Question

1. A company has a production at a rate of 200 units per day. 80 units will be sold daily. The production will take place five days a week, 48 weeks a year. It usually takes a full day to get the machine ready for another production run, at a cost of $300. Inventory holding costs will be $10 a year. (calculate to2 decimal places)

a. What is the optional run size and lowest annual cost for carrying and setup?

b. What are the cycle time and run time for the optimal run quantity?

c. If the company wants to run another production for a new product between runs of this item, and needs a minimum of 10 days per cycle for the other work, will there be enough time?

Answer 1

a) Total Annual Demand = 80 * 5 * 48 = 19200 units

Daily production rate = 200 units

Daily consumption rate = 80 units

Setup Cost = $300

Inventory carrying cost = $10

Economic Batch Quantity (EBQ) = sqrt[(2 * Demand * Setup cost) / (Inventory carrying cost {1 - (daily conumption rate / daily production rate)})]

Economic Batch Quantity (EBQ) = sqrt [(2 * 19200* 300) / (10 * {1 - 80/200})]

Economic Batch Quantity (EBQ) = 1385.64 =~1386 units

Optimal run size = Economic Batch Quantity = 1386 units

Annual Cost of carrying = The total cost of storing inventory = (Economic Batch Quantity / 2) * Annual Inventory carrying cost * (1- {daily consumption rate / daily production rate})

Annual Cost of carrying =  (1386 / 2) * 10 * (1 - { 80 / 200})

Annual Cost of carrying = $4158

Total Setup Cost = Number of setups * Setup cost for one run

Number of setups = Annual Demand / Optimal Run Size

Number of setups = 19200 / 1386 = 13.86 =~14 runs

Total Setup Cost = Number of setups * Setup cost for one run

Total Setup Cost = 14 * 300

Total Setup Cost = $4200

b) Cycle Time = Optimal Run Size / daily consumption rate

Cycle Time = 1386 / 80

Cycle Time = 17.33 days

Run time = Optimal Run Size / daily production rate

Run Time = 1386 / 200

Run Time = 6.93 days

c) Time for which machine is available between 2 consecutive runs = Days between product runs - Setup Time

Days between production runs = Total number of days of operations / Total number of setups

Days between production runs = 48 * 5 / 13.86 = 17.32

Time for which machine is available between 2 consecutive runs = 17.32 - 1

Time for which machine is available between 2 consecutive runs = 16.32 days

Thus, the company can run another production for a new product between the production runs of the existing item given that it takes less than 16.32 days to complete the run for this new product.

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