OM-II

J&G Distributors – Solution to Final questionSubmitted to: Prof. A H Kalro

3/30/2009OM-IIGirish , Section C, 2008PGP076C

Question

The question is about the inventory control model for a mix of products. In the case Sarah has to create a inventory control model (Q,r) for a set of 3 products which J&G orders together from an overseas vendor. All these products are ordered at one time (bundled order) and the current method of determining the order quantity of each is based on , EOQ-inventory at hand.

The overall order cost for a single order is $ 410 (Paper costs+ cost of shipment). The products A, B &C cost $10,$10 and $30 respectively. The lead time for the order is given as 6 weeks and the annual demand for these products is 1000, 1000, 500 respectively.

Sarah has to design a (Q,r) model for these products and has to compare with that of a local vendor who does not charge shipment cost but charges $1 extra on each product.

Solution

The current method of inventory order system is not optimal. The reason is that the number of orders done is not known. The order is only filled till the EOQ level, which means a standard quantity is not ordered.

Solution steps and assumptions:

The (Q,r) model should have a single EOQ, for the bundle of products. However, the ratio of the quantity of each product (A/B/C) in the EOQ should be the same as ratio of the total quantity demanded.

The EOQ is determined using the equivalent cost of each unit in the total demand of 2500 units (sum of all demands). Calculated using total cost purchase divided by total quantity demanded.

Once the EOQ is calculated the figure is rounded off to attain an integer value for the mix of products in the EOQ quantity.

The cost is calculated using the EOQ However, the reorder points, which is dependent on the buffer value of each products

will be different It is calculated using the average demand per period, lead time and the standard

deviation of demand for each of the units The calculation is done similarly for the local vendor to arrive at the optimum value

of (Q,r) and cost for the local vendor

The following table summarizes the calculations involved:

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  Foreign Supplier   Domestic Supplier

Cost / per order ($) 410.00   10.00Product  A B C   A B C Annual Demand (units)

1,000.00

1,000.00

500.00

  1,000.00

1,000.00

500.00

Total Quantity Demanded (units)

2,500.00

  2,500.00

Unit Cost ($) 10.00

10.00

30.00

11.00

11.00

31.00

Equivalent Cost 14.00

  15.00

Variance / per week 100.00

100.00

81.00

  100.00

100.00

81.00

Lead time (weeks) 6.00

      1.00

   

Std Deviation 10.00

10.00

9.00

  10.00

10.00

9.00

Probability of not stocking out = 99% (assumed), z =

2.33

  2.33

Safety Stock 56.98

56.98

51.29

  23.26

23.26

20.94

Weekly Demand (assuming 52 weeks)

19.23

19.23

9.62

  19.23

19.23

9.62

Re-order Point 173 173 109 43 43 31

EOQ 765.32

  115.47

Rounded of EOQ 765.00 *

  115.00 *

Quantity of each product in EOQ

306.00

306.00

153.00

  46.00

46.00

23.00

Number of Orders/year 3.27

  21.74

Annual Purchase Cost 10,000

10,000

15,000

  11,000

11,000

15,500

Ordering Cost 1,339.87

  217.39

Holding Cost 382.50

382.50

573.75

  63.25

63.25

89.13

Total Cost 37,678.62

  37,933.02

* The rounding off of the EOQ has to be done to achieve integer quantities of each product in the total

quantity. As rounding down (765) is closer to actual EOQ than rounding up (770). The lower value has

been used.

From the above table Sarah should continue with the overseas vendor. The reorder quantity she should consider is 765 units (with 306 A units, 306 B units and 153 C units). Further, the reorder point is when one of A or B or C reaches its reorder points. That is, when A reaches 173, B reaches 173 or C reaches 109 units.

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