Economic Order Quantities in production: From Harris to Economic Lot Scheduling Problems

This article provides a short historical overview from Harris and his Economic Order Quantity (EOQ) formula to the Economic Lot Scheduling Problem (ELSP). The aim is to describe the development of the ELSP field from the EOQ formula to the advanced methods of today in a manner that suits master and graduate students. The article shows the complexities, difficulties and possibilities of scheduling and producing several different items in a single production facility with constrained capacity. The items have different demand, cost, operation time and set-up time. Set-up time consumes capacity and makes the scheduling more complicated. Idle time makes the scheduling easier but is bad from a practical point of view since it creates unnecessary costs due to low utilisation of the facility. A heuristic solution method is used on a small numerical example to illustrate different solution approaches. The solution method creates a detailed schedule and estimates the correct set-up and inventory holding cost even if the facility works close to its capacity.