A small manufacturing system processes two high volume parts: P₁ and P₂. Each of 50 units of P₁ is first processed on M₁ and then sent to machine M₂ or M_4, where it is further processed and then sent to M₃ for final processing. In addition to P_1, the manufacturing facility processes 60 units of P_2, of which 30 are processed first on M₁, and then machine M₂. Because machine M₃ can do the same processing as machine M₁ for part P_2, the remaining 30 units of part P₂ are processed first on machine M₃ and then sent to machine M₂ for final processing. Two candidate Material Handling Systems, H₁ and H₂ with purchase costs 100,000 TL and 140,000 TL respectively, are being considered. The unit cost of transporting P₁ and P₂ on each of the MHSs between the machines are given in the following table. The corresponding transportation times per unit (in minutes) are provided in parentheses in the table. Assume that there are 7150 minutes in the planning period and each handling device is expected to make empty trips 30% of the time.

Determine the required MHS and assign the departmental moves to the selected MHS(s).

Hint: You should build an LP model and solve it by any optimization package.

M2 Mi Pi P2 Mi M3 M2 M4 (M3 From To M M2 M3 M4 P1 M H H2 7(10) 5(8) 8(5) 2(2) P M2 H H2 8(6) 4(5) P1 M4 H H2 8(8) 4(5) P2 Mi H H2 2(4) 1(2) P2 M3 H H2 20(6) 12(2)