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Lawnvana's Broadcast Spreader Assembly Operations:

Lawnvana Inc. manufactures a number of lawncare products at its plant in Chicago, Illinois. Recently hired general manager, Mike Portis, is concerned about the large inventories and manufacturing inefficiencies in the plant. The Chicago plant has several separate assembly lines for each of its products. Demand for one of its key products - the broadcaster spreader - has recently seen declining demand and the company has been losing customers to one of its main competitors - The Scott's Miracle-Gro Company. Given this information, Mike decides to tackle the broadcast spreader assembly process first. Mike has recently hired a summer intern, Eileen Mayer, who he asks to study the broadcast spreader assembly line and suggest ways to improve the process. Having recently completed a course on operations management, Eileen decides to create value stream map for the process. Over a period of several days, she collects the following information about the process.

The Assembly Line: The assembly line operates one 8-hour shift per day, 6 days a week.

The Product: Lawnvana makes one type of broadcast spreader. The product is typically used by homeowners and lawncare business owners to spread grass seed, fertilizer and other lawncare products. Lawnvana sells this product exclusively through retailer BigMart. The product is pictured below:

Demand for the spreaders is about 1500 spreaders per week.

Raw material storage: Raw material for the broadcast spreader assembly line consists of long metal tubes, bucket subassemblies and wheel subassembly. Both the bucket subassembly and the wheel subassembly are manufactured in the Forming Department elsewhere in the plant. The bucket subassemblies are made in batches of 1000 and brought to the assembly area and on average the amount of buckets in inventory is 500.

The wheel subassemblies are made in batches of 1500 and brought to the assembly area and on average the amount of wheel subassembly inventory is 750.

The long metal tubes are delivered by steel supplier, Steely Hollow, every week in batches of 3000 tubes, so there are on average 1500 tubes in inventory. In addition, there are screws, nuts, short bent metal tubes, release levers and cardboard boxes that are required. These are ordered in large bulk quantities and stored at the respective assembly stations. Because these parts are purchased in bulk externally, Eileen decides that she will make a note of them but not analyze them further.

The Manufacturing Process: To maintain correct alignment during assembly, at each stage of the manufacturing process, processing is done on a one-to-one basis. In other words, a single finished broadcast spreader is comprised of the following: 1 long metal tube, 1 bucket subassembly, 1 wheel and spreader subassembly, 1 spreader stand and 1 release lever. The manufacturing process in its order of operations is described below:

Long Metal Tube Bending: In this operation, the pre-hole-punched long metal tubes are bent in the shape of an U. There is no set-up required for this operation. Once tubes are bent into shape, the width is 12 inches and the length is 36 inches. The tube bending operation requires 3 minutes per metal tube and there are 3 bending stations. There are, on average, 600 long bent metal tubes waiting for the next processing step.

Bucket Assembly: In this operation, the spreader bucket is attached to the bottom portion of bent metal tubes with screws and nuts. There are 3 screws that are required for each side of the metal tube during this semimanual operation.It takes 4 minutes per spreader bucket and there are three assembly stations. At the end of this activity, there are 750 units in the work-in-process storage area waiting for the next operation.

Wheel Assembly: This subassembly is comprised of 2 wheels, and metal axis and a rotary mechanism that fits underneath the bucket. It is attached with screws and nuts to the ends of the bent metal tube. There are 3 stations in parallel for the operation. Each wheel subassembly requires 4 minutes to be attached to the bucket subassembly. Eileen observes that, on average, there are 1,020 units waiting ahead of the spreader stand operation.

Stand Assembly: A single short bent metal tube needs to be attached so that the spreader can stand on its own. This tube will be attached by inserting screws into the underside of the long metal bent tube. There is only one spreader stand assembly station and assembly. Eileen observes that within 1 hr, approximately 40 spreader stands can be attached. There are no setups required. Assembled units are sent to the release lever assembly on roller conveyors as soon as they are assembled and there is no intermediate inventory.

Release Lever Assembly: Release levers are attached to the assembled units and it takes 2 minutes to do the operation. There are 2 stations for release lever assembly. Units with levers attached are transported immediately on a rolling conveyor to packing to avoid damage to the finished broadcast spreaders.

Packaging: Incoming broadcast spreaders are packed in a cardboard box for shipping. Each spreader requires approximately 165 seconds to be boxed and there are two packaging stations. Packaged broadcast spreaders are shipped to BigMart once every two weeks. On average, therefore, there are about 1,500 packaged broadcast spreaders waiting to be shipped.

Planning and Scheduling: To understand how the different stations received instructions about their daily schedules, Eileen spent a day with the production planning department. She learned that BigMart sends a monthly forecast of demand for broadcast spreaders electronically on the 25th of each month. In addition, a set order for the week's requirement is faxed to Lawnvana on the previous Wednesday. Lawnvana's, planning department then looks at inventories and creates a work order for the week and a paper schedule is given to each station, except the Stand Assembly and Packaging stations. The planning department also sends a weekly order for long metal tubes (electronically) to Steely Hollow, and orders for buckets and wheel subassemblies (also electronically) to the Forming Department elsewhere in the plant.

To assist Eileen please answer the following questions.

1.Draw a Value Stream Map for the broadcast spreader assembly line. Show all activity steps, material flows, information flows and inventories. Draw a timeline showing processing times and waiting times.

(You may use any drawing package including powerpoint to create legible chart. You can also use a package such as Visio or Lucidcharts to draw your chart. You will need to make a free account to use Lucidcharts software

https://www.lucidchart.com/pages/examples/value-stream-mapping-software

2.Calculate the Takt time in minutes for the spreader assembly process (1 point)

3.For each step of the assembly process, calculate the cycle time in minutes and the capacity utilization (2 points)

4.Calculate the total lead time and total processing time in days, hours and minutes

5 Random variables X and yare independent random variables. The random variable x has chi- square distribution with 1 degree of freedom . The sum of random variables Xty has a chi- square distribution with 3 degrees of freedom. a,) The random variable yhas a distribution. I, normal II. Chebychev's V. F IL. binomial II. chi-square II. Not enough inform. b. The random variable yhas degrees of freedom I. D II. 2 V.4 I.1 IV.3 VI Not enough informationProb. 5 (20 points) (a) Let X be a random variable with pdf given by fx (x) = ex, x > 0. Find the CDF of the random variable Y = e and, hence, give an algorithm to generate a random variable Y. (b) A random variable is generated from X = FX1(U) = [-In(1 - U)]1/8, where U is a standard uniform random variable. Find the PDF of the random variable X