A toy manufacturer uses 48,000 rubber wheels per year for his popular dump truck series. The firm makes its own wheels which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup costs for a production run of wheels is $45. The firm operates 240 days per year. , Determine a) the optimum run size and b) minimum total annual cost for carrying and setup.
Answer:
Given data,
Annual demand (D) = 48000 wheels
Setup cost(S) = $45
Holding cost(H) = $1 per wheel per year
Daily production rate (p) = 800 per day
Daily demand rate (d) = Annual demand / Number of days in a year = 48000/240 = 200
a) Optimal run size (Q) = Sqrt of {2DS / H[1-(d/p)]}
= Sqrt of {(2 x 48000 x 45) / 1[1-(200/800)]}
= Sqrt of (4320000 / 0.75)
= Sqrt of 5760000
= 2400 wheels
b) Imax = (Q/p)(p-d) = (2400/800)(800-200) = 3 x 600 = 1800 wheels
Total annual cost for carrying and setup = Carrying cost + Setup cost
= [(Imax / 2)H] + [(D/Q)S]
= [(1800/2)1] + [(48000/2400)45]
= $900 + $900
= $1800
A toy manufacturer uses 48,000 rubber wheels per year for his popular dump truck series.
3) A toy manufacturer uses approximately 32,000 silicon chips annually. The chips are used at a steady rate during the 240 days a year that the plant operates. Annual holding cost is $5 per silicon chip. The optimal ordering quantity is 6030 chips per order. What is the total annual carrying cost under the optimal inventory management policy? Round to the nearest integer.