Shift Bidding

Shift bidding is a method of dividing up work in a way that gives priority to the preferences of the workers themselves. So far it has been used mainly in hospitals as a way to fill nursing shifts that are hard to fill like the graveyard shift. The way it works is this: nurses go to their computers and bring up a website that shows the unfilled shifts for the next week. Then they get to decide what shifts they would like to bid on, entering an hourly wage for that shift. The administrator of the website then chooses the person who has submitted the lowest hourly wage to fill a particular shift. This works to the advantage of the nurses since they can pick and choose what shifts they want to work, in what departments and for what wages. It works to the advantage of the hospital because they must seek nurses from an agency for unfilled shifts which generally costs them more money since the agency tacks on their fee to the hourly rate. On the other hand nurses can usually make more than their usual rate and still, the hospital will not have to pay as much as the agency rate.


The nurses get to choose the department they want to work in and, since they are usually associated with the hospital to begin with, are more dedicated than contract nurses from the agency. Letís say, for example, the normal daily rate is $35. per hour, and the agency rate is $50. per hour. A nurse might bid $40. per hour for a particular shift. If this is the low bid, the nurse will get to work that shift for that rate. This enables nurses to be part time workers or to work extra shifts for extra money depending on their personal circumstances. Even though theyíre still employees of the hospital, for all intents and purposes, theyíre contract workers when they do shift bidding. This works well because there is a nursing shortage, and they can bid up the price of labor. If there were a surplus of nurses, they would actually end up bidding down the hourly rate by shift bidding. Of course, the nurses must have the proper credentials for the area they wish to work and bid on. The advantages to the nurses are that they get to determine their own work schedule, make extra money and work when itís convenient for them.


The shifts might be at multiple hospitals, involve a variety of different categories of credentials and be of varying lengths. At Spartanburg Regional Healthcare System in North Carolina, ď[They] developed the system to encourage its own nurses to cover extra shifts rather than picking up hours at other hospitals, and to decrease use of agency nurses, said Darby Douglas, RN, Spartanburgís RN staffing coordinator.

ďOffering up extra shifts to in house nurses saves an average of $10,000 per week, Douglas said. The average winning bid, between $35 and $39 an hour, costs $14 to $20 an hour less than the fee for an agency nurse. The system fills more than 300 shifts per two-week pay period, she said.Ē

Shift bidding is a rudimentary form of Preferensism whose slogan is ďfrom each according to his preferences and to each according to her preferences.Ē Letís consider how this rudimentary system could be expanded into a more general Preferensist system. Preferensism is a combination of social choice and utilitarianism. Social choice involves the aggregation of individual preferences to come up with an overall choice for society. This is done in such a way as to give each individual the highest preference possible consistent with the constraint that, in this case, all the shifts get filled. Of course, if no one bids on a particular shift, then an agency nurse must be obtained. One could also imagine an additional constraint which would be an overall budget. The totality of all accepted bids would have to be less than or equal to the budget

Letís consider an example in which there are 6 nurses: Alice, Betty, Cathy, Diane, Elaine and Frances. Letís say there are 6 different shifts: shift 1:midnight to 4 AM; shift 2: 4 AM to 8 AM; shift 3: 8 AM to 12 noon; shift 4:12 noon to 4 PM; shift 5: 4 PM to 8 PM; and shift 6: 8 PM to midnight. The shift bidding covers just a 1 day period to simplify the example, and each nurse can bid on only 1 shift in that 24 hour period. Of course, in real life a nurse might bid on 1 or more shifts and also more than 1 nurse might be required on any particular shift, but this would complicate the example. The range of hourly rates can vary between $30. and $50. (The highest and lowest bids, respectively, are $50. and $30.) Letís say there are 6 shifts to fill, one for each time slot. Furthermore, each nurse can submit 6 preferences, the highest being her first preference and the lowest being her sixth preference. She doesnít have to bid on any particular shift if she doesnít want to, and any unfilled shifts will be filled by agency nurses at $60. an hour. The hospital has a budget of $270. for the day, and the total payout for all shifts must come in under but as close to this budget as possible. Letís assume for the purposes of this example that each nurse will be chosen once although this need not be the case in general.

The job of the software is to take all the nurses preferences as inputs, consider all combinations of preferences, give each nurse as high a preference as possible while staying at or under budget, and, if there are a number of ways to do this, choose that one that minimizes the inequality of preferences received among the nurses. Notice that weíre not trying to minimize the hospitalís pay out, but we are trying to maximize the nursesí preference utility by giving them as high a preference as possible while minimizing the inequality among them. Preference utility is defined as (number of allowed preferences -preference attained). In this example if Alice got her first preference her preference utility would be 6 Ė 1 = 0.

Letís consider the inputs of our 6 nurses each of whom find themselves in different circumstances. Alice, a single Mom, needs to work a regular day shift due to the fact that she has a family to support and needs to be home with them at night. She will bid on shift 4 later but for now letís just consider her first bid. Her preferences are the following:

1)      Shift 3 at $45.

2)      Shift 3 at $43.

3)      Shift 3 at $41.

4)      Shift 3 at $38.

5)      Shift 3 at $35.

6)      Shift 3 at $32.

Betty has a husband who works, no kids and only needs to work part time. She likes to be home in the evenings with her husband so she wonít work shifts 5 or 6. Her preferences are the following:

1)      Shift 4 at $45.

2)      Shift 3 at $45.

3)      Shift 1 at $50.

