Formulate a mathematical model for KG International.
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KG International produces T-shirts. KG International must decide how many T-shirts to produce each month. The company has decided to use a six-month planning horizon. The
During each month, there is enough production capacity to produce up to 30,000 T-shirts, and there is enough storage capacity to store up to 10,000 T-shirts after demand has occurred. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.)
The forecasted production costs per T-shirt for the next three months are $20, $17, and $22, respectively. The holding cost incurred per T-shirt held in inventory at the end of any month is 10% of the production cost for that month. KG International wants to determine the production
Formulate a mathematical model for KG International.
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- Scenario 3 Ben Gibson, the purchasing manager at Coastal Products, was reviewing purchasing expenditures for packaging materials with Jeff Joyner. Ben was particularly disturbed about the amount spent on corrugated boxes purchased from Southeastern Corrugated. Ben said, I dont like the salesman from that company. He comes around here acting like he owns the place. He loves to tell us about his fancy car, house, and vacations. It seems to me he must be making too much money off of us! Jeff responded that he heard Southeastern Corrugated was going to ask for a price increase to cover the rising costs of raw material paper stock. Jeff further stated that Southeastern would probably ask for more than what was justified simply from rising paper stock costs. After the meeting, Ben decided he had heard enough. After all, he prided himself on being a results-oriented manager. There was no way he was going to allow that salesman to keep taking advantage of Coastal Products. Ben called Jeff and told him it was time to rebid the corrugated contract before Southeastern came in with a price increase request. Who did Jeff know that might be interested in the business? Jeff replied he had several companies in mind to include in the bidding process. These companies would surely come in at a lower price, partly because they used lower-grade boxes that would probably work well enough in Coastal Products process. Jeff also explained that these suppliers were not serious contenders for the business. Their purpose was to create competition with the bids. Ben told Jeff to make sure that Southeastern was well aware that these new suppliers were bidding on the contract. He also said to make sure the suppliers knew that price was going to be the determining factor in this quote, because he considered corrugated boxes to be a standard industry item. Is Ben Gibson acting legally? Is he acting ethically? Why or why not?Scenario 3 Ben Gibson, the purchasing manager at Coastal Products, was reviewing purchasing expenditures for packaging materials with Jeff Joyner. Ben was particularly disturbed about the amount spent on corrugated boxes purchased from Southeastern Corrugated. Ben said, I dont like the salesman from that company. He comes around here acting like he owns the place. He loves to tell us about his fancy car, house, and vacations. It seems to me he must be making too much money off of us! Jeff responded that he heard Southeastern Corrugated was going to ask for a price increase to cover the rising costs of raw material paper stock. Jeff further stated that Southeastern would probably ask for more than what was justified simply from rising paper stock costs. After the meeting, Ben decided he had heard enough. After all, he prided himself on being a results-oriented manager. There was no way he was going to allow that salesman to keep taking advantage of Coastal Products. Ben called Jeff and told him it was time to rebid the corrugated contract before Southeastern came in with a price increase request. Who did Jeff know that might be interested in the business? Jeff replied he had several companies in mind to include in the bidding process. These companies would surely come in at a lower price, partly because they used lower-grade boxes that would probably work well enough in Coastal Products process. Jeff also explained that these suppliers were not serious contenders for the business. Their purpose was to create competition with the bids. Ben told Jeff to make sure that Southeastern was well aware that these new suppliers were bidding on the contract. He also said to make sure the suppliers knew that price was going to be the determining factor in this quote, because he considered corrugated boxes to be a standard industry item. As the Marketing Manager for Southeastern Corrugated, what would you do upon receiving the request for quotation from Coastal Products?Demand for stereo headphones and music players for joggers has caused Nina Industries to grow almost 50 percent over the past year. The number of joggers continues to expand, so Nina expects demand for headsets to also expand, because, as yet, no safety laws have been passed to prevent joggers from wearing them. Demand for the players for this year was as follows: MONTH DEMAND (UNITS) January 4,150 February 4,250 March 3,950 April 4,350 May 4,950 June 4,650 July 5,250 August 4,850 September 5,350 October 5,650 November 6,250 December 5,950 a. Using linear regression analysis, what would you estimate demand to be for each month next year? Using a spreadsheet, follow the general format in Exhibit 3.8. (Do not round intermediate calculations. Round your answers to 2 decimal places.) b. To be reasonably confident of meeting demand, Nina decides to use 3 standard errors of estimate for safety. How many additional units should be held to meet this…
