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Many organizations staff their personnel according to a number of non-overlapping daily shifts. Manufacturing plants, hospitals, and banks usually have 2 or 3 shifts per day with prespecified durations and starting times. For example, a hospital might have 3 daily shifts, each 8 hours in length, with 8:00am, 4:00 pm, and midnight as the starting times. In this model, you need to fill these shifts at the lowest cost--which is to say, with minimal overstaffing.
Another consideration is that worker preferences for certain shifts should be satisfied as much as possible. In fact, these may be not only preferences, but requirements under union work agreements. This is a two-stage model for this specific situation.
Objective of Optimization FIXED 1:
The objective is to minimize staffing costs for a single shift. The model creates the minimum cost schedule based on daily requirement figures, average cost per employee category, and the work patterns. It chooses the best out of all work patterns that meet the staffing requirements. It also specifies how many people to schedule according to each work pattern and, if desired, how many 'pool' people to hire on a temporary basis to satisfy requirements.
Objective of Optimization FIXED 2:
The objective of this model is to maximize the cumulative preference of the group while assigning staff members to the minimum-cost work patterns selected in stage 1.