Transtech Inc Produces Custom Transformers Per Order

Transtech Inc Produces Transformers Each Order Is Custom Designed And

Transtech Inc produces transformers. Each order is custom designed and manufactured for the customer. Each order goes through 3 phases: 1. Transformer Design, which takes 2 weeks 2. Procurement, which has a lead time of 8 weeks. 3. Assembly and testing, which takes 6 weeks. The design group can handle only 4 projects at any given time. The other groups are not capacity constrained. How many projects is Transtech able to complete per year? How much total work-in-process (number of projects started but not yet completed) does the company typically have? (Hint: Little's Law)

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Transtech Inc, a manufacturer of custom-designed transformers, operates under a multi-phase production process with distinct lead times and capacity constraints. The core challenge is to determine the company's annual project throughput and the typical work-in-process (WIP) inventory, given the capacity constraints and process durations. Applying principles from production management and queuing theory, specifically Little’s Law, facilitates an analytical approach to these questions.

Understanding the process phases and their durations is critical. The production process comprises three sequential phases:

• The design phase: lasting 2 weeks.
• Procurement phase: with an 8-week lead time.
• Assembly and testing phase: taking 6 weeks.

It’s important to recognize that while the design phase is capacity-constrained, with only 4 projects handled simultaneously, the other phases—procurement and assembly/testing—are not capacity-constrained. This implies that the overall throughput of completed projects largely depends on the capacity of the design team, as they serve as the bottleneck in the process.

In a production environment governed by a bottleneck, the overall throughput rate—the number of projects completed per unit time—is determined by the bottleneck’s capacity. Here, the design team's capacity constrains the flow. Since each project requires 2 weeks for design, and the team can handle only 4 projects at a time, we need to determine how many total projects can be initiated or completed per year based on this capacity.

The maximum number of projects the design team can handle simultaneously is 4. The cycle time for the design process, which is 2 weeks, indicates how often a new batch of projects can be started. In steady-state operation, the capacity of the design department (the bottleneck) can be expressed as:

Design capacity per week = (Number of projects that can be handled simultaneously) / (Design cycle time)

= 4 / 2 weeks = 2 projects per week.

Using this, the total number of projects completed annually is calculated by multiplying the weekly capacity by the number of weeks in a year (52 weeks):

Annual throughput = 2 projects/week × 52 weeks = 104 projects per year.

This throughput assumes continuous operation and no additional constraints or delays besides capacity limits.

Next, applying Little’s Law (L = λW), where:

• L represents the average number of projects in the system (Work-In-Process, WIP).
• λ (lambda) is the throughput rate (projects completed per unit time).
• W is the average time a project spends in the system (total process time from start to finish).

The total process time (W) is the sum of the durations of all phases:

W = Design (2 weeks) + Procurement (8 weeks) + Assembly & Testing (6 weeks) = 16 weeks.

Given the throughput rate (λ) is approximately 2 projects per week, we can express W as 16 weeks, and thus calculate the average work-in-process (L):

L = λ × W = 2 projects/week × 16 weeks = 32 projects.

This figure represents the average number of projects that are in various stages of completion at any given time, reflecting a steady-state WIP level.

Consequently, Transtech Inc can complete approximately 104 projects annually, constrained primarily by its capacity limit in the design phase, and typically has an average work-in-process inventory of about 32 projects during steady operation.

This analysis underscores the importance of capacity management across different process stages and highlights the utility of Little’s Law in operational planning and capacity utilization assessments.

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