Macon Controls produces three different types of control units used to protect i

Question

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 bottlenect. 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?

6.2 Table

Component Processing (hr/unit) Setup (hr/lot) Lost 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

Since plant operates two 8 hrs per week, 5 days/ week and 52 weeks year. Plants operates totaly 4160 hrs / year.

(A) The plant requires 2 machines to meet pessimistic demand, 2 machines to meet expected demand and 3 machines machines tomeet Optmistic demand.

Details of the work are as below,

A components : (0.05*60 units) + 1.0(setup hr) = 4 hrs to make 60 units of lot size

B components : (0.20*80 units) + 4.5 (set up hr) = 20.5 hrs to make 60 units of lotsize

C components : (0.05*120 units) + 8.2(set up hr) = 14.2 hrs to make 120 unit of lot size

Pessimistic demand = 5574.16 hrs can accomadate with 2 machines to meet the demand ( A component (15000 units) requires 1000 hrs + B component (10000 units ) requires 2562.5 hrs + C component (17000 units) requires 2011.66 hrs)

Expected demand = 7489.58 hrs can accomadate with 2 machines to meet the demand ( A component (18000 units) requires 1200 hrs + B component (13000 units ) requires 3331.25 hrs + C component (25000 units) requires 2958.33 hrs)

Optimistic demand = 10756.24 hrs can accomadate with 3 machines to meet the demand ( A component (25000 units) requires 1666.66 hrs + B component (17000 units ) requires 4356.25 hrs + C component (40000 units) requires 2958.33 hrs)

B) if the operation manger doubles the lot sizes, even though the plant requires 2 machines to meet pessimistic demand, 2 machines to meet expected demand and 3 machines machines tomeet Optmistic demand.

Details of the work are as below,

A components : (0.05*120 units(lot size double)) + 1.0(setup hr) = 7 hrs to make 120 units of lot size

B components : (0.20*160 units(lot size double)) + 4.5 (set up hr) = 36.5 hrs to make 160 units of lotsize

C components : (0.05*240 units(lot size double)) + 8.2(set up hr) = 20.2 hrs to make 240 unit of lot size

Pessimistic demand = 4587.08 hrs can accomadate with 2 machines to meet the demand ( A component (15000 units) requires 875 hrs + B component (10000 units ) requires 2281.5 hrs + C component (17000 units) requires 1430.83 hrs)

Expected demand = 6119.8 hrs can accomadate with 2 machines to meet the demand ( A component (18000 units) requires 1050 hrs + B component (13000 units ) requires 2965.63 hrs + C component (25000 units) requires 2104.17 hrs)

Optimistic demand = 8703.13 hrs can accomadate with 3 machines to meet the demand ( A component (25000 units) requires 1458.33 hrs + B component (17000 units ) requires 3878.13 hrs + C component (40000 units) requires 8703.13 hrs)

c) if the operation manger decides to reduce 20 percent of set uptime by improvement initiatives though the plant requires 2 machines to meet pessimistic demand, 2 machines to meet expected demand and 3 machines machines tomeet Optmistic demand.

Details of the work are as below,

A components : (0.05*60 units) + 0.8 (20 % reduce setup hr) = 3.8 hrs to make 60 units of lot size

B components : (0.20*80 units) + 3.6 (20 % reduceset up hr) = 19.6 hrs to make 80 units of lotsize

C components : (0.05*120 units) + 6.56(20 % reduceset up hr) = 12.56 hrs to make 120 units of lot size

Pessimistic demand = 5179.33 hrs can accomadate with 2 machines to meet the demand ( A component (15000 units) requires 950 hrs + B component (10000 units ) requires 2450 hrs + C component (17000 units) requires 1779.33 hrs)

Expected demand = 6941.67 hrs can accomadate with 2 machines to meet the demand ( A component (18000 units) requires 1140 hrs + B component (13000 units ) requires 3185 hrs + C component (25000 units) requires 2616.67 hrs)

Optimistic demand = 9935 hrs can accomadate with 3 machines to meet the demand ( A component (25000 units) requires 1583.33 hrs + B component (17000 units ) requires 4165 hrs + C component (40000 units) requires 4186.67 hrs)

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