1. Recall the nurse-scheduling problem (with full-time nurses only) introduced in class. We now know that...

1. Recall the nurse-scheduling problem (with full-time nurses only) introduced in class. We now know that this staffing plan cannot be achieved with fewer than 8 nurses. However, nurses prefer to work tour 7 because the days off are Saturday and Sunday. Nurses also like tours 1 and 6 because one day off is a Saturday or Sunday, respectively. Reformulate the problem so that it uses exactly 8 nurses but the number of nurses assigned to tours 1, 6 and 7 is maximized while meeting minimum daily staffing needs. How did you reformulate the decision variables, objective function and constraints?

THAT IS ALL I GOT i just need variables and formula

Solutions

Expert Solution

The general Model

The general form of the nurse scheduling problem takes the form of either a maximization problem (in the case of nurse preferences) or a minimization problem (in the case of nurse costs). Before we formulate the objective function, let us first declare the various sets and parameters that will be used in the formulation.

Sets of Values

S Shifts of the day (1 – AM, 2- PM, 3 - MN)

N =Nurse

D =Days of the planning horizon

L =Leave

M =Demand

O =Supply

P =Preference

C =Cost

E =No of duties required S1 Specific set S1

Sn =Specific set Sn

Parameters

Xnsd =Assignment for nurse n, shift s of day d (with S1, … ,Sn)

Pnd = Leave for nurse n for day d (with S1, … ,Sn)

Pnsd =Preference for nurse n, shift s of day d (with S1, … ,Sn)

Cnsd =Cost for nurse n, shift s of day d (with S1, … ,Sn)

Msd =Demand for shift s of day d (with S1, … ,Sn)

Osd =Supply for shift s of day d (with S1, … ,Sn)

Ens =No of shifts for nurse n for shift s (with S1, … ,Sn)

Thus the objective function can be declared as image uploaded

Nightingale answered 1 year ago

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