Relaxation Inc. is a furniture company that manufactures desks and chairs for offices. They have forecasted...
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Relaxation 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: Ordering Policy: Par A Qty: 2 July August DESKS Figure 1: Product Structure Tree 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. Month, Year Forecasted 2022 Demand Part 120 160 September 210 October 230 Table 1: Parts Requirements Part A 5 1 month 100 Minimum 500 parts November 310 December 360 Part D Qty: 1 Desk 400 400 450 500 Part B 8 600 600 Part C Qty: 3 2 months 30 none 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 Part C 4 2 months Part A 170 140 150 140 130 160 none 215 205 195 200 200 Production Cost/Unit Part B Part C 220 70 288822 80 Part E 90 20 Part D 7 1 month 40 none 80 80 Part E 2 2 months Part D 110 130 170 210 180 190 none ㎡ Part E 50 40 55 45 60 35 a. Formulate this problem as a linear, integer, or mixed integer, or goal 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? c. How many desks and parts are maintained in inventory monthly, and what is the total inventory cost for the whole half-year for each part? d. What is the total profit? e. Suppose that the ordering policy for part B changed to be only in multiples of 100 (i.e., the order comes in boxes of 100 parts each), how can your model be modified? Explain the new decision variables, objective function, and constraints, if any. Solution in Solver/Lingo is not required. f. The company is facing worker shortage in the very busy last quarter of the year, and they cannot produce desks to their full capacity anymore. The total hours available to produce desks is 1000 hours for each of the four months. However, there is enough time and capacity to produce all the necessary assembly parts. Each desk requires 4 hours of work to be produced. For every desk not delivered on time, the company will give out a voucher of 100 SR value to each customer as an apology, and the order will be canceled. Revise your formulation to reflect the new changes. Explain the new decision variables, objective function, and constraints, if any. Solution in Solver/Lingo is not required. Relaxation 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: Ordering Policy: Par A Qty: 2 July August DESKS Figure 1: Product Structure Tree 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. Month, Year Forecasted 2022 Demand Part 120 160 September 210 October 230 Table 1: Parts Requirements Part A 5 1 month 100 Minimum 500 parts November 310 December 360 Part D Qty: 1 Desk 400 400 450 500 Part B 8 600 600 Part C Qty: 3 2 months 30 none 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 Part C 4 2 months Part A 170 140 150 140 130 160 none 215 205 195 200 200 Production Cost/Unit Part B Part C 220 70 288822 80 Part E 90 20 Part D 7 1 month 40 none 80 80 Part E 2 2 months Part D 110 130 170 210 180 190 none ㎡ Part E 50 40 55 45 60 35 a. Formulate this problem as a linear, integer, or mixed integer, or goal 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? c. How many desks and parts are maintained in inventory monthly, and what is the total inventory cost for the whole half-year for each part? d. What is the total profit? e. Suppose that the ordering policy for part B changed to be only in multiples of 100 (i.e., the order comes in boxes of 100 parts each), how can your model be modified? Explain the new decision variables, objective function, and constraints, if any. Solution in Solver/Lingo is not required. f. The company is facing worker shortage in the very busy last quarter of the year, and they cannot produce desks to their full capacity anymore. The total hours available to produce desks is 1000 hours for each of the four months. However, there is enough time and capacity to produce all the necessary assembly parts. Each desk requires 4 hours of work to be produced. For every desk not delivered on time, the company will give out a voucher of 100 SR value to each customer as an apology, and the order will be canceled. Revise your formulation to reflect the new changes. Explain the new decision variables, objective function, and constraints, if any. Solution in Solver/Lingo is not required.
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Data Analysis and Decision Making
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