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I have this document with problem and solution attached. All I need is to translate the picture of the Excel document into an actual Excel
I have this document with problem and solution attached. All I need is to translate the picture of the Excel document into an actual Excel document with the necessary formulas in the right places and the right figures in the right places, etc.
There is a picture of an Excel file with the solution. I need an actual Excel file of the solution.
I need this within the next 30 minutes. Thank you!
Buckeye Manufacturing produces heads for engines used in the manufacture of trucks. The production line is highly complex, and it measures 900 feet in length. Two types of engine heads are produced on this line: the P-Head and the H-Head. The P-Head is used in heavy-duty trucks and the H-Head is used in smaller trucks. Because only one type of head can be produced at a time, the line is either set up to manufacture the P-Head or the H-Head, but not both. Changeovers are made over a weekend; costs are $500 in going from a setup for the P-Head to a setup for the H-Head, and vice versa. When set up for the P-Head, the maximum production rate is 100 units per week and when set up for the H-Head, the maximum production rate is 80 units per week. .:. Managerial Report Prepare a report for Buckeye's management with a production and changeover schedule for the next eight weeks. Be sure to note how much of the total cost is due to production, how much is due to inventory, and how much is due to changeover. SOLUTION: A mixed integer programming model can be used advantageously to assist in developing recommendations. We describe such a model here; it has 48 decision variables and 64 constraints. We show here how to use Microsoft Excel to formulate and solve the problem. The spreadsheet at the end shows how we set up the problem and the optimal solution. We describe the model now. Variables There are variables for production, inventory, setup, and changeover in each week. Pi = number of P-Heads produced in week i Hi = number of H-Heads produced in week i IPi = number of P-Heads in inventory at end of week i IHi = number of H-Heads in inventory at end of week i SPi = 1 if line is setup for P in week i, 0 if setup for H Changei = 1 if a changeover occurs at the beginning of week i, 0 otherwise Constraints There are constraints for production capacity, inventory balance, maintenance of safety stock, and enforcement of changeovers. Also, Excel requires that you identify the 0-1 (binary) variables in the Solver dialog box. The constraints as specified in the Excel Solver dialog box are as follows (references are to cells of the spreadsheet): B20:C27 B34:C41 production capacity, or nonnegativity of slack G20:G27 H34:H41 forces Changei to 1 when a changeover occurs G20:G27 I34:I41 D20:E27 D6:E13 ending inventory safety stock D34:E41 = B6:C13 beg. inv. + production - end inv. = demand F18:F25 = Bin setup variables must be binary Even though the Changei variable must also be integer it is not necessary to require it because minimization will never let it be any bigger than it has to be. And, the second set of constraints force it to be 1 whenever the setup variable changes from 1 to 0 or from 0 to 1. Objective We want to minimize total cost which is represented by cell J23 in the spreadsheet. It is the sum of production cost, inventory cost, and changeover cost. The Spreadsheet The first 14 rows of the spreadsheet contain the data for the problem; information on demand, safety stock, various costs and beginning inventories are given. Cells B20:G27, as shown contain the optimal solution to the problem. Before solving, those cells were empty. The spreadsheet formulation and solution are shown. A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Week 28 29 30 31 32 33 34 35 36 37 38 39 40 41 C D Product Demand P H P 1 2 3 4 5 6 7 8 9 15 16 Model 17 18 19 Week 20 21 22 23 24 25 26 27 B E F G H I J Production Scheduling 1 2 3 4 5 6 7 8 Week 1 2 3 4 5 6 7 8 55 55 44 0 45 45 36 35 35 P Safety Stock 38 38 30 0 48 48 58 57 58 H 18.00 100.00 100.00 0.00 0.00 0.00 0.00 0.00 Production Capacity P H 100 100 100 0 0 0 0 0 44 35.2 0 36 36 28.8 28 28 Inv. P 0.00 0.00 0.00 1.40 48.00 56.00 57.20 57.80 0 0 0 80 80 80 80 80 P H 88.00 133.00 189.00 189.00 144.00 99.00 63.00 28.00 30.4 24 0 38.4 38.4 46.4 45.6 46.4 Inv. H Setup P 105.00 67.00 37.00 38.40 38.40 46.40 45.60 46.40 Inventory Balance Beginning Inv. + Prod. Ending Inv. P H 55 55 44 0 45 45 36 35 H Production Cost 225 310 Max Weekly Rate Changeover Cost Weekly Inv. Rate Weekly Inv. Cost Beginning Inv. 100 500 0.00375 0.84375 125 80 500 0.00375 1.1625 143 Prod. Cost Inv. Cost Changeover Cost Min Total Cost 117374 1280.35125 500 119154.3513 Changeover 1.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 38 38 30 0 48 48 58 57 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 Week 1 2 3 4 5 6 7 8 Changeover Def. To P if 1 To H if 1 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 Solution Comments The spreadsheet contains the optimal solution. The minimum total cost is $119,154.35. The components of that cost are production: $117,374, inventory: $1280.35 and changeover: $500. From cells F20:F27 we see that the line will be setup to produce PHeads in weeks 1-3 and H-Heads in weeks 4-8. Cell G23 shows that there will be a changeover from producing P-Heads to H-Heads at the beginning of week 4. By adjusting the data for this problem (e.g. beginning inventories and the various costs) a number of variations of this problem can be created with the same basic model. Also, one might want to vary the safety stock requirements and the number of weeks in the planning horizon to create other variations of theStep by Step Solution
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