The author has direct experience using the case in an MBA required course in Managerial Decision Making (aka, Management Science). The course primarily helps to develop modeling and analysis capabilities using a spreadsheet environment. Core topics include problem framing and base case modeling, sensitivity analysis, optimization (mostly linear programming), Monte-Carlo simulation, and a brief treatment of regression.
Students in the course tend to be focused on using a model to get the solution to a problem, and to perform sensitivity analysis, rather than aspects of the methodology of algorithms.
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To utilize this problem in the MBA course, the author provides the background material presented in Case A, and a spreadsheet template for the hike selection portion of the problem. Problem data is also supplied electronically. The spreadsheet template provides the key structure for the hike selection portion of the problem. Cases A and B are then assigned as a single unit. It has been helpful to allocate 10-15 minutes of class time to introduce the concept of the case, the structure of the problem, and to mention some real- world applications of vehicle routing and scheduling problems. Typically this is a group assignment, where one or more groups will present their approach and findings as a basis for further discussion.
With this guidance, student groups are able to develop a spreadsheet model to help select the hikes, and a Solver optimization model to minimize hiking time subject to the constraints of visiting each peak at least once. After students have identified the hikes to perform, they are usually able to build a second optimization model that sequences those specific hikes in order to minimize total vehicle distance. Prior to this, the author presents an example of a Traveling Salesman Problem in class, solved using the Evolutionary Algorithm in Solver. The most challenging part of the hike sequencing model is typically figuring out how to look up the correct distances in the driving distance matrix, so that regardless of the sequence of hikes, the correct vehicle distance is computed. To do this, perhaps the easiest way is to transform the parking node distance matrix to a hike-to-hike vehicle distance matrix (i.e., Figure 9). In this assignment, there is not an expectation to try to automate the connection between the results of the two optimization models. This means that the fairly complex formula discussed in Section 3.3 to extract the Hike_ID values of the selected hikes is not needed. Nor is any VBA code required. The second optimization problem, sequencing the hikes, is usually specific to the hikes chosen in the first optimization problem (a few groups may try to resolve this issue, with varying levels of success). This makes the assignment feasible for most MBA students, especially when they work in teams. The assignment could also be made for undergraduate business students in a course covering prescriptive analytics. The spreadsheet template file provided to the students is available upon request from the author. It is primarily a data file (all formulas, Solver settings, and VBA code are removed). But the hike selection sheet contains the binary mapping between hikes and peaks, which tends to help students get started on the right track.
Suggestions for use in other academic courses follow.
Prescriptive Analytics Course (undergraduate/masters). In this type of course, the cases can be assigned similarly as the MBA course, but without providing the spreadsheet template, which greatly helps students to structure the problem (alternately, electronic data can be provided, but without the binary mapping of hikes to peaks). Case A and
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Case B could be used sequentially, so there can be discussion of the Case A work before moving on to Case B, and so students focus on problem structuring (i.e., modeling) before they worry too much about the actual optimization. The structuring of the data of the problem is essentially the core aspect of modeling the problem. Requiring students to do this without the assistance of the binary hike-to-peak mapping makes the problem much more challenging. After Case A has been completed and discussed, Case B would be assigned. The instructor can choose, depending on the background and capabilities of the students, whether to assign the hike sequencing portion as a manual setup from the results of hike selection, or to expect the selected hike ID values to populate the hike sequencing model.
Operations Research/Industrial Engineering/Applied Mathematics (undergraduate/masters). In a course where students have a stronger mathematical
foundation, Cases A and B could be assigned with two primary outputs in mind: a) formulation of the optimization problem (or problems, if the instructor wishes to explicitly separate the selection and the sequencing problems from the start); and b) spreadsheet tool that implements hike selection and hike sequencing in two phases.
Students would be challenged to automatically populate the hike sequencing model with the selected hikes from the hike selection model. If students have knowledge of VBA (or capability to figure enough out on their own), the instructor could make VBA aspects a challenge assignment (or make a Case C), that asks students to use VBA to build and solve the Solver models. An additional expectation could be that students identify the pros and cons of a simultaneous versus sequential solution approach.
Operations Research/Industrial Engineering/Applied Mathematics (masters/doctorate).
At this level, Cases A and B should probably be assigned simultaneously, with limited guidance. There should be an expectation of a mathematical model specification, solution procedure designed, and solution procedure implemented. There is room for innovation and stretching beyond what is presented in this paper. For example, solving the problem as an explicit dual-objective mathematical program with weights on the objective is much more challenging than the spreadsheet solution presented in this paper, and might lead to a possible conference or journal paper. Also, designing hikes as part of the solution process (versus pre-specifying the possible hikes) is an aspect that makes the problem much more difficult. This can be used to drive ideas for further research in vehicle routing problems in general.
Any of the above classes. Using VBA to automate some of the solution process can be demonstrated fairly easily. If students have no knowledge of VBA, a quick macro recording for some simple task (e.g., cell formatting or copying), followed by viewing the code generated, would be a good lead-in. The Solver add-in comes with a number of VBA
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procedures/functions, which are well-documented online (Microsoft, 2020). Depending on the background and interest level of students, the instructor can show how to use VBA to automate Solver, or can add that expectation to the case assignment. If students do not have prior experience with VBA, it is suggested the instructor first demonstrate VBA/Solver with a different example, say a linear programming problem that has already been covered previously in the course. The VBA code used on the Model_Sequence sheet to randomize the hike sequence, and to run Solver multiple times for different initial solutions, is somewhat more complex. If students have some background in computer programming, there is nothing conceptually difficult about the code, and it can offer a good opportunity to discuss the pros and cons of using a worksheet of the model to store intermediate calculations as the code runs (e.g., the Index_Randomizer sheet is used to compute a randomly generated starting sequence of hikes).