The term was first used in 1958 by professor Jack D. Rogers of Berkeley,[1] who extended the economic order quantity model to the case where there are several products to be produced on the same machine, so that one must decide both the lot size for each product and when each lot should be produced.
The method illustrated by Jack D. Rogers draws on a 1956 paper from Welch, W.
A single machine is available which can make all the products, but not in a perfectly interchangeable way.
Instead the machine needs to be set up to produce one product, incurring a setup cost and/or setup time, after which it will produce this product at a known rate
is charged based on average inventory level of each item.
N is the number of runs made, U the use rate, L the lot size and T the planning period.
To give a very concrete example, the machine might be a bottling machine and the products could be cases of bottled apple juice, orange juice and milk.
This product switching must not be done too often or the setup costs will be large, but equally too long a production run of apple juice would be undesirable because it would lead to a large inventory investment and carrying cost for unsold cases of apple juice and perhaps stock-outs in orange juice and milk.
7.Enter items in schedule and check it's feasibility Of great importance in practice is to design, plan and operate shared capacity across multiple products with changeover times and costs in an uncertain demand environment.
Beyond the selection of (expected) cycle times, with some amount of slack designed in ("safety time"), one has to also consider the amount of safety stock (buffer stock) that is needed to meet desired service level.
[3] The problem is well known in the operations research community, and a large body of academic research work has been created to improve the model and to create new variations that solve specific issues.