4)      Shift 2 at $50.

5)      Shift 3 at $40.

6)      Shift 4 at $40.

Cathy is a single woman who doesnít mind working odd shifts. Her preferences are as follows:

1)      Shift 5 at $50.

2)      Shift 6 at $50.

3)      Shift 2 at $50.

4)      Shift 1 at $50.

5)      Shift 1 at $45.

6)      Shift 5 at $45.

Diane needs to work 2 shifts but is very flexible. Sheíll bid on her second shift later. For now her preferences are as follows:

1)      Shift 1 at $40.

2)      Shift 2 at $40.

3)      Shift 3 at $35.

4)      Shift 4 at $38.

5)      Shift 5 at $40.

6)      Shift 6 at $40.

Elaine only wants to work one shift in the evening since she has another job during the day and needs extra money to pay off bills:

1)      Shift 5 at $45.

2)      Shift 5 at $40.

3)      Shift 5 at $35.

4)      Shift 5 at $30.

5)      Shift 6 at $45.

6)      Shift 6 at $40.

Frances needs 2 shifts and likes to work nights. Sheíll bid on shift 2 later. For now her preferences are as follows:

1)      Shift 1 at $50.

2)      Shift 1 at $43.

3)      Shift 1 at $41.

4)      Shift 1 at $39.

5)      Shift 1 at $37.

6)      Shift 1 at $35.

Now computer software would systematically consider every combination, consider that every shift was covered, and consider whether that combination was above or below budget. It would then throw out every combination that was over budget, and choose those combinations that maximized preference. If more than one combination did this, it would then choose the one that minimized inequality which would be defined as the absolute value of the differences for each individual of their attained utility and the average utility. The closer each individualís utility is to the average utility, the less would be the inequality for that individual. The sum of the individual inequalities would be the social inequality.

Letís consider a few combinations on an ad hoc basis and see if we can come up with one that meets our criteria.

Shift 1: Frances at $50., her first preference.

Shift 2: Cathy at $50., her third preference.

Shift 3: Alice at $45., her first preference.

Shift 4: Betty at $45., her first preference.

Shift 5: Elaine at $45., her first preference.

Shift 6: Diane at $40., her sixth preference

The total pay out would be $275. Oh oh. This is $5. over the hospitalís budget.

We could give Frances her third choice, shift 1 at $41., and this would get us under budget, or we could give Elaine her second preference of shift 5 at $40. Letís consider giving Elaine her second preference since it would put us right at budget (one of our criteria) and it would only result in lowering her preference utility by 1 instead of 2 for Frances if we switched her instead. Now we have

Shift 1: Frances at $50., her first preference.

Shift 2: Cathy at $50., her third preference.

Shift 3: Alice at $45., her first preference.

Shift 4: Betty at $45 here first preference.

Shift 5: Elaine at $40., her second preference.

Shift 6: Diane at $40., her sixth preference.

Now we ask could we make any changes that would increase anyoneís preference utility without going over budget? Yes we could switch Cathy and Diane giving Cathy shift 6 and Diane shift 2. This would result in an increase in preference utility for both of them. We now have:

Shift 1: Frances at $50., her first preference.

Shift 2: Diane at $40., her second preference.

Shift 3: Alice at $45., her first preference.

Shift 4: Betty at $45 here first preference.

Shift 5: Elaine at $40., her second preference.

Shift 6: Cathy at $50., her second preference.

Again we are right on budget at $270., and we have 3 first and 3 second preferences. I think this is the best we can do with the assumptions weíve made. If any slots had remained unfilled, we could have raised the maximum bid to $55.00 as the day we are bidding on grew closer in order to see if there were any takers at that maximum rate which would still be less than the agency rate of $60..

Our total preference utility is 5x3 + 4x3 = 27 out of a possible 30. Our average utility is 4.5, and our inequality is 3.

Now letís consider how this model could be generalized. First there could be more than one position to fill for each time slot, and the algorithm could consider maximizing preference utility and then minimizing inequality over the total number of positions. Second, we could have considered maximizing utility and minimizing inequality over a longer period of time like a week. Other than that we have a pretty good model of how job selection in Preferensism would work. However, in this particular example the law of supply and demand is in favor of the nurses if there is a nursing shortage. If there were an over supply of nurses, they would be bidding their hourly rate down below what would be acceptable. What constraints would there be in Preferensism that would constrain the law of supply and demand? If there were an oversupply of labor, labor would be shifted out of nursing and into some other field so that the demand for labor would be in balance with the supply. Then the total budget would be determined by consumer demand for healthcare. The goal is to keep a balance between supply and demand, with the average wage determined by the average demand.

In capitalism profits are generated by keeping the supply of labor greater than the demand for labor thus driving the total cost of labor down, and, since labor is one of the inputs to the production process, for any given amount of revenues and since profits equal revenues minus costs, profits will go up as aggregate labor costs go down. Therefore, it is advantageous to the capitalist (or owner of an enterprise) to have as large a labor supply as possible. This is why so many business owners favor immigration, legal or otherwise. It should be pointed out that profits will also increase as the aggregate cost of materials used in the production process decreases as well. Therefore, a capitalist who is able to make better deals in acquiring necessary materials will make greater profits as well. In Preferensism there is no need for profit, and individuals can only become wealthy through their work. Profit as a source of wealth is eliminated, but risk is also eliminated. Profits accrue to all more or less equally and risk is borne by all more or less equally.