Indian Institute of Management, Indore
Operations Management II
Sarah is facing with few issues on which certain decisions have to be taken. She gathered some data and this data needs to be analysed to arrive at optimum solutions to different problems. For each of the key issues our calculations and recommendations have been given below.
Inexpensive part:
Product: Resistor - #4915082 Lead time is 2 weeks
Cost of the part P = $0.12 Annual demand D = 60,000 units
The average demand, the variation in the demand and the standard deviation are given below: Probability (1) Quantity Variation (2) (1) x (2)2
0.5 0.5 2400 -354 62658 0.5 x 0.5 0.25 2900 146 5329 0.5 x 0.25 0.125 3150 396 19602 0.5 x 0.15 0.075 3400 646 31298.7 0.5 x 0.10 0.05 3600 846 35785.8 Variance 154673.5 Total 2754 Std. Deviation 393 EOQ Q* = sqrt(2DC0/CH) Q* = 6325 units
We have considered a 95% confidence interval. Z = 1.65 R = d x T + Z x sqrt(T) x Std. Dev
R = 3317 units
Safety Stock = 917 units
Hence the firm should procure the resistor in lots of 6325. It should maintain a safety stock of 917 units to take care of the variations in the demand.
But it is given that the resistor is an inexpensive part which is a commodity item and hence there is no harm in having excess inventory of the part.
So the maximum demand for the part in the lead time is 3600 units and we can procure the units in lots of 3600 units and have the excess units as our inventory. Under this condition the order quantity is 6325 units but the reorder point would be 3600 units.
Make or Buy (Packaging)
Given data
Product: Wire strippers (#4569802) Annual demand: 1,000 units Item cost: $0.7/unit
Cost of buying the wrapping service: $0.4/unit Cost of in house wrapping:
$0.1 in direct material and labour $0.3 as amortization cost
Since the machinery is already purchased, the $0.3 amortization cost is incurred in both make or buy the cases. Hence this value should not be considered for decision making.
Hence the actual relevant cost for in house wrapping is $0.1+$40/1000 = $0.14
This is lesser than the cost of getting the wire strippers wrapped from outside. Therefore, for the wire strippers it is advised to perform the wrapping in house.
Quantity Discounts
Given data
Product: Connectors
Annual demand: 10,000 units
Here there are two options for procuring the parts
Option #1: From Supplier 1 using all-unit discount pricing structure Option #2: From Supplier 2 using incremental discount pricing structure Total cost = Q/2 x CH + D/Q x C0 + P x D
Q* = sqrt(2DC0/CH)
C0 = $10, CH = P/4, D = 10,000 Option #1:
Order Size Unit Price D C0 CH Q*
<= 100 5 10000 10 1.25 400
101-500 4.75 10000 10 1.1875 411
501-1000 4.5 10000 10 1.125 422
>1000 4 10000 10 1 448
For calculating the total cost we should also consider the cost saving obtained due to the discount provided. We consider three order quantities to evaluate the most optimum order quantity.
Order
quantity Total cost
Q1 411 47987
Q2 501 45481
Q3 1001 40600
Hence, in option #1 the economic order quantity is Q* = 1001 units since the total cost incurred is least in this case.
Option #2:
Sample EOQ calculation for order quantity between 100 and 500 Inventory cost = Q/2 x CH + D/Q x C0
Here CH = P/4 and here P is the weighted average of the 100 units @ $5 and (Q-100) units @ $4.75
Therefore, IC = Q/2 x [5x100+(Q-100)x4.75]/4Q + 10000/Q x 10 + 10000 x [5x100+(Q-100)x4.75]/Q Once you get it, differentiate, equate it to zero and obtain Q*= 767.77. This is not in the given range. We do similar calculation for the next interval too.
If we perform the similar calculation as above we find out that the cost incurred in option #2 are higher than $40600.
