OPERATIONS MANAGEMENT (MGCR-472-061) - PageOut

OPERATIONS MANAGEMENT (MGCR-472-061)Productivity Practice Problems1. The South Dakota Clay Pigeon Corporation showed the following results for lastyear:(A) What was the total factor productivity?(B) What was the multi-factor productivity measure for total output to labor andmaterials?(C) What was the multi-factor productivity measure for finished output to laborand materials?(D) What was the partial productivity measure for total output to energy?(E) What was the partial productivity ratio for finished units to energy?2. Two types of cars (Deluxe and Limited) were produced by a car manufacturer in2001. Quantities sold, price per unit and labor hours follow. What is the laborproductivity for each car? Explain the problem(s) associated with laborproductivity.Quantity$ per unitDeluxe Car 4,000 units sold $8,000 per carLimited Car 6,000 units sold $9,500 per carLabor Deluxe 20,000 hours $12 per hourLabor Limited 30,000 hours $14 per hour3. 10,000 units produced, sold for $10/unit, 500 labor hours, labor rate: $9/hr, cost ofraw material: $5,000, cost of purchased material: $25,000.1

a. What is the labor productivity in units per hour and in unitless figure?b. What will be the labor productivity if 12,000 units are produced using 500labor hours (in units per hour and unitless figure)?c. How much labor hour should we use in order to reach the productivitylevel of part (b), if the product is 10,000 units.d. What will be the multi-factor productivity (MFP), in unitless figure and interms of units/dollar, taking into account the labor and material costs?e. Suppose we hire very efficient workers who can finish the job in 350hours. What is now the MFP with labor rate of $9/hour?f. However we have to pay higher wages for the more efficient workers.How much extra can we pay without reducing productivity from the levelof part (d) in units/dollar?Solution to Productivity Exercise Problems1.(A) What was the total factor productivity?1,050,000/650,000 = 1.62(B) What was the multi-factor productivity measure for total output to labor andmaterials?1,050,000/450,000 = 2.33(C) What was the multi-factor productivity measure for finished output to laborand materials?1,000,000/450,000 = 2.22(D) What was the partial productivity measure for total output to energy?1,050,000/25,000 = 42(E) What was the partial productivity ratio for finished units to energy?1,000,000/25,000 = 402

2. Deluxe = (4,000 units*$8,000/car)/(20,000 labor hour*$12/hour) = 133.33 (unitless);limited = (6,000 units *$9,500/car)/(30,000 labor hour*$14/hour) = 135.71 (unitless)Deluxe = (4,000 units/car)/(20,000 labor hour) = 0.2 unit/hour;limited = 6,000 units/30,000 labor hour = 0.2 unit/hourLabor productivity in terms of units/hour does not take into account the quality of theproduct (i.e., does not take into account the selling prices) and does not take intoaccount the skill level of the workers (i.e. does not take into account the labor rate).Labor productivity in unitless terms might be difficult for department managers tocomprehend who has a better idea about what units/hour mean. Unitlesss is mostlyused by high-level managers while units/hour is used by departmental managers.3. a. Labor productivity = 10,000 units/500 labor hour = 20 units/hour;Labor productivity = (10,000 units*$10/unit)/(500 labor hour*$9/hour) = 22.22(unitless)b. Labor productivity = 12,000 units/500 labor hour = 24 units/hour;Labor productivity = (12,000 units*$10/unit)/(500 labor hour*$9/hour) = 26.67(unitless)10,000unitsc. = 24 units/hour⇒24X= 10,000 ⇒ X = 416.7 ≈ 417 hoursXd. MFP = 10,000 units/$(500*9 + 5,000 + 25,000) = 0.29 units/dollar;MFP = (10,000*$10/unit)/$(500*9 + 5,000 + 25,000) = 2.9e. MFP = 10,000 units/$(350*9 + 5,000 + 25,000) = 0.3 units/dollar;f. MFP = (10,000 unit)/$(350*X + 5,000 + 25,000) = 0.2910,000= 0.29 ⇒ 10,000 = 0.29(350X+ 5000 + 25,000)(350X+ 5,000 + 25,000)⇒ 10,000 − 8700 = 101.5X⇒ X = 12.81At maximum, we can pay $12.81/hour.)3