Sub-contracting dyeing operations in a textile company: ABC textile mills manufactures fabrics with different colors | Assignment Help

Sub-contracting dyeing operations in a textile company: ABC textile mills manufactures fabrics with different colors. The factory has a high-quality dyeing unit but with limited capacity. It is thus necessary for ABC mills to subcontract some of its dyeing operations – but the logistics manager wishes to know which fabrics are to be subcontracted and the corresponding quantity. The problem, ignoring time scheduling and other complications, can be formulated as follows. Let nf = number of different colored fabrics, xi = quantity of fabric i dyed inhouse and yi = quantity of fabric i that is subcontracted out for dyeing. Let Pi = unit profit, ci = unit cost to dye in-house, si = unit cost to dye as charged by the subcontractor, and di = amount of fabric that needs to be dyed in a given time period (i.e., the demand). Further, let r = total amount of fabric that can be dyed in-house (of all types) and R = total fabric quantity that can be dyed by the subcontractor. A suitable objective function isthe maximization of totalrevenue = total profit – total cost. This leads to the problem

The “design variables” are the quantities xi and yi , and the total number of variables n = 2 nf . The solution of course depends on the data. Typically, it is more expensive to subcontract, especially the high-end dyeing operationsfor the more profitable fabrics. However, owing to limited resources in-house, there is no option but to subcontract some amount. For the data below: nf = 4, r = 50, R = 1000 (unlimited), d1 = 25, d2 = 45, d3 = 50, d4 = 60 (Pi – ci) = {10.0, 6.5, 6.0, 5.0} and (Pi – si) = {–2.0, 5.5, 5.0, 4.0} determine the net revenue, and the amount of each fabric dyed in-house vs. dyed outside