Respuesta :
Answer:
(a) 1,078.12 copies
(b) 6.68 runs per year
(c) 37.43 days
(d) 10.78 days
(e) 767.62 copies
(f) $2,003.48
(g) 432 copies
Explanation:
Given that,
Annual demand (D) = 7200 copies
Cost of the book (C) = $14.50
Holding cost (H) = 18% of cost of book = 18% of $14.50
= $2.61
Setup costs (S) = $150
Annual production volume = 25,000 copies
Number of working days = 250
Lead time (L) = 15 days
Daily demand (d) = Annual demand ÷ Number of working days
= 7200 ÷ 250
= 28.8 copies
Daily production (p) = Annual production ÷ Number of working days
= 25000 ÷ 250
= 100 copies
(a) Minimum cost production lot size (Q):
[tex]Q=\sqrt{\frac{2\times D\times S}{H\times (1-\frac{d}{p})}}[/tex]
[tex]Q=\sqrt{\frac{2\times 7,200\times 150}{2.61\times (1-\frac{28.8}{100})}}[/tex]
Q = 1,078.12 copies
(b) Number of production runs:
= Annual demand (D) ÷ Production quantity (Q)
= 7,200 ÷ 1,078.12
= 6.68 runs per year
(c) Cycle time:
= Production quantity (Q) ÷ Daily demand (d)
= 1,078.12 ÷ 28.8
= 37.43 days
(d) Length of a production run:
= Production quantity (Q) ÷ Daily production (p)
= 1,078.12 ÷ 100
= 10.78 days
(e) Maximum inventory (Imax):
= Q × (1 - d÷p)
= 1,078.12 × (1 - 28.8 ÷ 100)
= 767.62 copies
(f) Total annual cost:
= Annual holding cost + Annual setup cost
= [(Q ÷ 2) × H × (1 - d÷ p)] + [(D ÷ Q) × S]
= [(1,078.12 ÷ 2) × $2.61 × (1 - 28.8 ÷ 100)] + [(7,200 ÷ 1,078.12) × $150]
= $1,001.74 + $1,001.74
= $2,003.48
(g) Reorder point:
= Daily demand × Lead time
= 28.8 × 15
= 432 copies
Answer:
(a) 1,078.12 copies
(b) 6.68 runs per year
(c) 37.43 days
(d) 10.78 days
(e) 767.62 copies
(f) $2,003.48
(g) 432 copies
Given Data:
Annual demand (D) = 7200 copies
Cost of the book (C) = $14.50
Holding cost (H) = 18% of cost of book = ($14.50)*18% = $2.61
Setup costs (S) = $150
Annual production volume (P) = 25,000 copies
Number of working days (n) = 250
Lead time (L) = 15 days
Calculations:
(a) Minimum cost production lot size (Q):
[tex]Q=\sqrt{\frac{2*D*S}{H*(1-\frac{D}{P}) } } \\\\Q=\sqrt{\frac{2*(7200)*(150)}{(2.61)*(1-\frac{7200}{25000}) } }\\\\[/tex])
Q = 1,078.12 copies
(b) Number of production runs (PR):
[tex]PR = \frac{D}{Q}\\\\PR = \frac{7200}{1078.12}\\\\[/tex]
PR = 6.68 runs annually
(c) Cycle time ([tex]T_c[/tex]):
[tex]T_c = n*(\frac{Q}{D})\\\\T_c = 250*(\frac{1078.12}{7200})\\\\[/tex]
[tex]T_c[/tex] = 37.43 days
(d) Length of a production run (PRL):
[tex]PRL=n*(\frac{Q}{P})\\\\PRL=250*(\frac{1078.12}{25000})\\\\[/tex]
PRL = 10.78 days
(e) Maximum inventory ([tex]I_{max}[/tex]):
[tex]I_{max} = (1-\frac{D}{P})*Q\\\\I_{max} = (1-\frac{7200}{25000})*1078.12[/tex]
[tex]I_{max}[/tex] = 767.62 copies
(f) Total annual cost (TAC):
TAC = Annual holding cost + Annual setup cost -------------------- (1)
where,
Annual holding cost = [tex](\frac{1}{2})*I_{max}*H\\\\[/tex]
Annual holding cost = [tex](\frac{1}{2})*767.62*2.61\\\\[/tex]
Annual holding cost = $1001.74
and,
Annual setup cost = [tex](\frac{D}{Q})*S\\\\[/tex]
Annual setup cost = [tex](\frac{7200}{1078.12})*150\\\\[/tex]
Annual setup cost = $1,001.74
Equation (1) will become,
TAC = $1,001.74 + $1,001.74
TAC = $2,003.48
(g) Reorder point (R):
[tex]R = (\frac{D}{n})*L\\\\R = (\frac{7200}{250})*15\\\\[/tex]
R = 432 copies
