Assignment

This assignment has three phases and I have started one phase (see below) but I only need the answer to Phase II right now. Based on the given paper (Hospital call center) I must answer the following questions and include them in a final report. I must make sure I provide justification for these answers, including screen shots of any adjustments made to the model, and the subsequent results from AMPL.

1. How many Spanish-speaking operators and how many English-speaking operators does the hospital need to staff the call center during each 2-hour shift of the day to answer all of the calls such that the total cost is minimized?

2. Most full-time workers don't want to work late into the evening. Harry can find only one qualified English-speaking operator willing to begin work at 1 P.M. Given this new constraint, how many full-time English-speaking operators, full-time Spanish-speaking operators, and part-time operators should Harry hire? How does this effect the total cost?

3. Harry now considers hiring bilingual operators. If all operators are bilingual, how many operators should he hire to cover each 2-hour shift? How does this effect the total cost if bilingual operators make 20% more than their non-bilingual counterparts?

There are three phases that I must complete and I have the first one started (see model below) but it is not complete yet.

The first phase will focus on model development. You will be given an operations research problem and asked to formulate a complete mathematical model to solve the problem. The problem definition can be found here. This phase will be graded based on the accuracy of your model. It is possible your model will need to be refined before being submitted in Phase II.

paramEngPer = 0.8;
paramSpaPer = 0.2;
paramcph = 6;
paramAvgCall := 1 35 2 90 3 65 4 100 5 90 6 25 7 10;

paramEngPer; #percent of calls in english
paramSpaPer; #percent of calls in spanish
paramcph; #calls per hour per operator
paramAvgCall{1..7}; #Average calls each shift
varE{1..7} >=0; #English speaking workers for each shift i, 7 to include part timers
varS{1..5} >=0; #Spanish speaking workers for each shift i, 5th full time shift covers to close

#paramSmin{1..N}; #min S necessary to meet demand in each shift

#***objective function(s)***
#*Note: No Span operators accountable after 5th shift since no part timers
minimize z_eng: sum{i in 1..7}40*(E[1]+E[2]+E[3])+44*(E[4]+E[5]+E[6])+48*E[7];
minimize z_spa: sum{i in 1..5}40*(S[1]+S[2]+S[3])+44*(S[4]+S[5]);
#***constraints for each shift, accoutning for overlap***
s.t. EngShift1: E[1] >= ceil( (EngPer*AvgCall[1]) / cph); #avg calls demanded / cph
s.t. EngShift2: E[2] >= ceil( (EngPer*AvgCall[2]) / cph); #avg calls demanded / cph
s.t. EngShift3: E[1] + E[3] >= ceil( (EngPer*AvgCall[3]) / cph);
s.t. EngShift4: E[2] + E[4] >= ceil( (EngPer*AvgCall[4]) / cph);
s.t. EngShift5: E[3] + E[5] + E[6] >= ceil( (EngPer*AvgCall[5]) / cph);
s.t. EngShift6: E[4] + E[6] + E[7] >= ceil( (EngPer*AvgCall[6]) / cph);
s.t. EngShift7: E[5] + E[7] >= ceil( (EngPer*AvgCall[7]) / cph);

s.t. SpaShift1: S[1] >= ceil( (SpaPer*AvgCall[1]) / cph);
s.t. SpaShift2: S[2] >= ceil( (SpaPer*AvgCall[2]) / cph);
s.t. SpaShift3: S[1] + S[3] >= ceil( (SpaPer*AvgCall[3]) / cph);
s.t. SpaShift4: S[2] + S[4] >= ceil( (SpaPer*AvgCall[4]) / cph);
s.t. SpaShift5: S[3] + S[5] >= ceil( (SpaPer*AvgCall[5]) / cph);
s.t. SpaShift6: S[4] >= ceil( (SpaPer*AvgCall[6]) / cph);
s.t. SpaShift7: S[5] >= ceil( (SpaPer*AvgCall[7]) / cph);

This is what I need answered for now just the completion of Phase I and Phase II. What I have put together is okay but I think I have left out how to account for the idle time of the workers at the call center as well.

The second phase of this project will focus on AMPL implementation of your model. Given the model developed in Phase I, you will code a .mod and a .dat file that successfully solves the problem. The model and data files should include comments to explain each file, as well as comments explaining the implementation of your model in AMPL. This phase will be graded based on the implementation of your model into AMPL format. It should compile, solve, and produce a result. The credit earned in this phase is centered around whether your model from Phase I can be implemented into AMPL, and whether it solves.

The third phase of this project will focus on writing and formulating answers to the original problem. A series of operations-based questions pertaining to the problem is posted here, and you will have to answer them based on your model and results from Phase II. This phase also includes a professional report, and will be graded based on the following sections.

• Summary of the problem
• Mathematical formulation
• Details on AMPL implementation
• Responses to questions.

Attachment:- AMPL-Project-Problem-Definition.pdf