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In a lean environment, the batch-size decision for planning “A” items would be done by lot-for-lot (L4L). L4L is an inventory management technique that orders exactly the quantity needed to meet the demand for each period. This minimizes the work in process, cycle time, and inventory holding costs. L4L is consistent with the lean principles of reducing batch sizes, eliminating waste, and responding to customer pull. The other options are not suitable for a lean environment, as they either order more than the demand (least total cost, min-max system, periodic order quantity) or incur more setup costs (least total cost, periodic order quantity). References:

•[CPIM Part 2 - Section A - Topic 3 - Lean and Just-in-Time]

•Optimize Production Batch Sizes

•How to determine your Lot Size - Part 1

Mixed-model scheduling is a technique that allows multiple products to be produced on the same assembly line without changeovers, and then sequences those products in a way that smoothes the demand for upstream components12. In this case, the company is using mixed-model scheduling to produce three different products (A, B, and C) on the same line, and then alternating them in a pattern that minimizes the variation in the workload and the inventory levels. The other options are not correct because:

•Matrix scheduling is a technique that assigns tasks to workers based on their skills and availability3.

•Synchronized scheduling is a technique that coordinates the production and delivery of materials and components to match the demand of the final assembly4.

•Line balancing is a technique that distributes the workload evenly among the workers or machines on a production line5. References := 1 Create Mixed Model Flow in 5 Steps | Industrial Equipment News 2 Mixed Model Scheduling - Mountain Home Academy 3 Matrix Scheduling - an overview | ScienceDirect Topics 4 Synchronized Scheduling - an overview | ScienceDirect Topics 5 Line Balancing - an overview | ScienceDirect Topics

The mean time between failures (MTBF) is the inverse of the failure rate. The failure rate is given as 0.00055 failures per hour, so the MTBF is 1/0.00055 = 1,818.2 hours. This means that the average time the machine operates without failing is 1,818.2 hours. References: MTBF Formula | How to Calculate Mean Time Between Failure? - EDUCBA, Mean time between failures - Wikipedia

Fishbone diagrams would help a service organization determine the source of a quality-of-service issue. A fishbone diagram, also known as a cause-and-effect diagram or an Ishikawa diagram, is a tool for identifying and analyzing the root causes of a problem or an effect. It uses a fish-shaped diagram to display the potential causes of a problem in different categories, such as people, processes, equipment, environment, etc. A fishbone diagram can help a service organization to determine the source of a quality-of-service issue by allowing the organization to brainstorm and organize the possible factors that may affect the quality of the service delivered to the customers, such as staff training, customer feedback, service standards, equipment maintenance, etc. A fishbone diagram can also help the organization to prioritize and test the most likely causes, and to develop and implement solutions to improve the quality of service12. References: 1 What is a Fishbone Diagram? Ishikawa Cause & Effect Diagram | ASQ 3 2 CPIM Exam References - Association for Supply Chain Management 1