Answer:
(a) 863.07 copies
(b) 7.99 runs per year
(c) 31.27 days
(d) 10.04 days
(e) 586.08 copies
(f) $1,810.61
(g) 414 copies
Explanation:
Given that ;
Annual demand (D) = 6,900 copies
Cost of the book (C) = $13
Holding cost (H) = 15% of cost of book
= 15% × $13
= $1.95
Set up cost (S) = $155
Annual production volume= 21,500 copies
Number of working days = 250
Lead time(L)= 15
Daily demand (d) = Annual demand ÷ Number of working days
= 6,900 ÷ 250
= 27.6 copies
Daily production (P) = Annual production ÷ Number of working days
= 21,500 ÷ 250
= 86 copies
(a) Minimum cost of production lot size
Q = √ 2×D×S/H × (1-d/p)
Q = √2×6,900×155/1.95 × (1-27.6/86)
Q = 863.07 copies
(b) Number of production runs
= Annual demand (D) ÷ Production quantity (Q)
= 6,900 ÷ 863.07
= 7.99 runs per year
(c) Cycle time = Production quantity (Q) ÷ Daily demand (D)
= 863.07 ÷ 27.6
= 31.27 days
(d) Length of a production run = Production quantity (Q) ÷ Daily production (P)
= 863.07 ÷ 86
= 10.04 days
(e) Maximum inventory (IMAX)
= Q × (1-d÷p)
= 863.07 × (1-27.6÷86)
= 586.08 copies.
(f) Total annual cost
= Annual holding cost + Annual set up cost
= [(Q÷2) × H × (1-d÷p)] + [(D÷Q) × S]
= [(863.07÷2)×1.95×(1-27.6÷86)] + [(6,900÷863.07)×155]
= 571.43 + 1,239.18
= $1,810.61
(g) Reorder point
= Daily demand × lead time
= 27.6 × 15
= 414 copies
