4. Macon Controls produces three different types of control units used to protec

Question

4. Macon Controls produces three different types of control units used to protect industrial equipment from overheating. Each of these units must be processed by a machine that Macon considers to be their process bottleneck. The plant operates on two 8-hour shifts, 5 days per week, 52 weeks per year. Table 6.2 provides the time standards at the bottleneck, lot sizes, and demand forecasts for the three units. Because of demand uncertainties, the operations manager obtained three demand forecasts (pessimistic, expected, and optimistic). The manager believes that a 20 percent capacity cushion is best.

a. How many machines are required to meet minimum (Pessimistic) demand, expected demand, maximum (Optimistic) demand?

b. How many machines are required if the operations manager decides to double lot sizes?

c. If the operations manager has three machines and believes that the plant can reduce setup time by 20 percent through process improvement initiatives, does that plant have adequate capacity to meet all demand scenarios without increasing lot sizes?

Component Processing (hr/unit) Setup (hr/lot) Lot size (units/lot) Pessimistic Expected Optimistic A 0.05 1.0 60 15,000 18,000 25,000 B 0.20 4.5 80 10,000 13,000 17,000 C 0.05 8.2 120 17,000 25,000 40,000

Explanation / Answer

The plant operates on two 8 -hours shift, 5 days per week and 52 weeks year. The plant operates 4160 hours per year.

a. How many machines are required to meet minimum (Pessimistic) demand, expected demand, maximum (Optimistic) demand?

To meet pessimistic demand the plant will need 2 machines, to meet expected demand the plant will need 2 machines, and to meet maximum/optimistic demand, 3 machines.

The following are the details of the work:

Component A : (0.05 hour/unit * 60 units/lot) + (1.0 setup hour/lot) = 4 hours for making 60 units of lot size.

Component B : (0.20 hour/unit * 80 units/lot) + (4.5 setup hour/lot) = 20.5 hours for making 60 units of lot size.

Component C : (0.05 hour/unit * 120 units/lot) + (8.2 setup hour/lot) = 14.2 hours for making 120 units of lot size.

Pessimistic demand = Component A with 15000 units will require 1000 hours + Component B with 10000 units will require 2562.5 hours + Component C with 17000 units will require 2011.66 hours. 5574.16 hours with 2 machines for meeting the demand.

Expected demand = Component A with 18000 units will require 1200 hours + Component B with 13000 units will require 3331.25 hours + Component C with 25000 units will require 2958.33 hours. 7489.58 hours with 2 machines for meeting the demand.

Optimistic demand = Component A with 25000 units will require 1666.66 hours + Component B with 17000 units will require 4356.25 hours + Component C with 40000 units will require 2958.33 hours. 10756.24 hours with 3 machines for meeting the demand.

b. How many machines are required if the operations manager decides to double lot sizes?

component A : [0.05 hour/unit *120 units(double lot size)] + (1.0 setup hour) = 7 hours for making 120 units of lot size

component B : [0.20 hour/unit *160 units(double lot size)] + (4.5 setup hours) = 36.5 hours for making 160 units of lot size

Component C : [0.05 hour/unit *240 units(double lot size)] + (8.2 setup hours) = 20.2 hours for making 240 units of lot size

Pessimistic demand = component A with 15000 units will require 875 hours + component B with 10000 units will require 2281.5 hours + component C with 17000 units will require 1430.83 hours. 4587.08 hours required with 2 machines for meeting the demand

Expected demand = component A with 18000 units will require 1050 hours + component B with 13000 units will require 2965.63 hours + Component C with 25000 units will require 2104.17 hours. 6119.8 hours with 2 machines for meeting the demand required.

Optimistic demand = component A witth 25000 units will require 1458.33 hours + component B with 17000 units will require 3878.13 hours + Component C with 40000 units will require 8703.13 hours. 8703.13 hours with 3 machines for meeting the demand.

c) If the operations manager has three machines and believes that the plant can reduce setup time by 20 percent through process improvement initiatives, does that plant have adequate capacity to meet all demand scenarios without increasing lot sizes?

component A : (0.05 hour/unit *60 units) + 0.8 (20% reduction in setup hours) = 3.8 hours for making 60 units of lot size

component B : (0.20 hour/unit *80 units) + 3.6 (20% reduction in setup hours) = 19.6 hours for making 80 units of lot size

component C : (0.05 hour/unit *120 units) + 6.56 (20% reduction in setup hours) = 12.56 hours for making 120 units of lot size

Pessimistic demand = component A with 15000 units will require 950 hours + component B with 10000 units will require 2450 hours + component C with 17000 units will require 1779.33 hours. 5179.33 hours with 2 machines for meeting the demand

Expected demand = component A with 18000 units will require 1140 hours + component B with 13000 units will require 3185 hours + component C with 25000 units will require 2616.67 hours. 6941.67 hours with 2 machines for meeting the demand

Optimistic demand = component A with 25000 units will require 1583.33 hours + component B with 17000 units will require 4165 hours + component C with 40000 units will require 4186.67 hours. 9935 hours with 3 machines for meeting the demand

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