IOE 202: Operations Modeling WELCOME! Lecture 1 outline:

Transcription

1 IOE 202: Operations Modeling WELCOME! Lecture 1 outline: Logistics of the course Microsoft Excel spreadsheets (and Office) Introduction to (mathematical) operations modeling First example: Economic Order Quantity model IOE 202: Operations Modeling, Fall 2009 Page 1 Logistics of the course Instructors: Marina Epelman, mepelman@umich.edu Inderbir Dhillon, idhillon@umich.edu Chate Eamrungroj, chateae@umich.edu Web page: Schedule, readings, handouts, due dates, assignments, downloads, grades, etc. IOE 202: Operations Modeling, Fall 2009 Page 2

2 Course components Lecures: two-hour lectures with a 5 10-minute break approximately in the middle. Homework: four homework assignments to be done individually. Total worth 30% of the grade. Each homework will have: A write-up component to be submitted in class (we STRONGLY suggest you type these up, e.g., in MS Word) An Excel spreadsheet to be submitted through CTools by 10 am on the due date Group project: due at the end of the term, worth 10% of the grade. Exams: two two-hour exams, worth 30% of the grade each. Exam times: Exam I on Thursday, 11/19/09, 7:00 9:00 PM; Exam II on Friday, 12/18/09, 1:30 3:30 PM. IOE 202: Operations Modeling, Fall 2009 Page 3 Course Logistics Read the syllabus carefully, clear up any misunderstandings right away Honor code: all students are expected to be familiar with the Engineering Honor Code and are bound by its requirements. This includes following the individual work guidelines for the assignments and exams Lecture notes for the upcoming class will be uploaded the day before print them out and bring them to class There are 3 or 4 sets of office hours each week use them! Most of the material in the course is cumulative, so if any questions, problems or concerns arise, it is better to address them sooner rather than later! IOE 202: Operations Modeling, Fall 2009 Page 4

3 THE FLU!!!!! Two main points: If you think you have the flu, stay home and avoid contact with others Notify your professors right away, find out how you can keep up with courses from home, if you are up for it In this course, you can: Watch lectures on video the next day Obtain all handouts electronically With prior permission of instructors, submit entire homework electronically if you are absent due to illness You might also have to tolerate one of two lectures by podcast if Prof. Epelman gets ill Presenteeism hurts you and other members of our community Absenteeism could be an Honor Code violation IOE 202: Operations Modeling, Fall 2009 Page 5 Brief overview of Excel capabilities We will often use Excel to: Summarize the input data for our models Use formulas to express relationships between inputs and outputs of the models Use built-in algorithms to perform sophisticated analysis of complex models We will not make use of all the sophisticated tools described in textbooks! But we will learn some of them, as each of them becomes relevant to the types of models we are studying. IOE 202: Operations Modeling, Fall 2009 Page 6

4 Warning to Mac users: Microsoft Office 2008 for Mac does not have Excel capabilities we will need in this course! Your options: 1. Install Office 2004 (or just Excel and Office Tools) on your Mac and use it for this course. 2. If you are running Windows on your Mac, install any recent version of Excel for Windows 3. Use CAEN (or any other) computer labs; make sure you keep copies of all your files IOE 202: Operations Modeling, Fall 2009 Page 7 Spreadsheet guidelines Lay out your data in a logical, self-explanatory form Use different fonts or colors to separate and group different components of the spreadsheet (but do not overwhelm the reader!) If appropriate, separate the data across different sheets of one workbook, to avoid clutter Use text to list assumptions, explain formulas, etc. Use common sense. Imagine showing and explaining the workings and information in your spreadsheet to someone else! We will post spreadsheets used in classroom presentations on the web. IOE 202: Operations Modeling, Fall 2009 Page 8

5 IOE 202: Operations Modeling Topic of the course: Mathematical models of operational decisions and basic tools for solving the resulting models. We will discuss examples of optimization models (linear and integer), inventory models, models of problems involving uncertainty, such as queueing, etc. IOE 202: Operations Modeling, Fall 2009 Page 9 Operational decisions helped by mathematical models Allocation of phone operators for 911 call centers to make sure emergency calls are answered in a timely manner Providing minimal-time (or shortest-distance) driving directions on-line (Mapquest or Google Maps) or in-car (Garmin or TomTom GPS), incorporating real-time traffic information Companies with production facilities world-wide need to decide where to store spare parts for the production, and in what quantities, to minimize the overall cost of production, transporation, and storage Yield management models help airlines set ticket prices and sell customers tickets at close to the maximal price each of them is willing to pay Designing radiation therapy plans to improve treatment of cancer patients Scheduling games in sports leagues (e.g., MLB regular season) IOE 202: Operations Modeling, Fall 2009 Page 10

