ABSTRACT
DOCS is a computer program which generates the staff schedule. An accounting framework is combined with an optimization technique that searches for a schedule in which all accounts are simultaneously in balance. The search is accomplished using a Monte-Carlo process which shuffles staff within the schedule. The shuffling is biased according to each staffer's account balance: the staffer who owes the most is most likely to be scheduled.

THE PROBLEM
Staff scheduling is arduous and time consuming. The scheduler must: assign staff according to their relative obligations; apply often intricate rotation rules; distribute the burden of premium daytypes such as weekends and holidays; satisfy on/off requests; and provide an adequate accounting report.

THE SOLUTION
Doctors On-Call Schedule (DOCS) is a computer program which generates and optimizes the staff on-call and daily duty schedule. [1] DOCS is built around a framework of rigorous accounting principles. A ledger of accounts is created with one account for each staffer/ task/daytype combination. Every month, each account is assigned a debit according to the staffer's work requirement and receives a credit for days worked. The account balance, equal to debit minus credit, measures the amount of work owed by each staffer to each task for each daytype. A positive balance means a staffer has not worked enough days to fulfill his work requirement, while a negative balance means a staffer has worked more than enough days. The account balance is carried over from month to month, so that the ending balance for the prior month is the beginning balance for the next month. In order to illustrate the accounting framework used by DOCS, we present in Table 1 an example comprising a group of five staff who must cover a single task every day for a thirty day scheduling period. (Here, for simplicity, we ignore the daytype dimension, and assume that all days of the thirty day period are the same daytype.) The first column of the table identifies the staff (A, B, C, D, E). Column 2 shows the relative obligation of each staffer: B, C and E have twice the obligation of A and D. Column 3 shows the work requirement (debit) in days; this is calculated by multiplying each staffer's relative obligation by the total number of days to be scheduled (30) and dividing by the total relative obligation (8). Column 4 shows the number of days actually worked (credit) during the month. Column 5 shows the month-end account balance, equal to debit minus credit (Column 3 minus Column 4). The individual account balances total to zero, as they must.