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A Lot-Sizing Case Study of a Socket Manufacturer

November 10, 2010 Leave a comment

One of my customers is meeting with the following problem: how to optimize production batch size during an upcoming national promotion that will greatly increase demand?

The end products are sets of sockets, each of which has a different diameter.

An important challenge is that demand is in “set” that include many different diameters but actual production is grouped by “sockets of the same diameter”.

This is because significant change-over time is required to setup the bottleneck forming machine for production of a given diameter. Such change-over time varies from 2-4 hours. In some cases it can take an entire shift. Therefore until now, they have grouped sockets of the same diameter by product batches. Such “lot-for-lot” production is simple to execute and minimizes the number of change-over required.

However, their business model has recently changed. Marketing is trying to conduct a national promotion on certain sets. Therefore the demand of a number of sets will be greatly increased. This creates a new problem for using “lot-for-lot” rules in production. If you focus on making 1 diameter before making the next one, then you will accumulate a lot of inventory before you can ship sets. The cost of holding inventory and the responsiveness to demand fluctuation will become a much significant problem than when demand is in smaller batches. Given that, should you divide the demand quantity into smaller batches and if so, how should you determine the size of which?

Assuming that each set has 5 pieces and each piece cost $10, we can calculate the following 2 cases with setup cost estimated at $100 and inventory holding cost for each piece estimated at $0.04 per day.

Case 1 (Divide 10,000 pieces of demand into 2 batches, each of which 5000 pieces)

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Day 8

Day 9

Day 10

Demand

0

0

0

0

0

5000

0

0

0

0

5000

Production Qty

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

Inventory

1000

2000

3000

4000

5000

1000

2000

3000

4000

5000

Setup cost

100

100

100

100

100

100

100

100

100

100

1000

Holding cost

40

80

120

160

200

40

80

120

160

200

1200

Total Cost

140

180

220

260

300

140

180

220

260

300

2200

Case 2 (Produce 10,000 as 1 batch)

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Day 8

Day 9

Day 10

Demand

0

0

0

0

0

0

0

0

0

0

10000

Production Qty

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

Inventory

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Setup cost

100

100

100

100

100

500

Holding cost

40

80

120

160

200

240

280

320

360

400

2200

Total Cost

40

180

120

260

200

340

280

420

360

500

2700

Notice that when taking both setup cost and inventory holding cost into considerations, it is actually cheaper to divide the demand into 2 batches (Case 1).

Note that there is 5 change-over required for gather 5 diameters of sockets for each set. Therefore the smaller batches of demand, the higher setup cost but at the same time inventory holding cost is reduced.

What happen if we further divide demand into smaller batches?

Case 3 (Divide 10,000 pieces of demand into 5 batches, each of which 2000 pieces)

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Day 8

Day 9

Day 10

Demand

0

0

2000

0

2000

0

2000

0

2000

0

2000

Production Qty

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

Inventory

1000

2000

1000

2000

1000

2000

1000

2000

1000

2000

Setup Cost

200

300

200

300

200

300

200

300

200

300

2500

Holding Cost

40

80

40

80

40

80

40

80

40

80

600

Total Cost

240

380

240

380

240

380

240

380

240

380

3100

Our analysis is showing that further reduction of batch size from Case 1 to Case 3 has increased the total cost.

Therefore, under the given conditions, the optimal demand batch size exist somewhere between 2000 and 10,000.

How to determine the optimal batch size? At first glance, this may seem like a case that requires dynamic lot-sizing procedure of Wagner-Whitin or the like because demand is not constant. However, this problem actually can be simplified and hence solved in a similar way to EOQ calculation.

Without gong into the detail of the derivation of the formula, I will just give the results:

Therefore the optimal demand batch size is 10000/2=5000 which is case 1 and the total cost is about 18% lower than “lot-for-lot” production of case 2.

On the other hand, it is important to further reduce setup time in order to reduce overall cost and improve demand responsiveness. For example, if S is reduced from 500 to 100, N can be calculated to 4.47≈5 and hence a demand batch of 2000 with a total cost 30% of the original total cost of case 3.

From this calculation, we learn that :