FACULTY REQUIREMENTS PLANNING AND COURSE CYCLING INPART-TIME, ONLINE DEGREE PROGRAMS

Many universities are moving toward the offering of part-time, online degree programs particularly at the graduate level. Typically the dean or another administrator is responsible for devising a course cycling plan along with adequate supporting faculty resources that enables students to progress and graduate within a reasonable and expected span of time. This problem is difficult to resolve due to uncertainty of demand for specific courses contained in the program. For example: (i) the program may be delivered with flexibility in time-to-completion, meaning that students are not assigned at admission to a specific cohort that proceeds in lockstep fashion toward graduation; (ii) the curriculum may contain elective courses which inject an element of choice; (iii) some courses may require the completion of other courses as prerequisites creating demand dependencies; and (iv) not every matriculated student successfully completes the program, and empirically observed retention rates will need to be factored in. Here we propose an approach for planning faculty requirements and course offerings that meets student flow and other constraints. The methodology combines linear programming with well-known operations management concepts such as material requirements planning and flow analysis.


INTRODUCTION
Many universities are moving toward the offering of part-time, online degree programs particularly at the graduate level (e.g. online MBA programs). Such programs simultaneously offer challenges and opportunities for administrators in the planning and offering of an appropriate mix of courses each term along with a sufficient number of course sections. The aim is to ensure that student progress toward graduation is not impeded while also meeting constraints on institutional resources such as available faculty. When part-time degree programs are focused on flexibility and convenience, they tend not to be cohort-based. In such environments, it becomes difficult to predict actual enrollments on a term-by-term basis since students can stop out and resume at will. Other general challenges in academic planning that also apply to part time, online degree programs are: course prerequisites (which create demand dependencies), elective courses (with inconsistent and variable demand), and remedial courses (which may be required of some, but not all, admitted students). On the flip side however, the fact that these programs are offered in an asynchronous and online delivery mode mean that some of the usual constraints (classroom capacity, room and/or faculty time conflicts) that make such problems notoriously difficult to solve do not apply. In some sense, even geography is not a constraint since remote adjunct faculty could be tapped to teach online sections as long as any accrediting agency guideline on the ratio of part-time to full-time faculty is not exceeded.
Several distinct methodological approaches have been proposed in the literature to address academic course planning and the efficient utilization of resources in higher education. Johnes (2015) recently provided a review of operations research applications to the field of education in a broad range of areas including planning and allocation of resources. The prediction of student flow, a key concern in the literature, was addressed using Markov analysis in Bessent and Bessent (1980) and Kwak, Brown, and Schiederjans (1986). An alternative approach used simulation methodology (see e.g. Boronico (2000), Saltzman and Roeder (2012)). Plotnicki and Garfinkel (1986) describe a simulation approach to maximize student flow (or minimize student flow time) subject to staffing constraints. Operations management concepts such as the celebrated Little's Law was applied by Litteral and Walk (2010) to predict persistence to graduation, student productivity, and program growth trends. Another wellknown technique from operations management, MRP (Material Requirements Planning) was adapted to higher education planning by Cox and Jesse Jr. (1981).
In this paper, we propose a modeling approach to determine faculty requirements and course offering frequencies that meets student flow and other constraints. The approach merges linear programming with MRP and flow analysis. Our methodology is most closely related to that of Cox and Jesse. Jr (1981) but differs from their approach in at least three key respects: (i) linear programming is used to perform the MRP explosion calculus; (ii) empirical attrition rates are incorporated to account for losses in student flow; and (iii) elective course requirements are time-phased based on both predicted graduation counts as well as course cycling patterns.

A LINEAR PROGRAM FOR MATERIALREQUIREMEN TS PLANNING
Material Requirements Planning (Orlicky, 1975) is a production scheduling and material planning technique widely used in industry to derive time-phased production schedules for dependent-demand items (lower-level assemblies and raw materials) based on demand forecasts for the finished goods. This differs from other approaches such as reorder point planning and consumption-based planning which do not taken into consideration either demand forecasts for the finished good, or the dependencies between the items constituting the bill of materials. MRP attempts to minimize inventory costs by producing at the latest possible point in time (backward scheduling). Other features of the MRP calculus (Vollmanet al., 2005) include: the netting out of any existing inventories (gross-to-net explosion) and accounting for component manufacturing times (lead time offsetting). When lot-for-lot ordering is used

A METHODOLOGY FOR PLANNING COURSE OFFERINGS
Our approach for course cycle planning modifies the generic MRP model above to 43 account for student attrition rates as well as the presence of elective courses (similar to customer "options" in a manufacturing bill of materials). The methodology is described here using the example of a part-time, online MBA program that was being offered at a small, private university in the Northeast region of USA. The12-course program consisted of four "components": an initial cornerstone course, a core component, an elective component, and a final capstone course. All students began with thecornerstone course which introduces students to the triplethemes of corporate responsibility, social justice, and environmental sustainability,setting the stage for the subsequent coursework. Following this, the students moved into the core portion of the program which consisted of seven courses, one each from the standard b u s i n e s s d i s c i p l i n e s ( a c c o u n t i n g , o p e r a t i o n s , i n f o r m a t i o n s y s t e m s , management, marketing, economics, and finance). On completion of the core, students couldopt for a specialization by completing three elective courses, all taken from the same focus area. Six areas were available: accounting, enterprise resource planning, healthcare management, human resources, international business, and operations management. A seventh option, called "general", applies when a student chooses not to specialize, but mixes and matches elective courses from across disciplines. Thus there was a total of seven degree paths (the general and six specializations) to choose from. Finally all were required to take a capstone class in business policy to complete requirements for the degree. A schematic is given in Figure  3.1.