Suppose that a bus company is deciding where to locate its central hub. There are 6 possible destinations for the buses. Suppose that the center of town will be used as the reference for describing the possible destinations. A is located 5 miles South and 3 miles West. B is located 3 miles North and 2 miles East. C is located 1 mile South and 5 miles East. D is located 2 miles North and 3 miles West. E is located exactly in the center of town. F is located 10 miles North and 5 miles East. Assume that traffic to each destination will be equal. Where should the hub go so that travel time is minimized?

(a)  

A grocery chain is deciding on where to locate its new distribution center (DC). The new DC will serve four grocery stores, each with a demand of 10,000 units. If the coordinates of the stores are (112,108), (110,50), (40, 85), and (10, 25) where should the DC be located? Suppose now that each store instead had demand of 20,000 units. Where should the DC go in this case?

(a)  

A school district is considering four locations for a new high school. There are four factors the district is considering (cost of land, distance to students, land size, and traffic flow). The higher the factor score, the better. The district would like to compare results using two weighting systems. The first system would give each factor equal weight and the second would give the factors weights of .4, .2, .1, and .3 respectively. Use the factor rating method to determine which location is best for each weighting system. Which site should be selected under W(1) and W(2).

(a)  

Every month, a distribution center will deliver 14,000 units to Retailer A at coordinates (20, 10), 12,000 units to Retailer B at coordinates (30, -15), and 20,000 units to Retailer C at coordinates (4, 4). Assuming no constraints on location, at what coordinates should the distribution center be located (rounded to two decimal places)?

(a)  

A company is trying to balance production between 3 workstations on an assembly line. Currently there are 5 tasks that need to be performed. These tasks, ABCDE, have required times of 2 minutes, 4 minutes, 1 minutes, 3 minutes, and 10 minutes, respectively. The assembly line needs to produce 40 units per day to meet demand and can work for up to 8 hours each day.

What is the required cycle time?

(a)  

A company is trying to balance production between 3 workstations on an assembly line. Currently there are 5 tasks that need to be performed. These tasks, ABCDE, have required times of 2 minutes, 4 minutes, 1 minutes, 3 minutes, and 10 minutes, respectively. The assembly line needs to produce 40 units per day to meet demand and can work for up to 8 hours each day.

What is the theoretical minimum # of workstations?

(a)  

An assembly line with 11 tasks is to be balanced. The longest task is 2.4 minutes, the shortest task is 0.4 minutes, and the sum of the task times is 18 minutes. The line will operate for 600 minutes per day. What is the minimum number of stations needed if the maximum output rate is to be sought?

(a)