Old Oregon Wood Store

1. What is the fastest way to manufacture Old Oregon tables using the original crew? How many could be made per day?Decision VariablesTomLet’s denote the variable a1 to time taken for Tom’s preparationLet’s denote the variable b1 to time taken for Tom’s assemblyLet’s denote the variable c1 to time taken for Tom’s finishingLet’s denote the variable d1 to time taken for Tom’s packaging

GeorgeLet’s denote the variable a2 to time taken for George’s preparationLet’s denote the variable b2 to time taken for George’s assemblyLet’s denote the variable c2 to time taken for George’s finishingLet’s denote the variable d2 to time taken for George’s packaging

LeonLet’s denote the variable a3 to time taken for Leon’s preparationLet’s denote the variable b3 to time taken for Leon’s assemblyLet’s denote the variable c3 to time taken for Leon’s finishingLet’s denote the variable d3 to time taken for Leon’s packaging

CathyLet’s denote the variable a4 to time taken for Cathy’s preparationLet’s denote the variable b4 to time taken for Cathy’s assemblyLet’s denote the variable c4 to time taken for Cathy’s finishingLet’s denote the variable d4 to time taken for Cathy’s packaging Objective FunctionBased on the information provided for Tom, George, Leon and Cathy

Preparation

Assembly

Finishing

Packaging

Tom 100 60 90 25George 80 80 60 10Leon 110 90 80 10Cathy 120 70 100 25

Minimize Z = (100*a1 + 80*a2 + 110*a3 + 120*a4) + (60*b1 + 80*b2 + 90*b3 + 70*b4) + (90*c1 + 60*c2 + 80*c3 + 100*c4) + (25*d1 + 10*d2 + 10*d3 + 25*d4)

Constraints

So each person is only allowed to complete one task and variables are binary (0 or 1) Net Flow = Flow in – Flow out0 - (a1 + b1 + c1 + d1) = -1 (Tom)0 - (a2 + b2 + c2 + d2) = -1 (George)0 - (a3 + b3 + c3 + d3) = -1 (Leon)0 - (a4 + b4 + c4 + d4) = -1 (Cathy)

a1 + a2 + a3 + a4 = 1 (preparation)b1 + b2 + b3 + b4 = 1 (assembly)c1 + c2 + c3 + c4 = 1 (finishing)d1 + d2 + d3 + d4 = 1 (packaging)

Variables are binary and therefore are either 0 or 1

Based on Excel Solver, it was determined that Tom would be responsible for preparation while George would be responsible for finishing. Leon is responsible for packaging while Cathy is in-charge of assembly which amounts to 240min to manufacture a table. Approximately 4.8 tables could be made per day.

2. Would production rates and quantities change significantly if George would allow Randy to perform one of the four functions and make one of the original crew the backup person?

Decision Variables (inclusive of the ones mentioned in the previous part)RandyLet’s denote the variable a5 to time taken for Randy’s preparationLet’s denote the variable b5 to time taken for Randy’s assemblyLet’s denote the variable c5 to time taken for Randy’s finishingLet’s denote the variable d5 to time taken for Randy’s packaging

Objective Function

Preparation

Assembly

Finishing

Packaging

Tom 100 60 90 25George 80 80 60 10Leon 110 90 80 10Cathy 120 70 100 25Randy 110 80 100 10

Minimize Z = (100*a1 + 80*a2 + 110*a3 + 120*a4 + 110*a5) + (60*b1 + 80*b2 + 90*b3 + 70*b4 + 80*b5) + (90*c1 + 60*c2 + 80*c3 + 100*c4 + 100*c5) + (25*d1 + 10*d2 + 10*d3 + 25*d4 + 10*d5)

ConstraintsSo each person is only allowed to complete one task and variables are binary (0 or 1) and Randy could replace one of the people.

Net Flow = Flow in – Flow out0 - (a1 + b1 + c1 + d1) >= -1 (Tom)0 - (a2 + b2 + c2 + d2) >= -1 (George)0 - (a3 + b3 + c3 + d3) >= -1 (Leon)0 - (a4 + b4 + c4 + d4) >= -1 (Cathy)0 - (a5 + b5 + c5 + d5) >= -1 (Randy)

a1 + a2 + a3 + a4 + a5= 1 (preparation)b1 + b2 + b3 + b4 + b5 = 1 (assembly)c1 + c2 + c3 + c4 + c5 = 1 (finishing)d1 + d2 + d3 + d4 + d5 = 1 (packaging)


Based on Excel Solver, the results show that Randy would replace Cathy for packaging while George would be responsible for preparation, Leon is responsible for finishing while Tom was in-charge of assembly. The total time taken to manufacture a table is computed to be 230min.

3. What is the fastest time to manufacture a table with the original crew if Cathy is moved to either preparation or finishing?

When Cathy is responsible for preparation,

Objective function


Constraints

Net Flow = Flow in – Flow out0 - (a1 + b1 + c1 + d1) >= -1 (Tom)0 - (a2 + b2 + c2 + d2) >= -1 (George)0 - (a3 + b3 + c3 + d3) >= -1 (Leon)

0 - (a4 + b4 + c4 + d4) >= -1 (Cathy)0 - (a5 + b5 + c5 + d5) >= -1 (Randy)


a4 = 1, b4 = c4 = d4 = 0 (Cathy’s preparation)


Based on Excel QM, and the fact that Cathy is in-charge of preparation, Tom would be responsible for assembly. George would be responsible for finishing while Leon will take care of packaging. This would result in time taken of 250min.

When Cathy is responsible for finishing,

Objective function


Constraints

Net Flow = Flow in – Flow out0 - (a1 + b1 + c1 + d1) >= -1 (Tom)0 - (a2 + b2 + c2 + d2) >= -1 (George)0 - (a3 + b3 + c3 + d3) >= -1 (Leon)0 - (a4 + b4 + c4 + d4) >= -1 (Cathy)0 - (a5 + b5 + c5 + d5) >= -1 (Randy)


c4 = 1, b4 = a4 = d4 = 0 (Cathy’s finishing)


Based on Excel Solver, and the fact that Cathy is in-charge of finishing, Tom would be responsible for assembly. George would be responsible for preparation while Randy will take care of packaging. This would also result in time taken of 250min to manufacture the table.

4. Whoever performs the packaging function is severely underutilized. Can you find a better way of utilizing the four or five person crew than either giving each a single job or allowing each to manufacture an entire table? How many tables could be manufactured per day with this scheme?

For the case where each person is made to manufacture the table completely from start to finish, they can do 1.75 + 2.09 + 1.66 + 1.52 + 1.6 = 8.62 tables per day whereas where only 4 are required to build the tables, only 6 were made per day.

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Old Oregon Wood Store