- Rebalance Rebalance (RB) is a New England sneaker manufacturer that plans to release a high per-formance running shoe { the Rebalance Air (RBA) sneaker { in the US. RB divides the US into four major zones, each of which has come back with an estimate of demand. The planning team at RB needs to use this and other information to decide on a manufacturing quantity for the RBA sneaker in Fall 22 (the first season that will see the introduction of the RBA). 1. The RBA is manufactured in Mainland China and costs RB $60 per pair to manufacture. The sneaker retails for $220. So as to protect this nascent new design,RB will not put the sneaker on clearance (if at all needed) until Summer 23 at which point it expects to only recover $52 per sneaker. What service level should RB choose to manufacture to? 2. The East, West, Central and South teams each expect demand of 80,000 units. The demand planning teams in each of these regions are only somewhat accurate so you can expect the coefficient of…Wine Accessories Inc. (WAI) produces two models of corkscrews, the standard model and a deluxe model. WAI follows a level aggregate plan, producing 20,000 corkscrews per month, or 5000 corkscrews per week. Th e MPS is developed in weekly time periods. Th e forecasts for each model and the projected available are shown in the next two tables. Th e replenishment order quantity is 2000 units for the standard model and 1000 units for the deluxe model. Note that you can place multipleorders if a single order is insuffi cient to cover the forecast (you can produce 4000 units of the standard model if necessary, or 2000 or 3000 units of the deluxe model). Remember that total weekly production is limited to 5000 corkscrews. Develop an MPS for each of the products.Leather-All produces a line of handmade leather products. At the present time, the company is producing only belts, handbags, and attache cases. The predicted demand for these three types of items over a six-month planning horizon is as follows: Month No. of Belts Handbags Attache CasesWorking days1 22 2500 1250 2402 20 2800 680 3803 19 2000 1625 1104 24 3400 745 755 21 3000 835 1266 17 1600 375 45 The belts require an average of two hours to produce, the handbags three hours, and the attache cases six hours; all the workers have the skill to work on any item. Leather-All has 46 employees who each have a share in the firm and cannot be fired. There are an additional 30 locals that are available and can be hired for short periods at a higher cost. Regular employees earn $8.50 per hour on regular time, and $14.00 per hour on overtime. Regular time comprises a seven-hour workday and the regular employees will work as much overtime as is available. The additional workers are hired for…
- Lake Grove Confectionaries (LGC) sells chocolates for the holiday season in specially designed boxes. The firm sells four designs, and currently, all packaging is done in the plant as chocolates are manufactured. All manufacturing and packaging for the holiday season are completed before the start of the season. The demand forecast for each of the four designs is normally distributed, with a mean m=10,000 and a standard deviation of s=6,000. Each box costs $15 and is sold for $30. Any unsold boxes are discounted by $9. The cost of holding a box in inventory is $1. What is the expected profit of this policy?Market Company’s policy is to have 30% of the next month's sales on hand at the end of the current month. Projected sales for August, September, and October are 26,000 units, 21,000 units, and 31,000 units, respectively. How many units must be purchased in September?Comfort Plus Inc. (CPI) manufactures a standard dining chair used in restaurants. The demand forecasts for quarter 1 (January–March) and quarter 2 (April–June) are 3700 chairs and 4200 chairs, respectively. CPI has a policy of satisfying all demand in the quarter in which it occurs. The chair contains an upholstered seat that can be produced by CPI or purchased from DAP, a subcontractor. DAP currently charges $12.50 per seat, but has announced a new price of $13.75, effective April 1. CPI can produce the seat at a cost of $10.25. CPI can produce up to 3800 seats per quarter. Seats that are produced or purchased in quarter 1 and used to satisfy demand in quarter 2 cost CPI $1.50 each to hold in inventory, but maximum inventory cannot exceed 300 seats. Define the decision variables needed to model this problem. Give the objection function. Write the constraints. What is the final answer? Explain in detail.
- Develop a production schedule to produce the exact production requirements by varying the workforce size for the following problem. The monthly forecasts for Product X for January, February, and March are 940, 1,520, and 1,230, respectively. Safety stock policy recommends that half of the forecast for that month be defined as safety stock. There are 22 working days in January, 19 in February, and 21 in March. Beginning inventory is 570 units. Manufacturing cost is $170 per unit, storage cost is $5 per unit per month, standard pay rate is $8 per hour, overtime rate is $12 per hour, cost of stock-out is $9 per unit per month, marginal cost of subcontracting is $8 per unit, hiring and training cost is $160 per worker, layoff cost is $260 per worker, and worker productivity is 0.1 unit per hour. Assume that you start off with 44 workers and that they work 8 hours per day. (Leave the cells blank, whenever zero (0) is required. Input all values as positive values. Round up "Workers Required"…Develop a production schedule to produce the exact production requirements by varying the workforce size for the following problem. The monthly forecasts for Product X for January, February, and March are 1,020, 1,480, and 1,180, respectively. Safety stock policy recommends that half of the forecast for that month be defined as safety stock. There are 22 working days in January, 19 in February, and 21 in March. Beginning inventory is 480 units. Manufacturing cost is $160 per unit, storage cost is $6 per unit per month, standard pay rate is $6 per hour, overtime rate is $9 per hour, cost of stockout is $8 per unit per month, hiring and training cost is $140 per worker, layoff cost is $240 per worker, and worker productivity is 0.1 unit per hour. Assume that you start off with 42 workers and that they work 8 hours per day. (Round Workers Required up to the next higher whole number. Round all other variables off to the nearest whole number. Use previous rounded answers as required to…Develop a production schedule to produce the exact production requirements by varying the workforce size for the following problem. Also, evaluate the cost of the schedule. The monthly forecasts for Product X for January, February, and March are 1,000, 1,500, and 1,200, respectively. Safety stock policy recommends that half of the forecast for that month be defined as safety stock. There are 22 working days in January, 19 in February, and 21 in March. Beginning inventory is 500 units. Manufacturing cost is $200 per unit, storage cost is $3 per unit per month (based on expected end-of-month levels), standard pay rate is $6 per hour, overtime rate is $9 per hour, cost of stock-out is $10 per unit per month, marginal cost of subcontracting is $10 per unit, hiring and training cost is $200 per worker, layoff cost is $300 per worker, and worker productivity is 0.1 unit per hour. Assume that you start off with 50 workers and that they work 8 hours per day. Note: Leave the cells blank,…