Comfort Inc. is a furniture company that manufactures desks and chairs for offices. They have forecasted...

  

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Comfort Inc. is a furniture company that manufactures desks and chairs for offices. They have forecasted the demand of desks and chairs for the second half of this year, and currently they are at the planning phase for production. They figured out the manufacturing plan for their chairs, however they are still struggling to determine the optimal production schedule for their desks. Each desk is made up of three main assembly parts: A, B, and C. Part C is assembled from two other parts: D and E. Figure 1 shows the hierarchy of parts and the number of each used in assembling a single desk. Inventory Cost: Lead Time: Current Inventory: Part A Qty: 2 Ordering Policy: Part A 5 1 month Table 1 shows the monthly inventory cost per unit, the lead time, which is the time between when the part is ordered until it is received, the current inventory, and finally the ordering policy for each part. Notice that desks do not have inventory cost. 100 Minimum 500 parts (If an order is made for this part in a month, it will be for at least 500 parts) DESKS Qty: 1 Part B Qty: 1 Part D Qty: 1 Figure 1: Product Structure Tree 30 Table 1: Parts' Requirements Part B 8 2 months Part C Qty: 3 Any Amount Part C 4 2 months 0 Any Amount Part E Qty: 2 Part D 7 1 month 40 Any Amount Part E 2 2 months Any Amount The forecasted monthly demand for desks and the monthly production cost per unit of each part is given in table 2. Each desk is sold for 3000 Saudi Riyals. Table 2: Monthly Demand and Production Cost Month, Year Forecasted 2022 Demand July August 120 160 September 210 October 230 November 310 December 360 Desk 400 400 450 500 600 600 Part A 170 140 150 140 130 160 Production Cost / Unit Part B Part C 220 215 205 195 200 200 70 80 90 20 80 80 Part D 110 130 170 210 180 190 Part E 1892486 50 40 55 45 60 35 Answer the following questions: a. Formulate this problem as a linear, integer, or mixed integer program to maximize the total profit and determine the optimum number of parts to be produced each month. Make sure to define and explain the decision variables, objective function, and constraints. b. How many desks and parts of each should be made available monthly, and when should production start considering the Lead Time? Comfort Inc. is a furniture company that manufactures desks and chairs for offices. They have forecasted the demand of desks and chairs for the second half of this year, and currently they are at the planning phase for production. They figured out the manufacturing plan for their chairs, however they are still struggling to determine the optimal production schedule for their desks. Each desk is made up of three main assembly parts: A, B, and C. Part C is assembled from two other parts: D and E. Figure 1 shows the hierarchy of parts and the number of each used in assembling a single desk. Inventory Cost: Lead Time: Current Inventory: Part A Qty: 2 Ordering Policy: Part A 5 1 month Table 1 shows the monthly inventory cost per unit, the lead time, which is the time between when the part is ordered until it is received, the current inventory, and finally the ordering policy for each part. Notice that desks do not have inventory cost. 100 Minimum 500 parts (If an order is made for this part in a month, it will be for at least 500 parts) DESKS Qty: 1 Part B Qty: 1 Part D Qty: 1 Figure 1: Product Structure Tree 30 Table 1: Parts' Requirements Part B 8 2 months Part C Qty: 3 Any Amount Part C 4 2 months 0 Any Amount Part E Qty: 2 Part D 7 1 month 40 Any Amount Part E 2 2 months Any Amount The forecasted monthly demand for desks and the monthly production cost per unit of each part is given in table 2. Each desk is sold for 3000 Saudi Riyals. Table 2: Monthly Demand and Production Cost Month, Year Forecasted 2022 Demand July August 120 160 September 210 October 230 November 310 December 360 Desk 400 400 450 500 600 600 Part A 170 140 150 140 130 160 Production Cost / Unit Part B Part C 220 215 205 195 200 200 70 80 90 20 80 80 Part D 110 130 170 210 180 190 Part E 1892486 50 40 55 45 60 35 Answer the following questions: a. Formulate this problem as a linear, integer, or mixed integer program to maximize the total profit and determine the optimum number of parts to be produced each month. Make sure to define and explain the decision variables, objective function, and constraints. b. How many desks and parts of each should be made available monthly, and when should production start considering the Lead Time?

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