The lot scheduling problem in the hierarchy of decision models
The economic lot scheduling problem (ELSP) surfaces from competition among products for a scarce resource, usually machine time. When scheduling production of batches in this environment, two issues must be resolved: the size of batches and the start times for production of each batch. Standard approaches to the ELSP focus on scheduling multiple products on a single machine. This thesis addresses three important issues that put the scheduling problem in the context of its physical setting and range of parameters: idle time, the zero switch rule, and stochastic input to a bottleneck machine. In most scheduling heuristics, the reason for idle time is to balance cyclic production patterns. Idle time is also optimal in solutions to problems with high setup costs. We show that the condition for inducing idle time, given zero setup costs, is when one product has dominant holding costs and the remaining products have low machine utilization. A common policy in scheduling is to start production only after the inventory reaches zero. This policy is called the zero switch rule (ZSR) and is regarded as a good scheduling policy. We show that the condition when ZSR is not optimal is when the ZSR solution yields lumpy production patterns for a product with dominant holding costs.
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aggregate planning model algorithm approach assembly model Average inventory cost backlog Batch production bottleneck machine CHAPTER condition for inducing Consider constraint convex Cornell University cost product delivery issue distribution dominant holding costs dominant product dynamic programming Economic Lot Scheduling Exponential processing fcum Figure find the minimum formulate Gantt Chart Hence hierarchical ignore the delivery inducing idle input process inserting idle Lagrangian multiplier Lagrangian relaxation lost machine capacity Lot Scheduling Problem low machine utilization lower bound Machine Network Maxwell minimize ninv non-zero switch Normal Distribution optimal solution overall pa+ pb parameters Pillsbury Company Product Inventory Pattern production lot production pattern Production Planning products have low Robert Sheldon Scheduling Deliveries Scheduling Problem ELSP single machine started on machine stochastic inputs switch rule ZSR Three Product Inventory traditional ELSP Uniform processing value of lost value of machine variables zero setup costs zero switch rule ZSR solution