Support System for Production Scheduling. Solve this Mixed-Integer Programming Model problem with using following informations- notations and following Excel Spreadsheets that you can see in the question. Make assumptions for calculation. Build a model that suits to our following mathematichal formulas maybe. You can use estimated numbers and estimated examples, only the model you will set up must comply with mathematical operations (impressions like: minimization objective function and our constraints.) Please show screenshots of Excel formulas with Excel solutions. Important note: This problem was referenced by the optimization book Winston L.W., Operations Research: Applications and Algorithms. Duxbury Press, 3rdEd., 1994.) Other important note: Dynamic Capacitated Lot Sizing problem that you may find in the book also has mathematichal impressions like this one. It has also a model that suits the mathematichal impressions. Maybe this helps. Show that the assumptions. Submit everything that you wrote down to paper for calculation and your Excel solving.

Problem Description The aim of this project is to create a decision support system that will help the process of scheduling production in a manufacturing environment. We present here a simple example that demonstrates the challenges faced by the managers of a wood furniture manufacturing company when preparing a production schedule. The company produces a number of products such as different designs of wood desks, chairs, drawers, etc. The raw material used in the production process is oak wood. In the process of producing the final product, the raw materials (wood logs) have to go through a number of machineries. Not every machine is used in the process of producing a particular product. There is a limitation in the number of products that can be processed in each machine because of capacity constraints. There are limitations in the availability of raw materials, and finally there are limitations in the total number of final products produced because of the storage space. The managers are concerned about allocating the resources available (raw material and machines) to final products. Since demand for their products has been growing lately, the managers are interested in identifying ways to increase production. The following are alternatives they want to explore: increase the amount of raw materials available in the case that machines are not fully utilized, buy new machines, rent more space, etc Below we present a mixed-integer programming model that solves this resource allocation problem. Mixed-Integer Programming Model We use the following notation: The objective is to minimize the total production costs, manufacturing costs, and machine setup costs. The first set of constraints shows that the total amount of time machine j is used should be less than the corresponding production capacity. The second set of constraints shows that the raw material available should be used. The third set of constraints shows that there is an upper bound on the amount of product i produced. Excel Spreadsheets 1. Build a spreadsheet that presents the unit manufacturing costs and the production upper bound for product i(i=1,,P). 2. Build a spreadsheet that presents the fixed set-up costs and production capacity for machine j(j=1,,n). 3. Build a spreadsheet that presents the amount of raw material used to produce one unit of product i(i=1,,P). 4. Build a spreadsheet that presents the total amount of processing time product i requires on machine j(i=1,,P;j=1,,n). Problem Description The aim of this project is to create a decision support system that will help the process of scheduling production in a manufacturing environment. We present here a simple example that demonstrates the challenges faced by the managers of a wood furniture manufacturing company when preparing a production schedule. The company produces a number of products such as different designs of wood desks, chairs, drawers, etc. The raw material used in the production process is oak wood. In the process of producing the final product, the raw materials (wood logs) have to go through a number of machineries. Not every machine is used in the process of producing a particular product. There is a limitation in the number of products that can be processed in each machine because of capacity constraints. There are limitations in the availability of raw materials, and finally there are limitations in the total number of final products produced because of the storage space. The managers are concerned about allocating the resources available (raw material and machines) to final products. Since demand for their products has been growing lately, the managers are interested in identifying ways to increase production. The following are alternatives they want to explore: increase the amount of raw materials available in the case that machines are not fully utilized, buy new machines, rent more space, etc Below we present a mixed-integer programming model that solves this resource allocation problem. Mixed-Integer Programming Model We use the following notation: The objective is to minimize the total production costs, manufacturing costs, and machine setup costs. The first set of constraints shows that the total amount of time machine j is used should be less than the corresponding production capacity. The second set of constraints shows that the raw material available should be used. The third set of constraints shows that there is an upper bound on the amount of product i produced. Excel Spreadsheets 1. Build a spreadsheet that presents the unit manufacturing costs and the production upper bound for product i(i=1,,P). 2. Build a spreadsheet that presents the fixed set-up costs and production capacity for machine j(j=1,,n). 3. Build a spreadsheet that presents the amount of raw material used to produce one unit of product i(i=1,,P). 4. Build a spreadsheet that presents the total amount of processing time product i requires on machine j(i=1,,P;j=1,,n)