Suppose the airport management has to decide on allocating a pool of multi-skilled employees to the following four stations of quarantine procedures for arriving inbound travellers. The procedures carried out at each station are listed below with the estimated time taken per traveller given in square brackets: Station 1: Check (1) passport / Hong Kong identity card (2) health declaration QR code generated in the online declaration form completed before departure (3) vaccination record (4) negative result of polymerase chain reaction (PCR) test taken before departure. [3 minutes] Station 2 (Temporary specimen collection centre): Perform nuclei acid test and rapid antigen test (RAT). Issue a QR code indicating traveller's identity and initial health status. [5 minutes] Station 3: Check identity documents and enter updated health status into the system based on result available from the RAT test (Station 2). If the RAT test result is negative, issue provisional vaccine pass and permission to proceed to baggage collection. [7 minutes] Station 4: Check quarantine hotel booking confirmation letter, notify transport service and assign traveller to corresponding waiting line of transport to hotel by coach/minibus or self- paid designated taxi. [2 minutes] As the number of inbound travelers found at the airport with positive RAT test result (Station 3) is relatively low, it can be assumed that all inbound travellers have to pass through the four stations. The current staff supply mainly comes from the Airport Authority, Department of Health and other government units (including temporary contract staff from other industries). They can be classified into different groups according to their skills trained/qualified for performing the procedures in some of the above stations. The following table summarizes the skill set by group and station with the staff size of each group: Skills trained/qualified Staff group Al Station 1 Station 2 Station 3 Station 4 Staff size 10 8 A2 v 10 H 9 01 7 02 The objective is to maximize the (hourly) throughput rate of the system of stations by finding the smallest throughput rate among all stations (Theory of Constraints), subject to the staff availability in each group. Q1. Determine the optimal allocation plan for employees in the five groups to the four stations. Formulate the problem by an integer program in a mathematical model. (Hint: a mixed integer program is a type of integer program allowing integer and continuous decision variables to be formulated.) [18 marks] Q2. Develop an Excel spreadsheet model and use Solver to compute the optimal allocation plan and the maximum hourly system throughput rate. [20 marks] Q3. Some travellers experience long waiting time through the entire system and the airport management also desires to increase the system throughput rate. Which staff group(s) should recruit more employees and what is the minimum number required in order to increase the present throughput rate (result in Q2) by p percent? (a) Modify the formulation in Q1 in terms of p. [12 marks] (b) Modify the Excel spreadsheet model in Q2 for p = 10% and run Solver for the new solution. Repeat for p = 20% and 30%, respectively. [28 marks] Q4. Suppose Station 4 procedures could be merged into Station 1 (by information technology and additional training of staff group A1). This would enable the sum of time taken to be saved by 30 seconds, i.e., 4.5 minutes per traveller and result in only 3 stations (Merged Station 1 with 4, Station 2 and Station 3) with only 4 relevant staff groups (A1, A2, H and O1). Would this option be better than the current layout in terms of system throughput rate, total number of (current and new) employees utilized and new recruits? (a) Explore with Excel for the current layout and improvement percentage of p = 10%, 20% and 30%. (b) Furthermore, list two qualitative factors that should be considered. (You do not have to make the final decision.) -End- [24 marks] [4 marks]