Several items ordered together: Overseas vs. Domestic
Overseas:
Cost per order = $10 Shipping cost = $400 Total order cost = $410
There are 3 parts and let they be P1, P2 & P3. Total no. of units = 1000+1000+500 = 2500
Average unit cost = [1000*10+1000*10+500*30]/2500 = $14
P1 P2 P3 Total
Annual Demand (units) 1,000 1,000 500 2,500
Unit Cost ($) 10 10 30 14
Variance / per week 100 100 81 96.2
Lead time (weeks) 6 6 6 6
A 95% confidence interval is assumed and based on the variance value given the safety stock is calculated
Safety stock 40.4 40.4 36.4
Order Qty / per order 306.1 306.1 153.1 765.3
Number of Orders 3.3 3.3 3.3
Annual Purchase Cost 10,000 10,000 15,000
Ordering Cost 535.7 535.7 267.9 1,339.30
Holding Cost 382.7 382.7 574 1,339.30
Total Cost 37,679
Domestic:
Cost per order = $10 Total order cost = $10
There are 3 parts and let they be P1, P2 & P3. Total no. of units = 1000+1000+500 = 2500
Average unit cost = [1000*11+1000*11+500*31]/2500 = $15
P1 P2 P3 Total
Annual Demand (units) 1,000 1,000 500 2,500
Unit Cost ($) 11 11 31 15
Variance / per week 100 100 81 96.2
Lead time (weeks) 1 1 1 1
A 95% confidence interval is assumed and based on the variance value given the safety stock is calculated
Safety stock 16.5 16.5 14.85
Order Qty / per order 46.4 46.4 23.2 116 Number of Orders 21.6 21.6 21.6
Annual Purchase Cost 11,000 11,000 15,500
Ordering Cost 86.21 86.21 43.1 215.5 Holding Cost 63.8 63.8 87 214.60
By comparing the cost incurred in the above two options it is advisable that the company orders these parts from the overseas partner. The difference is due to the huge demand for the product and relatively low inventory holding cost compared to ordering cost and the shipping cost.
There some more issues which Sarah is facing which need to be resolved.
Sarah wondered if Jay should consider a radical change in J&Gs mission. Were his goals realistic?
Jay wanted to develop J&G as a customer focused distributor offering very good service. He wanted to provide 100% commitment to customer satisfaction and promised that J&G would provide 95% of the items in the catalogue are always available while 92% are shipped the same day and 99% within 24 hours.
Sarah is right in her thinking that, there needs to be some amount of flexibility about the mission and the goals which Jay wants J&G to follow. Since currently the amount of variation in even inexpensive parts is too high (50% for a special resistor), this would mean that the current forecasting methods need to be improved. Moreover certain items which are currently being procured from overseas suppliers and need to be clubbed would lead to overstocking unless there is a similar correlation with the demand too.
Assuming J&Gs path would not change, how will she determine how much inventory J&G should have? How should she think about the tradeoff between the need for service with the need for lower inventory? How should she value the capital tied up in inventory? How can she measure the value of service?
Since currently the major problem which J&G is suffering is that its service levels are falling and it is not in a situation to acquire more capital. J&G should try to realize as much value as possible in the tied up inventory. They should take a stock of their current inventory and categorize the items as slow, medium and fast rate of turnover. Based on the rates they should craft a policy to reduce the inventory and hence procurement for slow moving items and release as much locked capital as possible. At the same time the inventory for fast moving items should be replenished regularly so that the high level of customer satisfaction can be maintained. Since there are a lot of competitors maintaining a wide range of items is necessary to maintain business, however if this puts too much burden on the financials then the company should identify certain key suppliers and OEM customers and focus their inventory procurement more towards serving these customers. The value of service can be identified from the amount of incremental repeat business which the company is able to garner based on earlier higher levels of service.
How can she hope to implement change when there are so many items to manage?
She can hope to implement change by categorizing the number of items into groups based on the frequency of turnover of the inventory and then clubbing them again based on the OEM customers and their order item patterns. Since the items generally follow a pattern based on the trends in the
PC sales, monitoring PC sales trends can also give a better idea of the type and fluctuation of items from the portfolio.
Should she approach the problem as one of operating at minimum cost? What if there is a budgetary limit on the inventory investment? How might that affect her approach to the problem?
She should approach the problem on optimizing her current costs and not straight dive to minimize costs. This is because the company’s focus needs to remain on giving high level of customer service so that they can compete effectively with the national suppliers and maintain their customer base. The process of cost optimization should begin on the procurement side where the idea of “sole sources” should be refined so that the suppliers provide items at a competitive cost to the company while maintaining the expected product standards. Procuring items from a particular supplier out of old relations will not be in the best interest of the company unless the items are being supplied provide a competitive edge to the company either in price or supply regularity.
A budgetary constraint will contain her abilities to provide high levels of service satisfaction to all the customers. The company will have to make a tradeoff between the customers it can let go in order to provide high level of service to others.
Should she keep the (Q.r.) policy framework ? Is it appropriate for all of the items? If not then what other realistic options are there?
Yes she should keep the (Q.r.) policy framework, however for certain items which have a lot of variation in the requirements over the weeks, instead of the (Q.r.) policy framework, the company should adopt a time based approach where, the inventory is checked periodically to maintain a certain level of quantity of the items at all times. An example for this would be the Special Resistor, J&G part number 4915082. The demand for this item varies more than the EOQ almost 50% of the times, however the upper limit of the demand is also known, so we can decide on a periodic ordering time when the inventory would be replenished on regular intervals. Moreover since there are no advantages of ordering the parts together to save shipping, the items can be ordered as frequently as required in a varying quantity if required.
