Formulas

Question 1

Center-of-Gravity Coordinates

Answer 1

x = ∑ xi * Wi / ∑ Wi
y = ∑ yi * Wi / ∑ Wi

xi, yi = coordinates of existing facility i

Wi = annual weight shipped from facility i

Question 2

Little’s Law

Answer 2

L = λ * W

L = average number of items in the queuing system (e.g., work-in-progress inventory in the system)

W = average waiting time in the system for an item
λ = average number of items arriving per unit time

Question 3

Breakeven point

Answer 3

v = cf / (p - cv)

cf = fixed cost
cv = variable cost per unit
p = price per unit
v = volume (i.e., number of units produced and sold)

Question 4

Point of indifference

Answer 4

cf1 = fixed cost process 1
cf2 = fixed cost process 2
cv1 = variable cost per unit process 1
cv2 = variable cost per unit process 2

(cf2 - cf1) / (cv1 - cv2) |

Question 5

Assembly Line Efficiency

Answer 5

E = ∑ ti / n*Ca

ti = completion time for element i
n = actual number of workstations
Ca = actual cycle time

Question 6

Minimum number of workstations

Answer 6

N = ∑ ti / Cd

ti = completion time for element i
Cd = desired cycle time

Question 7

EOQ Total Cost

Answer 7

TC = (C0 * D / Q) + (Cc * Q / 2)

C0 = cost per order
Cc = per unit carrying cost
D = annual demand
Q = order size

Question 8

EOQ Optimal Quantity

Answer 8

Qopt = SQRT(2 * C0 * D / Cc)

Qopt = optimal order size
C0 = cost per order
Cc = per unit carrying cost
D = annual demand

Question 9

PQ Total Cost

Answer 9

TC = (C0 * D / Q) + (Cc * Q / 2) * (1 - d / p)

C0 = cost per order
Cc = per unit carrying cost
D = annual demand
Q = order size
p = daily rate order is received, also called production rate
d = daily rate inventory is demanded

Question 10

Reorder point

Answer 10

R = d * L

d = demand rate per period (e.g., daily)
L = lead time

Question 11

Reorder point with variable demand

Answer 11

R = d * L + z * od * SQRT(L)

d = average daily demand
L = lead time
z = number of standard deviations corresponding to the service level probability
od = the standard deviation of daily demand

z * od * SQRT(L) = safety stock

Question 12

EOQ Optimal Quantity with variable demand

Answer 12

Q = d(tb + L) + z * od SQRT(tb + L) - I

d = average demand rate
tb = the fixed time between orders
L = lead time
od = standard deviation of demand
I = inventory in stock

z * od * SQRT(tb + L) = safety stock

Question 13

Safety Stock

Answer 13

Safety stock = z * od * SQRT( L)