Often multiple production lines (or machines, cells, or departments) p
roduce a group of related products. In these environments, the followi
ng interrelated planning decisions must be made: 1. Choosing the speed
at which each line will run, 2. Determining which products to produce
on which lines, and 3. Determining the number of workers assigned to
each line. These decisions directly affect a plant's labor and capacit
y utilization and are quite complex if the number of products and line
s is large. For the purposes of cost estimating to bid on new work, la
bor negotiations, and training, these planning decisions must be made
before precise demand information is available. Yet in many industries
, such as the US automotive industry, restrictive labor agreements for
ce the plant to live with these planning decisions for long periods of
time. This paper enunciates this production planning problem actually
facing industry, formulates it mathematically, and provides a practic
al solution approach.