What is the optimal cash filling policy and the associated total inventory ordering and holding cost?
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- Beach Republic Bank operates a network of automated teller machines (ATMs). Cash withdrawals at a particular ATM average approximately $80 per transaction. The average number of withdrawals per ATM is 120 per week. The bank estimates that it costs about $100 to fill the ATM each time regardless of the amount of cash that is added to the machine. Assume that the cost of capital for the bank is 10%, and there are 52 weeks in a year.
- What is the optimal cash filling policy and the associated total inventory ordering and holding cost?
- Suppose that the standard deviation of weekly number of withdrawals is 20 and the lead time to fill an ATM is half a week (3.5 days), how much cash should the bank allocate to an ATM to be 99% confident of not running out of money between deliveries?
- Given the information from parts a and b, what would the cost savings be for reducing the number of ATMs from 100 to 20? Discuss the pros and cons of pooling the cash inventory in this context. What are the implications of pooling inventory for the bank overall? Is this something that should be considered?
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- The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the decision variable cells and the objective cell.The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?
- Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.Ascent, Inc. manufactures hiking boots. Demand for boots is highly seasonal. In particular, the demand in the next year is expected to be 3,000, 4,000, 8,000, and 7,000 pairs of boots in quarters 1, 2, 3, and 4, respectively. With its current production facility, the company can produce at most 6,000 pairs of boots in any quarter. Ascent would like to meet all the expected demand, so it will need to carry inventory to meet demand in the later quarters. Each pair of boots sold generates a profit of ₱1,000 per pair. Each pair of boots in inventory at the end of a quarter incurs ₱400 in storage and capital recovery costs. Ascent has 1,000 pairs of boots in inventory at the start of quarter 1. Ascent's top management has given you the assignment of modeling and analyzing what the production schedule should be for the next four quarters. In particular, you are asked to determine how many pairs of boots to produce in each quarter so that you satisfy the demand in each quarter. While doing…
- John own a local gold market that currently has 9870 x 870 subscriber in Instagram at a quarterly charge of R.O. 20. He notices that if he raises the price of his commodity to R.O. 24, he will lose 9870 subscriber. Assuming that subscriptions are linearly related to the price, what price should Jon charge for a quarterly subscription to maximize his revenue?opOil, a refiner in Indiana, serves three customers near Nashville, Tennessee and maintains consignment inventory (owned by TopOil) at each location. Currently, TopOil uses TL transportation to deliver separately to each customer. Each truck costs $800 plus $250 per stop. Thus delivering to each customer separately costs $1050 per truck. TopOil is considering aggregating deliveries to Nashville on a single truck. Demand at the large customer is 60 tons per year, demand at the medium customer is 24 tons per year, and demand at the small customer is 8 tons per year. Product cost for TopOil is $10,000 per ton and they are using a holding cost of 25 percent. Truck capacity is 12 tons. What is the optimal order quantity to each customer assuming TopOil develops a tailored aggregation policy?The Centurion apartment building in downtown Chicago has a total of 240 rental units. It offers its new tenants an 18-month lease, which is renewed on a month-to-month basis if the tenant chooses to stay longer than 18 months. The leasing office reports that The Centurion signs about 80 leases with new tenants in an average year, and that 60% of tenants who move in end up staying in the building longer than 18 months. On average, the building is 90% occupied. You may assume that a negligible number of tenants break their lease in the first 18 months. What is the average length of stay (in months) for those tenants who stay longer than 18 months (counted from when they first sign their original lease)?
- Cox Electric makes electronic components and has estimated the following for a new design of one of its products: Fixed Cost = $7,000 Material cost per unit = $0.15 Labor cost per unit = $0.10 Revenue per unit = $0.65 Production Volume = 12,000 Per-unit material and labor cost together make up the variable cost per unit. Assuming that Cox Electric sells all it produces, build a spreadsheet model that calculates the profit by subtracting the fixed cost and total variable cost from total revenue, and answer the following questions. (a) Construct a one-way data table with production volume as the column input and profit as the output. Breakeven occurs when profit goes from a negative to a positive value; that is, breakeven is when total revenue = total cost, yielding a profit of zero. Vary production volume from 5,000 to 50,000 in increments of 5,000. In which interval of production volume does breakeven occur? to units (b) Use Goal Seek to find the exact breakeven point.…PROBLEM The management of the Book Warehouse Company wishes to apply the Miller-Orr model to manage its cash investment. They have determined that the cost of either investing in or selling marketable securities is $100. By looking at Book Warehouse’s past cash needs, they have determined that the variance of daily cash flows is $20,000. Book Warehouse’s opportunity cost of cash, per day, is estimated to be 0.03%. Based on experience, management has determined that the cash balance should never fall below $10,000. 1. How much is the cost per transaction?(Use a number, no decimal value, no commas, no currency, no space) * 2. How much is the return point based on the Miller-Orr model of cash management? (Use a number, no decimal value, no commas, no currency, no space) * 3. How much is the upper limit based on the Miller-Orr model of cash management?(Use a number, no decimal value, no commas, no currency, no space) * PLEASE ANSWER ALL QUESTIONS. THANKS!A steel production plant manufactures bands and coils which sell at a profit of $25 and $30 per ton,respectively. The production rate of the plant for bands is 200 tons/hr, and that for coils is 140 tons/hr.Based on the market analysis, it has been identified that the weekly demand is at most 6000 tons and4000 tons for bands and coils, respectively . The plant operates for a maximum of 40 hours per week. 1. In Microsoft Excel, formulate a linear programming model instance for this problem, then solve. 2. Assume that the products need to be painted after manufacturing, and the painting departmentcan paint at a rate of 600 tons per hour for bands and 400 tons per hour for coils. The paintingdepartment works only for 20 hours. Update the linear programming model instance to accom-modate this requirement, and re-solve the problem. 3. The plant is planning to introduce another product “rods” to its production mix with the followingparameters:•Profit/ton = $40•Production volume = 150…