BA341 3rd EditionExam 3 Study guide Lectures 13-18Lecture 13 (October 15)Chapter 7(S)Break-even Analysis – a method of choosing among alternative layouts and process choices that relies on an analysis of cost/volume trade-offs. Seeks to find the production volume required tomake a profit on a certain process or piece of equipment. The point where Revenue = Cost. Go over all example problems in this lecture.- Single-Product BEP in units and dollarso Break-even demand = Fixed Costs/ (Unit Sale Price – Unit Variable Cost)o Break- even in dollars = Fixed Costs/(1-Unit Variable Cost/Unit Sale Price)- Go over the example of the single-product BEP approach to choose between alternatives, given a certain level of customer demand- Multi-product BEP in dollars, be able to find the sales/volume for a given product at BEoLecture 14 (October 20)QM A – Decision-Making ToolsDecision Trees (DT) – a graphical display of the decision process, indicating decision alternatives,states of nature and their probabilities, and outcomes/payoffs- Alternatives and States of Natureo Symbols used in DT Square – decision node from which different alternatives can be selected (decision point) Circle – state-of-nature (chance or uncertain) nodeo Example of how to read a DT A company seeks to introduce a new product family. This requires the construction of either a large or a small manufacturing plant. The market for the product can be either favorable or unfavorable. - Decision-making under Uncertainty - Assume a decision environment characterized by complete uncertainty (cannot assess probabilities of uncertain outcomes, e.g., introduction of a new, innovative product)o Identifying the best decision based on the following methods MaxiMax (Optimistic) – maximizes the maximum outcome for every alternative MaxiMin (Pessimistic) – maximizes the minimum outcome for every alternative  Equally likely – assumes that each state of nature is equally likely to occur;maximizes the average outcome for every alternative From the previous example of a DT we construct a payoff table - For Maximax approach: $200,000- For Maximin approach: 0- For Equally Likely approach: $40,000- Decision-making under Risk – assume that information on the probabilities of uncertain outcomes is available. Decisional alternatives can be assessed based on the expected monetary value (EMV).o How to compute the EMV: EMV (alternative i) = (payoff for 1st state of nature) x (probability 1st state of nature) + …+ (payoff for last state of nature) x (probabilitylast state of nature)o Identifying the best decision: Alternative with Max EMV is the besto Then all of the Decision-Making tools are put togetherLecture 15 (October 22)Conducted a DT example and went over the beginning of Managing Process Variability - The world is filled with uncertaintyLecture 16 (October 27) Module D – Waiting Line Analysis (queueing)M/M/1 Queueing System - Arrival Characteristicso Population: Infiniteo Pattern of Arrivals: Poisson distributed independent arrivals with ARRIVAL RATE (λ)- Queue Disciplineo Rule that determines the order in which arrivals are serviced: First-in first-out (FIFO), First-in-First-served (FIFS)o Customer Behavior: Wait until served- Service Characteristics o Single channel queueing system with one servero Independent service time with negative exponential distribution – SERVICE RATE (μ)- Note: λ <μM/M/1 (single-server) Queueing Systems- Inputs – arrival (λ) and service (μ) rateso Measured as jobs/time unit- Outputso Server utilization (p) = / arrival rate/service rate (probability that the server is idle = 1-) Lecture 17 (October 29)M/M/1 (single-server) Queueing Systemso average time in system (Ws), in queue (Wq), and in service (ts) – all these are measured in time unitsWs = Ls/ (Or Ws = 1/( - )  Wq = Ws -ts = Ws – 1/µ ts = 1/µo average number in system (Ls), in queue (Lq), and receiving service (i.e., ρ) – all these are measures in units, e.g., customers, jobs, parts, etc.Ls = /(1-) (Or Ls = /( - ))Lq = 2/[( - )] (Ls - Lq =  )o Probability of the server being busy (or idle)  = / o Probability that an arriving customer finds the system empty 1-pThere will be no questions on the test about multiple