Question

The Ambrosia Bakery makes cakes for freezing and subsequent sale. The bakery, which operates 6 days a week, 50 weeks a year, can produce cakes at the rate of 100 cakes per day. The bakery sets up the cake-production operation and produces until a predetermined number (Q) have been produced. When not producing cakes, the bakery uses its personnel and facilities for producing other bakery items. The setup cost for a production run of cakes is $600. The cost of holding frozen cakes in storage is $10 per cake per year. The annual demand for frozen cakes, which is constant over time, is 6000 cakes. Determine the following:

1. Optimal production run quantity (Q)

2. Total annual inventory costs

3. Optimal number of production runs per year

4. Optimal cycle time (time between run starts)

5. Run length in working days

Answer 1

A = Annual Production Requirement = 6000 cakes

O = Production Setup cost / Production order = $ 600

C = Holding cost / cake/ annum= $ 10

Optimal Production run Quantity = Q = Economic Production Quantity:

Q=2AOC

= √(2*6000*600)/10

=848.528

Q ≈ 849 cakes

Optimal number of production runs per year (P) = A/Q

P = 6000/849 = 7.06 ≈ 7 production runs per year

2. Total Annual Inventory costs:

Total annual Holding Cost = (Q/2)*C = (849/2)*10 = $4245

Total Annual Setup cost = P*O = 7*600 = $4200

Total Annual Inventory cost = Total annual Holding Cost + Total Annual Setup cost

=4245 + 4200

Total Annual Inventory cost = $8445

Optimal cycle time (time between run starts)

Per day production capacity = 100 cakes

Therefore,

Run length in working days to produce one optimal production run (Q) total days required

= Q / Per day production capacity

= 849/100 = 8.49 days

Time taken to complete all production runs = 8.49 days * 7 production cycles = 59.43 days

Total weeks Ambrosia bakery operates = 50 weeks

Days per week the bakery operates = 6 days

Total no. of working days = 50*6 =300 days

Idle days = 300 – 59.43 = 240.57 days

1

Idle

2

Idle

3

Idle

4

Idle

5

Idle

6

Idle

7

Optimal cycle time (time between run starts) = Time between 2 production runs = 240.57 / 6 = 40 days

Therefore the answer can be summarized as:

1. Optimal production run quantity (Q) = 849 cakes
2. Total annual inventory costs = $8445
3. Optimal number of production runs per year = 7 production runs per year
4. Optimal cycle time (time between run starts) = 40 days
5. Run length in working days = 8.49 days