Msc Logistics & Supply Chain Management
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[pic 1]SCHOOL OF ECONOMIC SCIENCESMSc LOGISTICS&SUPPLY CHAIN MANAGEMENTAcademic Year 2016-20171st SemesterClass: Operations ResearchAssignment Number 1Angelos Kottas&Christos Karagkounis Exercise 2Our team has chosen the Exercise 2 (named “askhsh2” in the attached PDF files sent by the class instructor).Modeling of the Linear ProblemLet the following variables:-x1 : the quantity of produced tables-x2 : the quantity of produced chairs-x3 : the quantity of produced desks-x4 : the quantity of produced librariesGiven the fact that every produced table, chair, desk, and library requires 5, 1, 9 and 12 m3 Type 1 wood respectively, having 1500 m3 of Type 1 wood available, then the first constraint is written as follows:5×1 + x2 + 9×3 + 12×4 ≤ 1500 (Constraint 1)Given the fact that every produced table, chair, desk, and library requires 2, 3, 4 and 1 m3 Type 2 wood respectively, having 1000 m3 of Type 2 wood available, then the second constraint is written as follows:2×1 + 3×2 + 4×3 + 1×4 ≤ 1000 (Constraint 2)Given the fact that every table, chair, desk, and library requires respectively 3, 2, 5 and 10 hours of labour respectively, having 800 hours of labour available, then the third constraint is written as follows:3×1 + 2×2 + 5×3 + 10×4 ≤ 800 (Constraint 3)Given the fact that a minimum of 40 tables are required, then the fourth constraint is written as follows:x1 ≥ 40 (Constraint 4)Given the fact that a minimum of 130 chairs are required, then the fifth constraint is written as follows:x2 ≥ 130 (Constraint 5)Given the fact that a minimum of 30 desks are required, then the sixth constraint is written as follows:x3 ≥ 30 (Constraint 6)Given the fact that a maximum of 10 tables are required, then the seventh constraint is written as follows:x4 ≤10 (Constraint 7)As far as concerning the objective function, in our case it will represent the obtained profit. Taking into account that each produced table, chair, desk, and library provides 12, 5, 15 and 10 monetary units of profit respectively (1,000 drachmas represents a monetary unit), then the objective function is as follows:
maxz= 12×1 + 5×2 + 15×3 + 10×4 (Objective Function)Due to the fact that we want to maximize our obtained profit, the objective function represents a maximization linear problem.Of course, the non-negativity constraint must hold for the decision variables.Hence, xi≥0 (i=1,2,3,4)Solving the Modeled Linear ProblemLINDO™ Software UsedAccording to the LINDO™ Tutorial (accessed & downloaded the weblink