Optimization of Ski Resort Layouts Students: Nate Tharnish and Chris Recla Project Description. Our project in ENPM 641 focused on a ski resort chairlift as a system, with human actors as riders, operators, and ski patrol. The design optimized the lift for speed, efficiency, cost, etc while maintaining safety. The project, however, focused mainly on the functionality of a single lift. In ENPM 642, the design expands to optimize a small ski resort containing multiple chairlifts. The objective is to equally disperse skiers and riders around the resort, on both the Runs and lifts to prevent crowding and lengthy lift lines. Each Run is categorized under a specified difficulty level and each lift operates at a constant speed and capacity. Riders are assumed to move ata certain rate down the mountain depending on the difficulty level of the Run. The design is determined through analysis of flow what type and how many lifts best optimize the mountain. The optimization of the ski resort layout is expanded further in ENPM 643 through the use of full and fractional factorial design. The input parameters of each layout are observed to determine which parameter is most sensitive to the system response. For an existing mountain with a predetermined layout of lifts, a ski resort planner weighs the cost effectiveness of lifts with varying speed, number of seats per chair, and length to make each run. Rather than performing all possible experiments, this model provides a quick and accurate estimate to show which parameter has the greatest effect on increasing the lift and run capacity, which reduces the number of people waiting in the lift lines. What is Factorial Design? A full factorial design measures the system response of every possible combination of input variables and levels. These responses are analyzed to provide information about every main effect and interaction effect. Main effects of one independent variable are averaged across the levels of the other independent variables, revealing the sensitivity of the system response to each variable. The sensitivity of the interactions can also be calculated with a full factorial design. The interaction effects show how one independent variable depends upon the level of the other independent variables. A full factorial design is practical when few input variables are investigated. Testing all combinations of levels becomes too expensive and time-consuming with many variables. When many variables are investigated, fractional factorial designs are useful to produce nearly the same result as full factorial designs, but with fewer experiments. The ASQC (1983) Glossary & Tables for Statistical Quality Control defines fractional factorial design in the following way: "A factorial experiment in which only an adequately chosen fraction of the treatment combinations required for the complete factorial experiment is selected to be run" (10). All fractional factorial designs should be balanced and orthogonal to obtain the most accurate results because it eliminates correlation between the estimates of the main effects and interactions. Any suitably chosen fractional factorial design has columns that are all pair-wise orthogonal and sum to zero. Application of Factorial Design. When planning the layout of a ski resort, the optimal design for maximizing lift and run capacity is not obvious without a method of weighing different input variables. It is easy to come up with a system that simply gets people to thetop of a mountain and allows them to ski down, but it can be difficult to verify that it is done in the most efficient manner. By using factorial design, we are able to see how the parameters of the ski resort layout affect the overall capacity of the resort. The larger the capacity of a resort, the greater population it can accommodate. The information produced from this process is helpful in making decisions based on cost. When given multiple designs for a particular mountain, factorial design can help the resort planner budget money to maximize lift and run capacity while minimizing cost. For example, if high speed double lifts are less expensive than regular speed quad lifts, the planner may opt to implement a smaller chair size with a high-speed chairlift motor. Requirements and Assumptions. The main objective in optimizing a ski resort is to minimize the time waiting to board a lift. The model used to determine wait time has seven input variables: chair size, chair spacing, lift speed, lift length, difficulty of run, length of run, and resort population. In order to minimize wait time, lift and run capacity must be maximized. Of the seven variables, resort population has no effect on lift or run capacity, chair spacing is generally constant among all types of lifts, lifts generally stretch from the base to the summit, and difficulty of a run, which determines the average speed down a run, is a result of the pitch of its location on the mountain. The remaining three variables (chair size, lift speed, and length of run) were selected as controllable design parameters for a given mountain. Testing these three variables in a factorial design allows the resort planner to maximize total lift and run capacity, which will minimize the wait time for a given population, chair spacing, difficulty of run(s), and lift length. System Models and Experiments. 1 Lift, 1 Run (full factorial design)L1 S1Graphical representation of three variable (23) full factorial design Model used for calculation of yield for “Test 1” in the three variable (23) full factorial design The model above shows the total slope and lift capacity for the minimum value of each of three input parameters, labeled below as chair size, lift speed, and run length. The slope and lift capacity shown in red above is copied into the main effects calculation below for test 1. The input parameters are varied according to the chart below, where “1” represents the maximum value and “-1” represents the minimum value of each variable. The slope and lift capacity is recorded as the yield for each test.Main effects of three variable (23) full factorial design The next step is to determine the main effects and two and three factor interactions for each input variable. Each “1” and “-1” is multiplied by its corresponding yield and the resulting values are summed for each variable. The average of positive values in each column is