Quantitative practice problems Supply Chain Management-case Exercise

 Quantitative practice problems Supply Chain Management 


Transportation 

HP produces printer components in the US and ships them for final assembly to Europe. The European plant is running at a fixed rate, and needs 7000 units of the component per week. The HP plant in the US produces JIT, and holds no inventory at the factory beyond what is being produced for a current order. The company needs 1 week to finish the production of these 7000 units, which are then shipped out immediately by sea transport. The transportation time takes usually 4 weeks, though delay can occur at the ports. Due to these time delays, the lead-time demand is variable, with a standard deviation of lead time demand being 3000 units, and the European plant holds enough inventory to cover such delays 99% of the time. 

Part (i): What is the total annual inventory holding cost of this supply chain, if the per unit holding cost is 50 Euro cents? (For simplicity, assume the same inventory holding costs at all stages of the supply chain.) 

Part (ii): HP is considering to switch to air transport. If you were a consultant to HP, which costs would you consider in this comparison? How (in which direction) would you expect these costs to change relative to the sea transportation case? (No calculations required.)

Location and lead time pooling 

A company has 50 regional distribution centers in Europe and sources a particular product sold at these outlets from an Asian supplier. The weekly demand at each regional distribution center (RDC) is normally distributed with mean = 100 and standard deviation = 30. All RDCs use a continuous review system with orders being placed with the Asian supplier on average every 2 weeks. The delivery lead time for shipments from Asia is 8 weeks. 

(1) What is the appropriate replenishment level at each RDC, if the RDCs want to guarantee a service level of 99%? What is the total safety stock held at all RDCs? The company is considering to replace the RDCs by one central distribution center (CDC). The CDC would continue to place orders on average every 2 weeks, and the delivery lead time from Asia will remain 8 weeks. 

(2) What is the weekly demand and standard deviation of weekly demand at the CDC, assuming the demands at the RDC are independently distributed?

 (3) What is the appropriate replenishment level, if the CDC wants to guarantee a service level of 99%? What is the safety stock at the CDC? (4) Compare solutions (1) and (3). What effect does the company benefit from? What other factors should the company consider before making a decision? Based on your response to 

(4) the company decided to consider an alternative option: Keep the RDCs and add a CDC. The lead time from the Asian supplier to the CDC remains unchanged. The delivery lead time from the CDC to the RDC is one week. Continue to assume a 99% service level both at the RDCs and CDC (and ignore the effect of a stockout at the CDC on the reorder point at the RDC). 

(5) What is the appropriate reorder point at the RDC? At the CDC? What is the total safety stock (at all RDCs and the CDC together)? What effect does the company benefit from in this case?

















































































































































Solution:

Transportation Part (i): The cycle inventory at each of the factories is Q/2; that is 2*7000/2=7000 in total. The US plant holds no safety stock; the European assembly plant has to hold safety stock, however, due to potential delivery delays: z_99%=2.33, safety stock = 2.33 * 3000= 6990 Finally, there is in transit-inventory: D*L=4*7000=28000. The total inventory level is 41,990 and the holding costs 41,990*0.5=Euro 20995 Part (ii) The first cost that changes is going to be the per unit transportation cost, which will tend to be more expensive by air than by sea. However, HP will save in inventory costs. Air-shipments can be done in smaller lot sizes, reducing the cycle inventory at both factories. In addition, they tend to be less variable reducing the safety stock needed. Finally, HP will for sure save inventory holding costs for intransit inventory, which is directly proportional to the lead time. Beyond these factors given in the question, there are a number of other costs that might change: the handling costs might differ, the required packaging might differ, resulting in different costs of labor and material; finally the import duties will change, since they are calculated including the transportation costs. (Would not expect all of these last point, but a recognition that other costs need to be considered should be there.) Location and lead time pooling 

Part 1: Reorder point = 8 * 100 + 2.326 * 30 * √8= 998 

Safety stock at one RDC = Reorder point – mean demand = 198 units 

Total safety stock = 198 * 50 = 9,900 units 


Part 2: Weekly mean demand = 50 * 100 = 5000; 

standard deviation of weekly demand= 30 * √50 = 212.132


 Part 3: Reorder point = 8 * 5000 + 2.326 * 212.132 * √(8) = 41,396 

Safety stock at CDC = Reorder point – mean demand = 1,396 units


 Part 4: The company has to invest in 8504 units less of safety stock. This is due to location pooling: Part of the uncertainty faced by the individual RDCs offsets each other when the inventory is pooled at the single CDC. Other factors to consider: E.g., changes in transportation cost (can be lower or higher, depending on increase local transportation costs versus international transportation cost savings); effect of being further removed from the customers.

Part 5: Reorder point at RDC = 100 + 2.326 * 30 = 169.8 

Safety stock at one RDC = Reorder point – mean demand = 69.8 

Total safety stock at RDCs = 69.8 * 50 = 3,490 units

 Reorder point at CDC = 41,396 (same as 3) 

Safety stock at CDC = 1,396 units (same as 3) 

Total safety stock = 4,886 units 

The company has to invest in 5014 units less of safety stock than in solution (1). This is due to lead time pooling. During the lead time from the Asian supplier the company does not have to decide where to ship the ordered units, but only has to fix a total quantity. Based on the demand observed during the lead time, the CDC can then allocate the orders to the individual RDCs better matching the supply with the actual demand. Since both the CDC and the RDC hold safety stock, lead time pooling is a lot less effective than location pooling, but has the benefit of lower local transportation costs and being close to the customer

 

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