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# hw5-sol - ISyE 4803 Homework 5 Due(15 Points NOTE In...

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ISyE 4803 – Homework 5 Due: November 12, 2009 (15 Points) NOTE: In answering these questions, do not copy-paste text from the articles. Use your own words. 1. (6 points) A clinic has S doctors. A schedule needs to be created for the doctors to satisfy the patients’ needs during the working hours of the hospital. The clinic is open for T hours per day. There is a forecast of patients arriving at each hour, and it is denoted by f j , j=1, …, T. The time (in hours) needed to attend each patient is 1. Let b ij =1 if doctor i works during hour j, and b ij =0 otherwise. a. (2 points) Write a set of constraints to ensure that there are enough doctors working at each hour to attend all the patients forecasted to arrive during that hour. j S i ij f b = 1 j=1,…,T b. (2 point) Write the objective function to minimize the total number of doctor hours needed during the day. minimize ∑∑ = = S i T j ij b 1 1 c. (2 points) Formulate a set of constraints to ensure that the work hours of doctor i are consecutive, for all i=1,…,S. (For example, if the doctor is working during the hours of 3,4,5, and 6, and is not working on the 7 th hour, then he should be off duty for the remaining hours of that day.) 1 1 ) 1 ( + + = + - ij ij T j k ik Mb b M b for i=1,…,S, j=1,…,T-1 where M is a large number (e.g., M=T is a sufficiently large number to make this constraint work) 2. (2 points) Please refer to the Big Depot Game case: a. (1 points) Uncertainty in the size and the location of a disaster were identified as important factors leading to logistics challenges when planning for a disaster. Among other challenges faced during disaster preparedness and response are (i) the uncertainty in the timing of the disaster (and the resulting demand) and (ii) the uncertainty in supply availability. How are these challenges similar or different from the ones faced during day-to-day operations of a company such as Big-Depot?

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There is not only demand uncertainty in size and location, but there is also uncertainty in timing. This timing uncertainty requires a constant state of preparedness from the supply chain that could be achieved with strategies such like inventory propositioning. In addition, the supply uncertainty needs to be
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hw5-sol - ISyE 4803 Homework 5 Due(15 Points NOTE In...

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