SCM447: Logistics and Transportation Management Fall 2024 Homework 1 Due: October 1, 2024, 7pm 1. Why does a push-based supply chain react more slowly to changing demand than a pull- based system? (0.25 points) 2. WhiteGlove House Call Health provides a service where patients within predefined service areas can receive primary health care visits at home or at work, 365 days per year, 8 am to 8 pm. Suppose WhiteGlove guarantees same-day service to all patients requesting visits during operating hours. (0.5 points) (a) Describe an appropriate measure of the effectiveness of the WhiteGlove same-day service guarantee. (b) Describe two alternative measures of the efficiency of the WhiteGlove same-day service guaranted 3. A computer manufacturer ships partially assembled computers (hereafter called units from an assembly plant in Thailand to a distribution center in Oregon. We want to determine if'it is more economical to ship in 40ft containers by ocean carriers or in airline containers by air carriers. Shipment by ocean costs $11,000 per container, and a 40ft container can hold 5,000 units. Handling cost 1s $2000 per 40ft container. The journey by sea takes 20 days on average. Shipment by air costs $20,000 per container, and an airline container can hold 1,400 units. Handling cost is $1000 per airline container. The journey by air takes 2 days on average (door to door). The forecasted demand is 120,000 units for the next year, which is also the planned production quantity. No safety stock is kept at the assembly plant, and a shipment is sent to the distribution center as soon as a container is filled. Safety stock of 1,000 units is kept at the distribution center. A unit is valued at $600 at the assembly plant and $800 at the distribution center. The inventory holding cost rate is estimated at 20% of value per vear. The space cost is estimated as $30 / unitvear at the assembly plant and $40 /unit*vear at the distribution center. (3 points) (a) What are the annual inventory holding costs at the assembly plant (include the space and holding cost in this calculation)? (b) What are the annual inventory holding costs at the distribution center (include the spacecand holding cost in this calculation)? {c) What are the annual in-transit inventory costs for each mode? {d) What are the annual transportation costs for each mode (don't forget to take the shipment handling cost into consideration when calculating these costs)? (e) What are the total annual cost equations for each mode of transportation? (f) Assume that the shipper will always ship full loads. Determine the most cconomical transportation service to use in this case. (g) Now assume that the shipper may use less than full loads. Determine the most cconomical transportation service to use in this case. . How many arcs are included in a path that visits n nodes? (0.25 points) . Can a graph be connected if it includes exactly 5 nodes and exactly 3 arcs? Why or why not? (0.5 points) . The shortest path tree rooted at s for the graph depicted below includes the following arcs: #(s,A), (5,B), (A,C), (A,D), (D,t)}. Use this information to answer questions (a) through (d) below. (a) Using the format v(7)[pred(7)], give the minimum cost path label of cach node, as specified by the shortest path tree rooted as 5 described in the problem statement. To get you started, the label at node s 1s 0[0]. (1.5 points) (b) If the cost on arc (A,C) increases from 3 to 4, what labels must be re-examined to test whether the set of minimum cost path labels is still optimal? Only specify those arcs which must be examined, and justify your answer for each arc you list. (0.5 points) (c) If the cost on arc (A,B) increases from 2 to 3, what labels must be re-examined? Support your answer. (0.5 points) fu'i 2 = G 1 i 7 4 . % 2 6 t - v & 3 B i 5 I 3 = 7. Using an appropriate algorithm that we discussed in class, identify the minimum spanning tree on the network and draw the graph. Determine the total cost of the minimum spanning tree. The travel cost matrix is provided for your reference