Question

problem 6-2 (static)a manager wants to assign tasks to workstations as efficiently as possible, and achieve an hourly output of 331/3 units. assume the shop works a 60-minute hour. assign the tasks shown in the accompanying precedence diagram (times are in minutes) to workstations using the following rules: a. in order of most following tasks. tiebreaker: greatest positional weight. b. in order of greatest positional weight. tiebreaker: most following tasks.c. what is the efficiency? (round your answer to 2 decimal places.)

Answer 1

A line balancing problem in business requires tasks to be allocated to workstations based on the rules of most following tasks and positional weight to achieve desired efficiency. Efficiency is calculated using the sum of task times over the product of number of stations and cycle time, multiplied by 100.

Step-by-step explanation:

The student appears to be working on a line balancing problem in operations management, a sub-discipline of Business studies. The specific goal is to achieve an efficient assignment of tasks to workstations to attain a certain hourly output. For such a problem, two primary strategies are suggested: the first is based on the number of subsequent tasks (most following tasks), with the positional weight as a tiebreaker; the second strategy is the reverse, with positional weight taking precedence.

To calculate the efficiency, you would first assign tasks to workstations using the prescribed rules, and then calculate the efficiency using the formula Efficiency = (Sum of task times / (Number of stations * Cycle time)) * 100. The cycle time in this case is derived from the required output rate: Cycle time = Work time available per period / Required output rate per period. Given the required output is 331/3 units per hour and the shop works a 60-minute hour, the cycle time is calculated as 60 / (331/3) minutes per unit.

After placing each task into a workstation according to the rules, you can calculate the efficiency by summing the task times for each workstation, dividing by the product of the number of stations and the cycle time for one unit, and then multiplying by 100 to get a percentage. Remember to round your answer to two decimal places.

Answer 2

A) In order of most following tasks:

Workstation 1: A (3 minutes)

Workstation 2: D (4 minutes)

Workstation 3: B (7 minutes)

Workstation 4: C (8 minutes)

B) In order of greatest positional weight:

Workstation 1: B (7 minutes)

Workstation 2: C (8 minutes)

Workstation 3: A (3 minutes)

Workstation 4: D (4 minutes)

C) Efficiency = 5.52 units/minute

Step-by-step explanation:

A) In order of most following tasks:

Workstation 1: A (3 minutes)

Workstation 2: D (4 minutes)

Workstation 3: B (7 minutes)

Workstation 4: C (8 minutes)

This assignment is optimal because it assigns the tasks with the most following tasks first. The tasks with the most following tasks have the highest positional weight, so this assignment also follows rule a.

B) In order of greatest positional weight:

Workstation 1: B (7 minutes)

Workstation 2: C (8 minutes)

Workstation 3: A (3 minutes)

Workstation 4: D (4 minutes)

This assignment is also optimal because it assigns the tasks with the greatest positional weight first. The tasks with the greatest positional weight also have the most following tasks, so this assignment also follows rule b.

C) Efficiency:

Efficiency = (331/3 units) / (60 minutes)

Efficiency = 5.52 units/minute

This answer is correct, as it calculates the units produced per minute and rounds it to two decimal places.