Case Study 2: Flexible Manufacturing Systems A manufacturing facility has decided to purchase a new, top-of-the-line Flexible Manufacturing System (FMS) to take over a large portion of the production of their widgets manufacturing operation. The company currently makes all its products using a craftsman approach, where a single worker makes each product from beginning to end. Each worker is paid for the time spent in production, and there are three different pay rates, depending on the worker's skill. The company has been in discussions with several manufacturers and have settled on a specific FMS as the best option. This FMS has six stations, each performing different tasks, and a material handling system. The supplier has estimated how much time would be required for each widget at each station. Each station also has an associated operating cost per minute. The attached file Case2Data.xlsx in sheet CandidateParts contains information on each of the 80 candidate parts that the company is considering to produce in the FMS. The data includes average monthly demand for each part, current processing time per unit (in minutes), type of craftsman required, as well as the time required at each station of the FMS per unit (also, in minutes). Separate tables in the same sheet have the operating costs of each station of the FMS per minute and the per minute cost of each type of craftsman (in cents) The company wants to use this information to decide which parts to assign to the new FMS for production, considering they work three shifts of eight hours, seven days a week. This will be the first FMS that this manufacturer purchases. Therefore, they are also interested in developing a method for planning production in the FMS. The company normally plans their production weekly. The attached file Case2Data.xlsx in sheet PartsToPlan contains information on 26 products that are representative of the types of parts that the company is likely to make in the FMS (note, this is not the optimal set of products from the Candidate list). In sheet OrdersToPlan there is information about a typical set of orders for a week, including the product, the amount and the time period (shift) when the order is due Note there are 21 shifts in one week. Note also that no information on tools is provided, this is because the tool magazines in the FMS are large enough to hold all the necessary tools to produce all 26 parts without changes. Hence, you may assume that the time to setup between different products is negligible This company has hired you as a consultant to help them transition part of their craftsman-style pro- duction to the FMS. They want you to recommend a set of products to move to the FMS and propose a methodology and a tool to do the weekly batching of production into shifts. After some preliminary work, you have settled on four specific tasks that you are going to perform. Your job is to perform the four tasks and present a report with your findings. Tasks 1. Write an optimization model in general form to decide which products should be produced in the FMS to maximize the savings, without exceeding the capacity. Hint: The model should be similar to the knapsack model covered in class (except we don't have an obvious bottleneck) Case Study 2: Flexible Manufacturing Systems A manufacturing facility has decided to purchase a new, top-of-the-line Flexible Manufacturing System (FMS) to take over a large portion of the production of their widgets manufacturing operation. The company currently makes all its products using a craftsman approach, where a single worker makes each product from beginning to end. Each worker is paid for the time spent in production, and there are three different pay rates, depending on the worker's skill. The company has been in discussions with several manufacturers and have settled on a specific FMS as the best option. This FMS has six stations, each performing different tasks, and a material handling system. The supplier has estimated how much time would be required for each widget at each station. Each station also has an associated operating cost per minute. The attached file Case2Data.xlsx in sheet CandidateParts contains information on each of the 80 candidate parts that the company is considering to produce in the FMS. The data includes average monthly demand for each part, current processing time per unit (in minutes), type of craftsman required, as well as the time required at each station of the FMS per unit (also, in minutes). Separate tables in the same sheet have the operating costs of each station of the FMS per minute and the per minute cost of each type of craftsman (in cents) The company wants to use this information to decide which parts to assign to the new FMS for production, considering they work three shifts of eight hours, seven days a week. This will be the first FMS that this manufacturer purchases. Therefore, they are also interested in developing a method for planning production in the FMS. The company normally plans their production weekly. The attached file Case2Data.xlsx in sheet PartsToPlan contains information on 26 products that are representative of the types of parts that the company is likely to make in the FMS (note, this is not the optimal set of products from the Candidate list). In sheet OrdersToPlan there is information about a typical set of orders for a week, including the product, the amount and the time period (shift) when the order is due Note there are 21 shifts in one week. Note also that no information on tools is provided, this is because the tool magazines in the FMS are large enough to hold all the necessary tools to produce all 26 parts without changes. Hence, you may assume that the time to setup between different products is negligible This company has hired you as a consultant to help them transition part of their craftsman-style pro- duction to the FMS. They want you to recommend a set of products to move to the FMS and propose a methodology and a tool to do the weekly batching of production into shifts. After some preliminary work, you have settled on four specific tasks that you are going to perform. Your job is to perform the four tasks and present a report with your findings. Tasks 1. Write an optimization model in general form to decide which products should be produced in the FMS to maximize the savings, without exceeding the capacity. Hint: The model should be similar to the knapsack model covered in class (except we don't have an obvious bottleneck)