Final Exam Review
73-220 Lecture 23
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Agenda ●
Review of last class. – Economic order quantity (EOQ) model with quantity discount.
University policies re final exam. ● Review for final exam. ●
– Format and coverage of final exam. – Weight of final exam – Review of topics after midterm ●
Next Class
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Place and Time Date: Mon, December 11 ● Time: 12:00-15:00 ● Place: SD, Center 29-44 ● Similar seating plan will be adopted for final exam. As some students dropped the course after the midterm, please verify with the website for your new seat number. ● You are required to sign in during the exam and sign out after the exam. ●
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Policies Re Final Exam The following regulations will be strictly enforced at all final examination sessions: ● A valid student photo ID card is required. Students who do not present a valid photo ID card will be asked to leave the examination centre. ● No students will be permitted to leave the examination hall within the first 30 minutes. ● No student will be allowed to enter the examination hall after the first 30 minutes. ● Students are asked to arrive 15 to 20 minutes prior to the scheduled examination time. Doors of the St. Denis Centre examination hall will be opened approximately 10 minutes prior to the scheduled examination start time. ● Students having to go to the washroom after the first 30 minutes must raise their hand and be escorted by an invigilator. ● All regulations ensuring a high level of academic integrity at examinations will be strictly enforced. For more information, consult the university's Rules for Conduct of examinations.
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Format and Coverage ●
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One page single-sided-letter-sized aid sheet is allowed. Please do not write on the other side at any time during the exam, otherwise, it will be confiscated. Formulation (LP and IP), problem solving (LP sensitivity, PERT/CPM, inventory management). 6 to 8 questions in total. Cumulative, including both pre- and post-midterm materials. Lecture notes and assignments are a good starting point for final review. Excluding: graphical solution for two-variable LP models. Post- vs. Pre-midterm weights: – Roughly 60-70% vs 30-40%.
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Integer Programming ●
LP relaxation – Drop integer constraints, relax the IP model, solution tends to be better – For max: Z(LP) > Z(IP) – For min: Z(LP) < Z(IP)
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IP formulation – Similar to LP formulation, remember the integer requirement re DVs. – May have to introduce binary DVs.
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IP -- Binary Variables ●
Review the questions we discussed in class.
– Understand some typical ways to use binary DVs, e.g., fixed vs. variable cost; two-step decisions (set up or not and, then, how many units to produce or ship, etc).
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Typical binary constraints. – – – – – – – –
At least k out of n. At most k out of n. Exactly k out of n. If A then B, or equivalently, B if A (A
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PERT/CPM ●
PERT/CPM with known activity times. – Project network to describe the interrelationships among activities (immediate predecessors). – Know how to calculate ES and EF (move forward), LS and LF (move backward). – Develop activity schedule, and determine critical activities and critical path.
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PERT/CPM ●
PERT/CPM with uncertain activity times.
– Know how to calculate mean and variance of activity times (β distribution). – Use mean activity times to determine critical path. – Calculate the mean and standard deviation of the project completion time. Understand that the project completion time follows normal distribution. – Look up normal table to find probability of certain given project completion time. – Look up normal table to determine project completion time given a certain service level (probability that a deadline can be honoured).
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PERT/CPM: Time-Cost Trade-off ●
Use LP models to determine which activities should be crashed to minimize crashing cost. – Determine crashing cost per unit time for each activity. – Compute max possible reduction time. – Three groups of constraints: » Activity completion time (cannot start until its immediate predecessor(s) is (are) completed). » The overall project completion time should meet a shortened deadline (one vs multiple activities directly linked to the finish node). » Max reduction time.
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Inventory Management ●
Basic EOQ model – Record the EOQ model on your information sheet. – Note that the demand in the EOQ model is annual demand. – Understand cycle time, reorder point (in terms of inventory position or inventory on hand). – Aware of EOQ model’s important properties: robust, two costs considered, two costs are the same at EOQ.
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EOQ Model with Discount ● ● ●
Difference from the basic EOQ model. Three costs are considered here (ordering, holding, and purchase costs). Understand the procedures to determining optimal order quantity and minimal total cost. – Basis is the EOQ model, but we have to determine if a quantity is feasible or not. – Note also that the total cost is different from basic EOQ model as the purchase (or material) cost has to be considered. – Please go through the example given in class. – You may wish to work on Questions 20-22 in the textbook to practice how to solve EOQ model with quantity discounts.
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Next Class ●
Good luck for your final exam.
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Review some questions based on input from the class. You are more than welcome to contribute questions to our class discussions. If you have any specific questions for me to go through, please send me your questions by posting a message on the discussion board, by email or by phone at 3456.
YOU LEARN DECISION ANALYSIS BY DOING DECISION ANALYSIS!! 13