Question

The production floor produces 8500 units/day and the associated direct-operated store sells 50 units/hour with the selling price at $120/unit. The direct-operated store operates 12 hours/day and 365 days/year, but the production works for 250 working days/year. Given that the production setup cost per production run is $1500 and the holding cost per year is $5/unit.

1. (a) Calculate the optimal batch size for each production run.

2. (b) What is the maximum inventory level with regard to the optimal batch size?

3. (c) How many production runs per year in that case?

4. (d) Estimate the time interval in production working days between the start of 2 consecutive production runs.

5. (e) How long will a production run last in working hours if the production works for 8 hours per working day?

Answer 1

Given data ceniks yeer Demand rate (R or D) = 600 x 365 = 219000 = 8500 X250 = 2125o00 inity Production rate (K) yer Setup cost (Cs) $1500 %3D holding $5 Cast (6) = = $ 120 selling price (P ) %3D a) Q* = obtimal batch size %3D 2KDCS (K-R) CC 2x6500x250)<1500 x219000 (2125000 -219000) x5 = 12103. 6

Q* = 12103.6 level = ToI.C at Qt marimum mventory (b) T.I.(]atar = Dcs+ c+ Dap I.C]ar Qt %3D x5+(219000x126) 12103-6 219000 x IS00.+ 12103.6 12103.6 xS+(리1900o시 20) 27140-6 + 1-1<]at a* = 2633 7399. 6 I production nung per year Ck), 8500 x 250 2125 000 unityear (d) Production ycle time 365 days >219000 t days 12103-6 365 x 12103. 6 219000 = 20-17 days

(e) if production works for 8 hours then K' = 8x250 = 2000 X8500 24 = 708333 Original production. rate (k) = 2125000 %3D last m production run %3D 2125000 - t08333.3 141666 6 67 units day
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