determine a production cycle time that minimizes the expected total cost per unit time including setup, inventory carrying, and defective costs. A solution approach of finding a near-optimal solution is provided.