UNION AIRWAYS is adding more flights to and from its hub airport, and so it needs...

  

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UNION AIRWAYS is adding more flights to and from its hub airport, and so it needs to hire additional customer service agents. However, it is not clear just how many more should be hired. Management recognizes the need for cost control while also consistently providing a satisfactory level of service to customers. Therefore, an OR team is studying how to schedule the agents to provide satisfactory service with the smallest personnel cost. Based on the new schedule of flights, an analysis has been made of the minimum number of customer service agents that need to be on duty at different times of the day to provide satisfactory level of service. The rightmost column of the table below shows the number of agents needed for the time periods given in the first column. The other entries in this table reflect one of the provisions in the company's current contract with the union that represents the customer service agents. The provision is that each agent works an 8-hour shift 5 days per week, and the authorized shifts are Shift 1: 6am-2pm Shift 2: 8am-4pm Shift 3: Noon to 8 pm Shift 4: 4pm to midnight Shift 5: 10 pm to 6 am. Marks in the main body of the table show the hours covered by the respective shifts. Because some shifts are less desirable than others, the wages specified in the contract differ by shift. For each shift, the daily compensation (including benefits) for each agent is shown in the bottom row of the table. The problem is to determine how many agents should be assigned to the respective shifts each day to minimize the total personnel cost for agents, based on this bottom row, while meeting (or surpassing) the service requirements given in the rightmost column. Time period 1 2 3 4 5 Min.number of agents needed 8ат 48 8 – 10am 79 10 - noon 65 — 2рт 2 — 4рт 4 — брт 6 — 8рт 8— 10рт 10 – midnight midnight – 6am daily cost per agent 170 noon - 87 64 73 82 43 52 15 160 175 180 195 Formulate an LP model for this problem. 8 8 8 8 UNION AIRWAYS is adding more flights to and from its hub airport, and so it needs to hire additional customer service agents. However, it is not clear just how many more should be hired. Management recognizes the need for cost control while also consistently providing a satisfactory level of service to customers. Therefore, an OR team is studying how to schedule the agents to provide satisfactory service with the smallest personnel cost. Based on the new schedule of flights, an analysis has been made of the minimum number of customer service agents that need to be on duty at different times of the day to provide satisfactory level of service. The rightmost column of the table below shows the number of agents needed for the time periods given in the first column. The other entries in this table reflect one of the provisions in the company's current contract with the union that represents the customer service agents. The provision is that each agent works an 8-hour shift 5 days per week, and the authorized shifts are Shift 1: 6am-2pm Shift 2: 8am-4pm Shift 3: Noon to 8 pm Shift 4: 4pm to midnight Shift 5: 10 pm to 6 am. Marks in the main body of the table show the hours covered by the respective shifts. Because some shifts are less desirable than others, the wages specified in the contract differ by shift. For each shift, the daily compensation (including benefits) for each agent is shown in the bottom row of the table. The problem is to determine how many agents should be assigned to the respective shifts each day to minimize the total personnel cost for agents, based on this bottom row, while meeting (or surpassing) the service requirements given in the rightmost column. Time period 1 2 3 4 5 Min.number of agents needed 8ат 48 8 – 10am 79 10 - noon 65 — 2рт 2 — 4рт 4 — брт 6 — 8рт 8— 10рт 10 – midnight midnight – 6am daily cost per agent 170 noon - 87 64 73 82 43 52 15 160 175 180 195 Formulate an LP model for this problem. 8 8 8 8

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