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IEOR 153 - Quiz 2 Practice Problems
Spring 2024
1. Four logistics hubs are each confronted with demands that are normally distributed, as follows: D1 ~ N(30, 25), D2 ~ N(25, 36), D3 ~ N(20, 16), and D4 ~ N(15, 9). Each hub incurs a holding charge of h = 2 per item. Unmet demands are lost with a penalty cost of p = 10 per item. Suppose that they all face one-shot demands thus make newsvendor type of stocking decisions.
(a) Determine the aggregated expected cost for a scenario where each hub operates independently.
(b) Assuming that demand fluctuations between the hubs are not related (ρij = 0 for all i,j ), compute the expected cost when the centralized system.
(c) Assume that ρ 12 = ρ34 = 0.5 while ρ 13 = ρ 14 = ρ23 = ρ24 = -0.5, and calculate the expected cost for this centralized system.
2. There are two potential distribution centers, where facility 1 has the fixed opening cost of $2, 000, and the facility 2 has the fixed opening cost of $1, 500. There are three potential customers to be served, with each has one unit of demand. The transportation costs for each customer are listed as follow:
• From Facility 1:
(a) To Customer A: $500
(b) To Customer B: $300
(c) To Customer C: $400.
• From Facility 2:
(a) To Customer A: $800
(b) To Customer B: $400
(c) To Customer C: $600.
(a) Please formulate this problem as UFLP, where the objective is to minimize the total cost (fixed opening and transportation costs), and the decision variables are the facilities to open and assignments of customers to facilities.
(b) Determine the optimal solution to this UFLP and report the optimal assignments.
3. Consider a joint inventory-location problem where there are two customer locations A and B in a line city with corrdinates A = (2, 0) and B = (5, 0). The demands per unit time at these two customer locations are IID distributed. Suppose that the supplier is located at S = (10, 0). The company is facing a choice between opening a warehouse at A or B to serve all customer demands. Calculate which location has lower total cost including facility cost, inbound transportation cost from the supplier to the warehouse, outbound transportation cost from the warehouse to the two customers, as well as the inventory and fixed ordering cost at the warehouse. You can assume that the fixed cost, inventory holding cost rate at the two locations are identical, lead time and fixed ordering cost from the supplier are proportional to distance. Similarly, inbound and outbound transportation costs are proportional to distance and volume transported. You can also assume that the firm gives you a required type-I service level α .