Winter_IE6315(HW3)_2024_SS

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Apr 3, 2024

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WSU – Industrial and Systems Engineering ISE 6315 Production Systems Instructor: Jeremy L. Rickli Assignment #3: News Vendor, Basestock, (Q,r) Department of Industrial and Systems Engineering Wayne State University Teams: Teams of two (maximum – no teams great than two allowed) Points: 10 points possible Deliverables: Homework Submission in PDF format (submitted to Canvas – Lastname(s)_HW1.pdf). Write all equations and derivations in Word using equation editor for one extra point (use this assignment file as a template for font size and formatting). 1. (5) Slaq Computer Company manufactures notebook computers. The economic lifetime of a particular model is only four to six months, which means that Slaq has very little time to make adjustments in production capacity and supplier contracts over the production run. For a soon- to-be-introduced notebook, Slaq must negotiate a contract with a supplier of motherboards. Because supplier capacity is tight, this contract will specify the number of motherboards in advance of the start of the production run. At the time of contract negotiation, Slaq has forecasted that demand for the new notebook is normally distributed with a mean of 10,000 units and a standard deviation of 3,500 units. The net profit from a notebook sale is $650 (note that this already includes the cost of the motherboard, as well as all other material, production, and shipping costs). Motherboards cost $250 and have no salvage value (i.e., if they are not used for this particular model of notebook, they will have to be written off) – (Chapter 2 - #11). a. (5) Use the news vendor model to compute the optimal order quantity of motherboards that balances the cost of lost sales and the cost of excess material. b. (5) Now assume that the distribution follows an exponential distribution with a mean of 0.0001. What is the optimal order quantity now? Mean(μ) = 10000 units Standard Deviation(σ) = 3500 unit Shortage Cost (C s ) = 650 Overage cost (C o ) = 250 Now, G(Q) would be 𝐺(𝑄) = 𝑐 𝑠 𝑐 𝑜 + 𝑐 𝑠 𝐺(𝑄) = 650 650 + 250 = 0.72 By using Standard table (z-value table) to find (0.58) = 0.72 Hence, z = 0.58 and Quantity (Q*) = Mean(μ) + Z * Standard Deviation ( σ) = 10000 + 0.58*3500 = 12,030 units (answers may vary based on rounding or table used for z value)
WSU – Industrial and Systems Engineering ISE 6315 Production Systems Instructor: Jeremy L. Rickli a. (5) Comment on the appropriateness of the news vendor model for this capacity planning situation. What factors are not considered that might be important? F 𝐺(𝑄) = 1 − 𝑒 −𝑄 ∗ 10000 = 𝑐 𝑠 𝑐 𝑜 + 𝑐 𝑠 1 − 𝑒 −𝑄 ∗ 10000 = 0.72 ln 𝑒 −𝑄 ∗ 10000 = 0.28 𝑄 ∗ = −10000 ∗ ln 0.28 𝑄 ∗ = 12730 2. Consider that a manufacturer has an inventory of two replacement parts for two pieces of equipment that often fails. Part 1 costs $175 and has demand of 8 per month. Part 2 costs $20 and has demand of 25 per month (a month is 30 days). The lead time for Part 1 is 30 days and for Part 2 is 15 days. Answer the following questions below using this information. a. (2) Assume demand is Poisson distributed, what base stock is required for Part 1 and Part 2 so that a fill rate of 98% is achieved (show your table and submit your excel file for the Poisson distribution). Calculate the expected backorders and on-hand inventory for each part given this Q* values and a service level of 98% b. (3) Assume holding cost is 3% per month and order costs are $5. What is the Q* using EOQ for each part? Is there a difference in the expected backorder level and on-hand inventory? If different, explain. c. (4) Assume backorder cost per unit per month is $10, recalculate reorder points. Now, using Q values from part b compare average on-hand inventory and backorder level. d. (1) Explain how you would modify the model(s) if lead time is variable. A.
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