T

Number of time periods.

N

Number of products.

t

Index of time periods. Where.

Index of products. Where corresponds to the raw material and to the finished products.

Demand for item at period.

Unit production cost of finished product in period.

Setup cost of finished product in period.

Unit holding cost of finished product in period.

Available capacity at period t.

External demand for item available at period k that should be produced before period t.

Initial inventory of item.

Launching production of item in period t requires a setup time i from the joint resource.

Requires units of the joint resource.

represents the aggregate demand in period t, i.e.. Without loss of generality we assume that each of the items has a distinct time window.