A component used in a manufacturing facility is ordered from an outside supplier. Estimated demand (in thousands) over the next 10 weeks is in the table below. The components cost 55 cents each and the interest rate used to compute the holding cost is 0.5% per week. The fixed order cost is estimated to be $300. Week 1 2 3 4 5 6 7 8 9 10 Demand 22 34 32 12 8 44 54 16 76 30 Determine the lot sizes using part period balancing.
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A component used in a manufacturing facility is ordered from an outside supplier. Estimated demand (in thousands) over the next 10 weeks is in the table below. The components cost 55 cents each and the interest rate used to compute the holding cost is 0.5% per week. The fixed order cost is estimated to be $300.
Week |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
Demand |
22 |
34 |
32 |
12 |
8 |
44 |
54 |
16 |
76 |
30 |
- Determine the lot sizes using part period balancing.
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- In Problem 12 of the previous section, suppose that the demand for cars is normally distributed with mean 100 and standard deviation 15. Use @RISK to determine the best order quantityin this case, the one with the largest mean profit. Using the statistics and/or graphs from @RISK, discuss whether this order quantity would be considered best by the car dealer. (The point is that a decision maker can use more than just mean profit in making a decision.)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?The annual demand for a product of XYZ company is 12.000. The cost of ordering this product is CU25 and the holding cost is CU0.5/(piece year). The company in question wishes to follow the "Pending Order" stock policy and the holding cost is CU5/(piece year). The lead time for this product is 2 days and it is worked for 300 days a year. In this case, calculate the economic order quantity, the highest pending order quantity and the highest stock level3-2) The optimal quantity of the three products and resulting revenue for Taco Loco is: A) 28 beef, 80 cheese, and 39.27 beans for $147.27. B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27. C) 1.45 Z, 8.36 Y, and 0 Z for $129.09. D) 14 Z, 13 Y, and 17 X for $9.81. 3-3) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix? A) 26 to 38.22 pounds B) 27.55 to 28.45 pounds C) 17.78 to 30 pounds D) 12.22 to 28 pounds
- A book shop is planning to order calendars for sale starting in October. Only one order is placed. The calendars cost $1.50 and the shop sells them for $3 each. At the end of December, the shop reduces the calendar price to $1 and can sell all the surplus calendars at this price. The October-to-December demand can be approximated by a normal distribution with = 500 calendars and = 120 calendars.1. What inventory model should be used to determine the order quantity to maximize the total expected proÖt? Why?2. What is the optimal service level?3. How many calendars should the shop order so as to maximize the total expected proÖt?The "Footcandy" shoes store supplies men's black formal shoes. Every 3 months the "Footcandy" shoes store can sell approximately 500 pairs of shoes at a constant price. The store is currently ordering 500 everytime they order. It costs $ 30 to place the order. 20% is the annual rate for the storage fee. With an order of 500 pairs of shoes, the store got the lowest price at $ 28 per pair. The order quantity discounts offered by the manufacturer are as follows Quantity Price 1 0-99 $36 2 100-199 $32 3 200-299 $30 4 300 $28 a. What is the minimum cost order amount for the shoes? b. What is the annual savings from Footcandy Store?1. At the beginning of each semester, BOOKY can order 60, 80, or 100 copies of the book from the publisher, each with differing discounts per book. The ordering costs are listed in the following table. Number of Books Ordered 60 80 100 Ordering Costs 6100 7700 9100 2. BOOKY can either sell the book at the retail price ($130 per copy) or offer a 10% discount ($117 per copy). The demand distributions under different selling prices are listed in the following tables. The demand distribution for the textbook when the selling price is $130 per copy. Demand Probability 70 0.6 90 0.4 The demand distribution for the textbook when the selling price is $117 per copy. Demand Probability 80 0.15 100 0.85 3. Any unmet demand for the textbook will be irrecoverable There are two decision variables in this decision problem: the ordering quantity and the selling price of the textbook. a) If BOOKY is allowed to return unsold textbooks to the publisher for a refund of…
- The campus store at a large Midwestern university sells writing tablets to students, faculty, and staff. They sell more tablets near exam time. During a typical 10-week quarter,the pattern of sales is 2,280, 1,120, 360, 3,340, 1,230, 860, 675, 1,350, 4,600, 1,210.Thepads cost the store $1.20 each, and holding costs are based on a 30 percent annual interest rate. The cost of employee time, paperwork, and handling amounts to $30 per order.Assume 50 weeks per year.b. The bookstore manager has decided that it would be more economical if thedemand were the same each week. In order to even out the demand he limits weeklysales (to the annoyance of his clientele). Hence, assume that the total demand forthe 10-week quarter is still the same, but the sales are constant from week to week.Determine the optimal order policy in this case and compare the total holding andordering cost over the 10 weeks to the answer you obtained in part (a). (You may assume continuous time for the purposes of your…The campus store at a large Midwestern university sells writing tablets to students, faculty, and staff. They sell more tablets near exam time. During a typical 10-week quarter,the pattern of sales is 2,280, 1,120, 360, 3,340, 1,230, 860, 675, 1,350, 4,600, 1,210.Thepads cost the store $1.20 each, and holding costs are based on a 30 percent annual interest rate. The cost of employee time, paperwork, and handling amounts to $30 per order.Assume 50 weeks per year.a. What is the optimal order policy during the 10-week quarter based on theSilver–Meal heuristic? Using this policy, what are the total holding and orderingcosts incurred over the 10-week period?The Chisokone Company located in Chimwemwe manufactures typewriters called AK4 model Z. The company has an average total inventory of K15, 000,000 and places 12,000 orders every year. Order details are as follows:Purchase department expenses……………………………..K400, 000Stores warehouse personnel salary……………………......K400, 000Obsolescence, spoilage, etc…………………………………K120, 000Floor space charge related to stores activities…………….K260, 000Cost of collecting materials…………………………………..K60, 000Cost of receiving materials…………………………………...K70, 000Cost of Inspection……………………………………………..K100, 000Cost of material handling for warehousing activities………K300, 000Cost of bill payment……………………………………………K170, 000Interest…………………………………………………………..11.5%Insurance charges………………………………………………1.9%The company wants to buy a certain component, whose cost is K24 each and the annual requirement is 34,560 units. Calculate the following:i. The cost of carrying inventory as a percentage of inventory ii. The carrying cost as a…