Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing

Table 1

Concept Comparison of the 𝑝-median Problem to Glass Cutting Problem.

Concept	𝑝-median	Glass Cutting
Objective	Minimise cost; see (9)	Minimise Wastage
Task	Satisfy demand points with located facilities	Assign orders to be cut from generated blanks
Finite constraint	Can locate 𝑝 facilities, see Constraint 10	Can choose 𝑁 blanks
Hard constraint	Every demand must be satisfied, see Constraint 8	Every order must be satisfied
Integrality constraint	A demand point 𝑗 is satisfied by one facility 𝑖. Implication: employ binary decision variable 𝑥𝑖𝑗	An order is cut within one blank and only one blank