Reference no: EM132229948

A textile firm is developing its aggregate production plan for the next T months. The firm owns two plants that are closely located: a yarn manufacturing plant that converts cotton and other synthetic fibers into yarn, and a fabric manufacturing plant that converts yarn into fabric. An aggregate item is defined for the fabric. The demand for fabric (in meter squares) in month t is given by Dt .1 ton of yarn can be used to produce e YF meter squares of fabric. The firm can keep inventory either as yarn or as fabric. Monthly inventory holding costs for one ton of yarn is hY and one meter square of fabric is hF . Production costs in month t for one ton of yarn are ct Y and one meter square of fabric is ct F . Monthly physical (technological) capacity of the yarn plant is BY tons and the fabric plant is BF meter squares. The two plants can share the workers as they are located closely. Producing a ton of yarn requires aY man-months and a meter square of fabric requires a F man-months. The firm has a total permanent workforce of Wp which is paid c p per employee per month. Additional seasonal workers can be employed in any given month for a wage of c S per employee per month. It is not possible to change the size of the permanent workforce, but there is no additional hiring and laying off costs for the seasonal employees. Define additional parameters to the above given, if needed, and define decision variables for the model. Formulate the problem as a linear programming problem, assuming continuity of the decision variables.