Comprehensive Solutions for Supply Chain Management Problems

This document provides detailed solutions to various supply chain management questions, focusing on economic order quantity (EOQ), total relevant cost (TRC) analysis, and creative thinking related to order quantity optimization. It includes a numerical analysis of MOQ impact, cost-price relationship, average flow time calculation for cycle inventory, and the effect of changing order quantities on annual ordering and carrying costs. The analysis uses EOQ models and considers scenarios with discounted prices, aiming to minimize total costs. Furthermore, it explores the application of EOQ shortage models, incorporating annual demand, ordering costs, and holding costs to determine optimal order quantities under different price conditions. The document concludes with a discussion of the assumptions underlying the EOQ model and provides references for further study. Desklib offers a wealth of similar solved assignments and past papers for students.

Question and answer
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Supply chain management

Question and answer
Contents
Solution_ Q 1...................................................................................................................................3
Solution_ Q 2...................................................................................................................................3
Solution_ Q 3...................................................................................................................................4
Solution_ Q 4...................................................................................................................................5
Solution_ Q 5...................................................................................................................................5
Solution_ Creative thinking_1.........................................................................................................5
Solution_ Creative thinking_2.........................................................................................................6
References........................................................................................................................................8
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Question and answer
Solution_ Q 1
As we can see that, the number of MOQ, which equalize the TRC cost at Regular price and
discounted price is 442 unit/order.
0 200 400 600 800 1000 1200
-40000
-30000
-20000
-10000
0
10000
20000
30000
40000
EOQ
T TRC- RC_
Figure 1-Graph of TRC and TRC_ differences
From the graph, the point at 442 unit is producing zero difference TRC and TRC_. In this this
condition, we can say that MOQ = 442 produces no change in overall cost of regular price and
discounted price.
The information is useful for seal point in such a way that, at regular price, the TRC is fixed but,
for discounted price, the TRC_ is going up, this data is useful for decision making to for regular
verses discounted option.
Solution_ Q 2
For any company, the cost of product is the direct cost for its operation, for this condition the
cost of product should be as minimum as possible.
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Question and answer
8.8 9 9.2 9.4 9.6 9.8 10
-5000
0
5000
10000
15000
20000
25000
30000
35000
3121530900
-161-304697841099141417292044
Prod ct Priceu
T TRC- RC_
Figure 2- Product per unit price for TRC
But to some extent it is not possible because, supplier is working for charity. In this condition, if
supplier insists on 1000 unit of MOQ, then the price should be as low as $ 9.649. In this
condition the TRC for regular as well as discounted price will be same.
Solution_ Q 3
The average flow time for cycle inventory is calculated as 17 days for regular price and 122 day
for discounted price. The means, we must purchase the lot, which will be consumed in 17 days.
This is as per EOQ model,
0 10 20 30 40 50 60 70 80 90 100
0
50
100
150
0
141.4 Order Received
Usage Rate
Reorder Point
Time Horizon
Quantity
Figure 3-average flow time Cycle inventory graph
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Question and answer
The average inventory cycle stock is 71 unit and number of orders per year is around 21.
Solution_ Q 4
For reducing order quantity, we must equalise the MOQ with EOQ, in this condition when order
quantity is reduced, we can that, the total TRC is going to increase marginally, this is due to
increase in order cost of the material. When ever we place order, the annual order cost is going to
increase and this result increase in TRC. At EOQ level ordering cost is $212, and when we
decrease the MOQ, say it 50 unit, it becomes $600.
Solution_ Q 5
Since my demand in fixed at 3000 and following EOQ model does not affect the MOQ for the
entire operation, in this condition, my option will go with reducing the unit price of the product.
We have seen earlier that reducing the unit price at $9.649. the regular and reducing price
becomes equal. In this condition, my target will be to keep the price below $9.649. This will
helpful in most of the time in future business.
Solution_ Creative thinking_1
Since we can see that, Actual order quantity is the cell reference for economic order quantity,
therefore by changing directly actual order quantity down effect on other annual result of the
given data. But if we change economic order quantity, then all data getting changes especially
annual ordering cost, annual holding cost. There no effect of annual purchasing cost on change
of data of order quantity.
40 60 80 100 120 140 160 180 200 220 240
0
100
200
300
400
500
600
700
Annual ordering cost Annual inventory carrying cost
Figure 4- Effect of change of order quantity
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Question and answer
From the graph we can see that, if we increase order quantity starting from 50 to 230, we can see
that, Annual order cost is decreasing, while annual inventory carrying cost is increasing linearly.
At cross point around 140. This is the best optimum order quantity where annual ordering cost
and carrying cost bot are equal and minimum for that condition. There is no change in Annual
purchase cost because it is directly related with annual demand of the data.
Solution_ Creative thinking_2
There is certain assumption, which is being done before choosing the basic economic order
modelling, for this given problem. The consideration of shortage is taken in to account for EOQ
model. But especially for this problem, we will model this problem as a EOQ shortage model.
As per data given in question,
Demand = 20000 sq ft, Annual demand = 20000 * 12 = 240,000 sq ft.
Ordering cost (S) = $ 400/order
Annual Holding cost (h) = 20%,
The price condition is given as
Cost of product (C) = $ 1 (Between 0 to 20000 sq ft)
Cost of product (C) = $ 0.98 (Between 20000 to 40000 sq ft)
Cost of product (C) = $ 0.96 (when more than 40000)
Fist I have to calculate Economic order quantity as per the given data
Economic order quantity (For $=1) Q = √ 2 DS
hC =
√ 2∗240000∗400
0.2 x 1 = 30983.86 sq ft
Similarly,
Economic order quantity (For $=0.98) Q = √ 2 DS
hC =
√ 2∗240000∗400
0.2 x 0.98 = 31293.43 sqft
Economic order quantity (For $=0.98) Q = √ 2 DS
hC =
√ 2∗240000∗400
0.2 x 0.96 = 31622.78 sq ft
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Question and answer
Since all the economic order quantity come between the range of 20,000 and 40000 sq ft. In
this condition we have to calculate the price range of 31298.43 and 40000 as shown in the
table.
Total c ost= D
order quantity xS + order quantity
2 x h x unit price+unit price XD
Therefore, total cost for 31298.43
¿ 240000
31298.43 x 400+ 31298.43
2 x 0.2 x 0.98+ 0.98 x 240000=$ 241334.50
Similarly for the case 40,000 sq ft
¿ 240000
40000 x 400+ 40000
2 x 0.2 x 0.96+0.96 x 240000=$ 236640
After calculation it was found that, order quantity 40000 sq ft is giving lower cost, therefore
order quantity = 40,000 sq ft.
Cycle inventory = lot ¿ ¿ 2=20000 sq ft ¿
If the discount is not given the order quantity (Price at $ 0.96)
Cycle inventory = 31622.78
2 =15811.39 sq ft
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Question and answer
References
David Alan Collier, J. R. (2012). Operations Management (2nd ed.). New York: Cengage
Learning.
Robert Jacobs, R. C. (2013). Operations and Supply Chain Management (14th ed.). New York:
McGraw-Hill Higher Education.
Steve Brown, J. R. (2013). Strategic Operations Management (3rd ed.). New York: Routledge.
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