Problem 1: You are a purchasing manager in charge of stocking a certain type of transformer for a large electric utility. Weekly demand among your field crews for these transformers is normally distributed, with a mean of 100 and a standard deviation of 50. Holding costs are 25 percent, and you must hold a level of inventory corresponding to a cycle service level of 95 percent. You are faced with two suppliers, Reliable Components and value Electric that offer the following terms. Reliable sells the transformer for $5000 with a minimum order of 100, and a lead time of 1 week with a standard deviation of 0.1 week. Value sells the transformer for $4,800, has a minimum batch of 1,000, a lead time of 5 weeks, and a lead-time standard deviation of 4 weeks.
a. What is the annual cost of using Reliable components as a supplier?
b. What is the annual cost of using Value Electric as supplier?
c. Which supplier would you choose?
d. If you could use both suppliers, how would you structure your orders?
Problem 2: Consider a manufacturer selling DVDs to a retailer for $6 per DVD. The production cost of each DVD is $1 and the retailer prices each DVD at $10. Retail demand for DVDs is normally distributed, with a mean of 1,000 and standard deviation of 300. The manufacturer has offered the retailer a quantity flexibility contract with α = β = 0.2. The retailer places an order for 1,000 units. Assume that salvage value is zero for both the retailer and the manufacturer.
a. What is the expected profit for the retailer and manufacturer?
b. How much will profit increase for the retailer if α increases to 0.5?
c. How much will profit increase for the retailer if β increases to 0.5 (keeping α at 0.2)?
Problem 3: Stacks of paper arrive at a trimming process with interarrival times of EXPO (10); all time are in minutes and the first stack arrives at time 0. There are two trimmers, a primary and a secondary. All arrivals are sent to the primary trimmer. If the queue in front of the primary trimmer is shorter than five, the stack of paper enters that queue to wait to be trimmed by the primary trimmer, an operation of duration TRIA (9, 12, 15). If there are already five stacks in the primary queue, the stack is balked to the secondary trimmer (which has an infinite queue capacity) for trimming, of duration TRIA (17, 19, 22). Run your simulation for a single replication of 5,000 minutes. Collect information about cycle time, resource utilization, number in queue, and time in queue.