6 Some presentations at INFORMS What Foreclosed Homes Should a Municipality Purchase to Stabilize Vulnerable Neighborhoods? The large increase in residential mortgage foreclosures has hurt homeowners, renters and communities. In response, government and nonprofits have considered purchasing such properties for resale to stabilize affected neighborhoods. However, there are few guidelines by which this might be done. We present multi-criteria and optimization-based decision models for property acquisition and demonstrate significant tradeoffs between ease of use and social impact through testing with practitioners. 1 INstitute For Operations Research and Management Sciences IOE 202: Operations Modeling, Fall 2009 Page 11 Some presentations at INFORMS 2008 Dynamic Approach to the Dose Optimization in Radiotherapy We propose a novel treatment planning strategy that dynamically includes patients radiobiological responses. The dose delivery is thus optimized not only spatially as in IMRT but also temporally. Preliminary results for simplified scenarios will be presented. IOE 202: Operations Modeling, Fall 2009 Page 12

7 Some presentations at INFORMS 2008 Network Routing under Active Congestion Control: Theory and Practice We present formulations of network routing models that incorporate active congestion control and show each is NP-Hard. We next present iterative methods for solving these models and show that the resulting routing policies outperform the current routing policies in the backbone network of the Internet2 community. To conclude we generate a robust routing policy to handle network demand fluctuations. IOE 202: Operations Modeling, Fall 2009 Page 13 Some presentations at INFORMS 2004 How Many Games Should a Playoff Series Have? Suppose that two teams enter a playoff series such as the NBA Finals or the World Series. The goal of the series is to determine which of the two teams is better. How long should the series be in order to make the correct determination with a high, pre-specified probability? We formulate and discuss an indifference zone selection procedure to answer this question. IOE 202: Operations Modeling, Fall 2009 Page 14

8 Example: ordering cameras for a store CubicleMin office supply store sells 100 units of basic digital cameras per month (for $130 apiece), and the demand pattern throughout the year is very steady. The store always wants to have these cameras available for customers. The store wants to determine how often it should order cameras, when it should place orders, and how many cameras it should order in each shipment to maximize net profit from this line of cameras. The store orders its cameras from the manufacturer s regional warehouse, and it usually takes a week for the cameras to arrive after an order has been placed. The store pays the manufacturer $100 for each camera ordered. Each time an order is placed, an ordering cost of $35 is incurred. The physical storage cost is $10 per camera per year. IOE 202: Operations Modeling, Fall 2009 Page 15 Inventory Replenishment Problems The above example describes a situation in which one needs to decide how to maintain and replenish inventory (either by producing, or ordering items), i.e., when to order, and how much to order. These situations arise, and have important implications in Retail sales, Supply chain management, Multi-stage manufacturing processes planning, etc. IOE 202: Operations Modeling, Fall 2009 Page 16

9 Typical Costs in Inventory Problems/Models Ordering/setup cost: fixed cost incurred every time an order is placed or a batch is produced Unit purchasing/production cost: cost of each additional item ordered/produced (may include quantity discounts) Holding/storage cost: financial (opportunity cost of money tied up in inventory), cost of storage space, insurance, etc. Shortage/penalty cost: lost business, loss of goodwill, potential emergency orders, etc. Balancing act: Keep enough on hand, so that not to run out of products that customers demand, or the manufacturing process requires; also, consider the cost of ordering Keep as little as possible to minimize the storage cost, amount of money tied up in inventory, etc. IOE 202: Operations Modeling, Fall 2009 Page 17 Observations about the CubicleMin inventory problem Long-term problem, with Constant, known demand rate The price company charges for each unit of product is fixed Fixed ordering cost each time the product is ordered Fixed unit cost of purchasing the product from the manufacturer Constant, known lead time for delivery of the product No planned stockouts are allowed i.e., the company must never run out of inventory on purpose The annual holding cost is proportional to the average inventory on hand Number of units in inventory is always known to the manager (this is known as continuous review) IOE 202: Operations Modeling, Fall 2009 Page 18

10 Ideas towards building a model of the CubicleMin problem Idea: ordering batches of product of size Q every time the store is about to run out, with just enough time to let the order arrive when the inventory is depleted. (Why is this a reasonable approach?) Let us represent inventory level over time graphically... Note the cyclical pattern! The time between inventory replenishments ( cycle time ) depends on Q Due to the steady, cyclical nature of proposed solution, makes sense to look at profits per unit of time (e.g., annually, monthly, etc.) Model we are building referred to as the Economic Order Quantity (EOQ) or Economic Lot Sizing model. IOE 202: Operations Modeling, Fall 2009 Page 19 Inventory level vs. time IOE 202: Operations Modeling, Fall 2009 Page 20

11 Inputs and outputs of EOQ models a Explanation Demand per unit of time In CubicleMin problem: L Lead time K Setup cost for ordering one batch c Cost for purchasing one unit h Holding cost per unit per unit of time held Q Order Quantity (batch size) TBD Time between orders TBD T (Q) Cost per unit of time TBD Note: sales revenue does not depend on ordering policy, as long as we never run out of inventory. So, to maximize net profit, we simply need to minimize the cost of ordering and holding inventory. IOE 202: Operations Modeling, Fall 2009 Page 21 One ordering cycle: details Cycle length = Production/ordering cost per cycle = Holding cost per cycle = Total cost per cycle = IOE 202: Operations Modeling, Fall 2009 Page 22