# Zodiac is well known brand in the fashion industry.

Case 7.2: Zodiac Apparel

Zodiac is well known brand in the fashion industry. It manufactures different types of shirts in different sizes, neck ties and other fashion accessories for professionals. Recently, it decided to make use of some latest techniques in order to help itself in the cloth cutting operation.

The cutting operation for shirts is extremely time-consuming and gives rise to high set-up costs. A large amount of cloth were also being wasted in the cutting operation. The process of cutting involved putting several layers of cloth of standard width on a table and putting stencils, i.e. the templates in order to cut the cloth. However, the choice of the templates was based on judgement, which was leading to a lot of wastage. To overcome this problem, the services of R&D department were seeked, so as to minimize the setup cost and excess, subject to certain constraints:

(i) number of layers that can be cut is limited by the length of the knives and the thickness of the fabric, and

(ii) length of the cutting table, which limits the number of stencils that can be cut in one operation. As the length of the stencils for the different sizes is almost equal, the maximum number of stencils on the cutting table is actually independent of the combination of the stencils used. Assumed that all stencils have equal length.

The following data on cutting operation of a shirt, and demand pattern for different sizes is as follows:

The spreading of the fabric on the cutting table, the fixing of the layers and stencils, and the cutting itself are extremely delicate and time-consuming operations. Therefore, the number of these operations should be minimized. The problem then reduces to find the optimal combination of the number of layers of cloth on the cutting table and the associated set of stencils to reduce minimum number of setups, while satisfying the demand with no variation.

There was an upper bound on the number of layers at 35 and the cutting table length could hold at most four stencils. Three cutting patterns were to be used.

Develop an appropriate mathematical model to suggest an optimal solution to this problem.

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