The Oakton River had long been considered an impediment to the development of a certain medium sized metropolitan area in the southeast. Lying to the east of the city, the river made it difficult for people living on its faster bank to commute to jobs in and around the city and to take advantage of the shopping and cultural attractions that the city had to offer. Similarly, the river inhibited those on its western bank from access to the ocean resorts lying one hour to the east.
A personnel task force has been established to recruit, train and schedule the workers needed to operate the toll facility. It has taken as part of its mandate the requirement that personnel costs be kept as low as possible. One particular area of concern is the number of toll collectors that will be needed. The bridge is scheduling three shifts of collectors: shift A from midnight to 8am, shift B from 8am to 4pm, and shift C from 4pm to midnight. Recently the state employees union negotiated a contract with the state which requires that all toll collectors be permanent, full time employees. In addition, all collectors must work a five-on, two-off schedule on the same shift. Thus, for example, a worker could be assigned to work Tuesday, Wednesday, Thursday, Friday and Saturday on shift A, followed by Sunday and Monday off. An employee could not be schedule to work, say Tuesday on shift A followed by Wednesday, Thursday, Friday, and Saturday on shift B or on any other mixture of shifts during a five day block. The employees would choose their assignments in order of their seniority.
The task force has received projections of traffic flow on the bridge by day and hour. (minimum number of collectors required per shift, per day to handle the anticipated traffic load.
Minimum number of toll collectors require per shift
Shift Sun Mon Tue Wed Thu Fri Sat
A 8 13 12 12 13 13 15
B 10 10 10 10 10 13 15
C 15 13 13 12 12 13 8
The numbers in the table include one or two extra collectors per shift to fill in for collectors who call in sick and to provide relief for collectors on their scheduled breaks. Note that each of the eight collectors needed for shift A on Sunday, for example could come from any of the A shifts scheduled to begin on Wednesday, Thursday, Friday, Saturday or Sunday.
Questions
1. Determine the minimum number of toll collectors that would have to hired to meet the requirements expressed in the table.
2. The union had indicated that it might lift its opposition to the mixing of shifts in a five day block in exchange for additional compensation and benefits. By how much could the numbers of toll collectors required be reduced if this were done.
Use this format
1. IP Model (the IP equations), assumptions that clarify the development of the model.
2. The EXCEL Model
3. A recommendation to the problem.