Are You Optimizing Your Workforce? Personnel scheduling often involves juggling issues such as constantly shifting staff level requirements, and complicated company and union work rules. Generating and assigning efficient schedules can be critical. Good schedules can mean lower payroll costs, improved customer service, and higher employee morale. It's a wonder some companies still try to manually schedule their workforce. Applying optimization methods to workforce scheduling problems is not a new idea. Almost 50 years ago the operations research pioneers Edie and Dantzig used linear programming to schedule staff at toll booths around Man-hattan to cut traffic delays. Since then, similar methods have been used in numerous areas including: a) the telephone industry to select work patterns for phone personnel in call centers, b) airline crews, c) nurses in hospitals, and d) labor force in factories.

The general form of these problems is that we have a collection of work objects (typically a 15 minute interval), which each have a requirement for the number of personnel on duty. Personnel are hired to work individually scheduled work patterns. A work a pattern covers one or more work objects. The difficulty is that only a limited number of work patterns are available. For example, a typical work pattern over a week is five days on, followed by two days off. At telephone call centers, a typical work pattern may be 8 hours consisting of the sequence: at least one hour of work, a 15 minute break, at least one hour of work, a half hour break, at least one hour of work, a 15 minute break, and at least one hour of work. In airline crew scheduling, the work objects are flights. These work patterns are limited by complicated rules regarding how many hours can be spent flying in a given interval of time such as a day.

A typical approach for solving these problems is to enumerate a candidate set of all possible interesting work patterns and then solve the optimization problem:

The candidate set may be modest in size (e.g., seven for weekly staffing where there are only seven ways of taking two days off in a row during a week) or rather large (e.g., over a million candidate work patterns in some airline crew scheduling problems). When the candidate set is large, these linear/integer programs can be quite difficult to solve, even by commercial optimizers that have been developed with years of fine tuning.

There are a number of additional details that are sometimes included in these models. For example, some catalog merchants with telephone call centers have used queuing models to convert customer service requirements (e.g., specification on maximum probability of having to wait) into requirements for number of people to have on duty each hour. Sometimes a distinction is made between staffing and rostering, the latter usually meaning that a solution is obtained down to the detail of individual personnel. Some large firms, for example, only solve the staffing problem of how many units of each work pattern should be worked. The detailed, or rostering, problem is then solved by letting the individual pilots, nurses, etc. bid on which of the selected work patterns they would like to work over the next planning period.

A major tele-communications company, recently contacted us about a What'sBest! app-lication for rostering on-call technicians. The application assigned on-call schedules to individual technicians for the entire year. Each tech was to be assigned the same number of weeks. The assignments were constrained such that technicians could not be on-call during their vacations, no technician could be assigned more than two consecutive weeks, and the scheduling for the major holidays would be spread equitably among all technicians.

Sometimes there are multiple types of work to be covered. For example, in the scheduling of health care personnel, one may have to schedule first, second, and third level "on-call" personnel. When emergency work arises, first the first level person is called, if more work arises, then the second level person is called, etc. In multilingual markets, there may be requirements, for example, on how many English speaking personnel must be on duty, how many Spanish speakers must be on duty, and how many personnel in total must be on duty. In such situations, multi-skilled personnel tend to be desirable. There are generally upper limits on how many people of a given type can be assigned to a given type of work pattern (e.g., only 4 flight tours can start in Auckland because only 4 pilots are based there). Most of the above kinds of detail can be incorporated into the general optimization model outlined above.

With growing pressure to increase efficiency, raise customer service, and control costs, businesses can no longer afford to rely on manually producing solutions to their complex scheduling problems. Optimization can take into account the complex set of work rules and preferences to produce the most efficient and cost effective solutions.

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