CYCLICAL SCHEDULING. Hospital administrator Doris Laughlin wants to staff the oncology ward using a standard 5-day workweek with two consecutive days off, but also wants to minimize the staff. However, as in most hospitals, she faces an inconsistent demand. Weekends have low usage. Doctors tend to

Question

CYCLICAL SCHEDULING. Hospital administrator Doris Laughlin wants to staff the oncology ward using a standard 5-day workweek with two consecutive days off, but also wants to minimize the staff. However, as in most hospitals, she faces an inconsistent demand. Weekends have low usage. Doctors tend to work early in the week, and patients peak on Wednesday then taper off.
APPROACH [latex]\blacktriangleright[/latex] Doris must first establish staffing requirements. Then the following five-step process is applied.

Accepted Answer

SOLUTION [latex]\blacktriangleright[/latex]
1. Doris has determined that the necessary daily staffing requirements are:

DAY	MONDAY	TUESDAY	WEDNESDAY	THURSDAY	FRIDAY	SATURDAY	SUNDAY
Staff required	5	5	6	5	4	3	3

2. Identify the two consecutive days that have the lowest total requirement and circle these. Assign these two days off to the first employee. In this case, the first employee has Saturday and Sunday off because 3 plus 3 is the lowest sum of any 2 days. In the case of a tie, choose the days with the lowest adjacent requirement, or by first assigning Saturday and Sunday as an “off” day. If there are more than one, make an arbitrary decision.
3. We now have an employee working each of the uncircled days; therefore, make a new row for the next employee by subtracting 1 from the first row (because one day has been worked)—except for the circled days (which represent the days not worked) and any day that has a zero. That is, do not subtract from a circled day or a day that has a value of zero.
4. In the new row, identify the two consecutive days that have the lowest total requirement and circle them. Assign the next employee to the remaining days.
5. Repeat the process (Steps 3 and 4) until all staffing requirements are met.

Doris needs six full-time employees to meet the staffing needs and one employee to work Saturday.

Notice that capacity (number of employees) equals requirements, provided an employee works overtime on Saturday, or a part-time employee is hired for Saturday.

INSIGHT [latex]\blacktriangleright[/latex] Doris has implemented an efficient scheduling system that accommodates 2 consecutive days off for every employee.
LEARNING EXERCISE [latex]\blacktriangleright[/latex] If Doris meets the staffing requirement for Saturday with a full-time employee, how does she schedule that employee? [Answer: That employee can have any 2 days off, except Saturday, and capacity will exceed requirements by 1 person each day the employee works (except Saturday).]
RELATED PROBLEMS [latex]\blacktriangleright[/latex] 15.26, 15.27

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