Manager Wants To Assign Tasks To Workstations For Efficiency

Manager Wants To Assign Tasks To Workstations As Efficien

A manager aims to assign tasks to workstations in the most efficient manner to achieve an hourly output of 3 units. The department operates with a working time of 54 minutes per hour. The goal is to distribute tasks based on the provided precedence diagram, with task durations specified in minutes. The assignment must follow specific rules: (a) prioritize tasks in order of most following tasks with a tiebreaker of greatest positional weight; (b) prioritize tasks based on greatest positional weight; and (c) determine the overall efficiency of the task assignment. The assignment involves analyzing task relationships, computing task times, and optimizing workstation utilization to meet the output and efficiency goals.

Paper For Above instruction

The process of effectively assigning tasks to workstations to optimize productivity involves careful analysis of task times, dependencies, and workstation capacities. In this scenario, the goal is to ensure that the department achieves an hourly output of 3 units while working within a 54-minute work period per hour. To achieve this, the manager must carefully consider the precedence relations among tasks, their durations, and the rules for task assignments, which include prioritization methods such as the number of following tasks and positional weights.

Initially, understanding the tasks and their durations is critical. Assume tasks are labeled T1 through Tn, with known processing times. The precedence diagram illustrates the sequence constraints, indicating which tasks must be completed before others. This diagram helps identify task dependencies and possible sequences for assignment. The main challenge is to allocate tasks to workstations in a way that utilization is maximized without exceeding the workstation capacity, which is constrained by the working time of 54 minutes per hour.

The first prioritization rule involves selecting tasks based on the number of followers—tasks that have the most subsequent tasks are considered first. Ties are broken by the positional weight, a measure indicating the relative importance or influence of a task within the sequence. Tasks with higher positional weights are given precedence when multiple tasks have the same number of followers. This method ensures that the most critical or influential tasks are assigned early, facilitating more efficient workflow and reducing idle times.

The second rule shifts focus directly to the positional weights, choosing tasks with the greatest weights for assignment. This approach emphasizes the importance of task influence over simply the number of followers, helping to streamline the sequence based on task criticality. Once tasks are prioritized according to these rules, they are grouped into workstations, aiming to fill each workstation’s capacity of 54 minutes as closely as possible without exceeding it.

Determining the efficiency involves calculating the total time spent on tasks divided by the total available workstation time, then multiplying by 100 to get a percentage. Since the problem requests the efficiency percentage without the percent sign and rounded to two decimal places, the final calculation provides a clear measure of how well the task assignment utilizes available time.

In practice, after assigning tasks based on the given rules and constraints, the efficiency can be computed as:

Efficiency = (Sum of task times assigned to workstations) / (Number of workstations × workstation capacity) × 100

Assuming all tasks are assigned optimally, this process results in an effective balance between workload and capacity, minimizing idle time and maximizing output.

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