Concept explainers
Suppose we are considering the question of how much capacity to build in the face of uncertain demand. Assume that the cost is $20 per unit of lost sales due to insufficient capacity, Also assume that there is a cost of $7 for each unit of capacity built. The probability of various demand levels is as follows:
Deman d- X Units | Probability of X |
0 | .05 |
1 | .10 |
2 | .15 |
3 | .20 |
4 | .20 |
5 | .15 |
6 | .10 |
7 | .05 |
- a. How many units of capacity should be built to minimize the total cost of providing capacity plus lost sales?
- b. State a general rule regarding the amount of capacity to build.
- c. What principle does this problem illustrate?
a)
To determine: The number of capacity units required to minimize the total cost of providing capacity plus lost sales.
Introduction:
Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.
Explanation of Solution
Given information:
It is given that the cost of the lost sales is $20 per unit, due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:
Demand - X units | Probability of X |
0 | 0.05 |
1 | 0.10 |
2 | 0.15 |
3 | 0.20 |
4 | 0.20 |
5 | 0.15 |
6 | 0.10 |
7 | 0.05 |
Build 0 units of capacity:
It is calculated by adding capacity cost and penalty cost.
Build 1 unit of capacity:
It is calculated by adding capacity cost and penalty cost.
Build 2 units of capacity:
It is calculated by adding capacity cost and penalty cost.
Build 3 units of capacity:
It is calculated by adding capacity cost and penalty cost.
Build 4 units of capacity:
It is calculated by adding capacity cost and penalty cost.
Build 5 units of capacity:
It is calculated by adding capacity cost and penalty cost.
Build 6 units of capacity:
It is calculated by adding capacity cost and penalty cost.
Build 7 units of capacity:
It is calculated by adding capacity cost and penalty cost.
Hence, the number of capacity units required (that has the minimum total cost of $38) to minimize the total cost of providing capacity plus lost sales is 4 units.
b)
To determine: The general rule regarding the amount of capacity to build.
Introduction:
Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.
Explanation of Solution
Given information:
It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:
Demand - X units | Probability of X |
0 | 0.05 |
1 | 0.10 |
2 | 0.15 |
3 | 0.20 |
4 | 0.20 |
5 | 0.15 |
6 | 0.10 |
7 | 0.05 |
General instruction regarding the amount of capacity to build:
The general instruction regarding the amount of capacity to build is to minimize the total cost of capacity plus lost sales.
c)
To determine: The principle that is illustrated in the problem.
Introduction:
Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.
Explanation of Solution
Given information:
It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:
Demand - X units | Probability of X |
0 | 0.05 |
1 | 0.10 |
2 | 0.15 |
3 | 0.20 |
4 | 0.20 |
5 | 0.15 |
6 | 0.10 |
7 | 0.05 |
Determine the principle that is illustrated in the problem:
In the given problem, the trade-off between excess capacity and lost sales is illustrated.
Want to see more full solutions like this?
Chapter 11 Solutions
OPERATIONS MANAGEMENT IN THE SUPPLY CHAIN: DECISIONS & CASES (Mcgraw-hill Series Operations and Decision Sciences)
- 1: Suppose the company has identified the following three possible demand scenarios: Demand (Units per year) Probability 25,000 0.3 60,000 0.4 100,000 0.3 1. If the capacity is set at 80,000, how much of a capacity cushion is here? What is the capacity utilization? 2. What is the probability of idle capacity if the capacity is 80,000? 3. If it costs $25 per units lost business and $50 to build a unit of capacity, how much capacity should be built to minimize total cost?arrow_forwardAgarwal Technologies was founded 10 years ago. It has been profitable for the last 5 years, but it has needed all of its earnings to support growth and thus has never paid a dividend. Management has indicated that it plans to pay a PO.25 dividend 3 years from today, then to increase it at a relatively rapid rate for 2 years, and then to increase it at a constant rate of 8.00% thereafter. Management's forecast of the future dividend stream, along with the forecasted growth rates, is shown below. Assuming a required return of 11.00%, what is your estimate of the stock's current value? Year 0. 1 3 6. Growth rate NA NA NA NA 50.00% 25.00% 8.00% Dividends PO.000 PO.000 PO.000 P0.250 PO.375 PO.469 PO.506 O P10.45 O P10.99 OP9.94 O P10.72 O P10.19arrow_forwardA manager is trying to decide whether to buy one machine ortwo. If only one machine is purchased and demand provesto be excessive, the second machine can be purchased later.Some sales would be lost, however, because the lead timefor delivery of this type of machine is 6 months. In addition,the cost per machine will be lower if both machines are pur-chased at the same time. The probability of low demand isestimated to be 0.30 and that of high demand to be 0.70. Theafter-tax NPV of the benefits from purchasing two machinestogether is $90,000 if demand is low and $170,000 if demandis high.If one machine is purchased and demand is low, the NPV is$120,000. If demand is high, the manager has three options:(1) doing nothing, which has an NPV of $120,000; (2) subcon-tracting, with an NPV of $140,000; and (3) buying the secondmachine, with an NPV of $130,000.a. Draw a decision tree for this problem.b. What is the best decision and what is its expected payoff?arrow_forward
- 2. A toy manufacturer has three different mechanisms that can be installed in a doll that it sells. The different mechanisms have three different setup costs (overheads) and variable costs and, therefore, the profit from the dolls is dependent on the volume of sales. The anticipated payoffs are as follows. Light Demand 0.25 $325,000 $300,000 -$400,000 Heavy Demand 0.3 Probability Wind-up action Pneumatic action Electrical action Moderate Demand 0.45 $190,000 $420,000 S170,000 $400,000 $800,000 $240,000 a. What is the EMV of each decision alternative? b. Which action should be selected? c. What is the expected value with perfect information? d. What is the expected value of perfect information? e. What is the expected opportunity loss?arrow_forwardCost Estimation; Average Cost Chloe’s Cafe bakes croissants that it sells to local restaurants andgrocery stores. The average costs to bake the croissants are $0.55 for 2,500 and $0.50 for 5,000.Required If the total cost function for croissants is linear, what will be the average cost to bake 4,200?arrow_forwardSuzy's Temporary Employee (STE) business, located in a big city, can do an online criminal background check in-house for $1.95 per search with a fixed cost of $23,000. A third-party online security firm offered to do a similar security search for $9.00 per person with an annual service contract with STE. If STE's forecast is 2,900 searches next year, should STE continue to do the search in-house or accept the third- party offer? Use the Excel template Break-Even to determine the best decision. Round your answer for the breakeven quantity to the nearest whole number and round your answer for the amount of saving/loss to the nearest dollar. Breakeven quantity: Since the demand forecast of 2,900 searches is -Select-than the breakeven quantity, STE -Select- ✓outsource the work. STE -Select- $ by outsourcing. searchesarrow_forward
- Suzy's Temporary Employee (STE) business, located in a big city, can do an online criminal background check in-house for $3.48 per search with a fixed cost of $30,000. A third-party online security firm offered to do a similar security search for $9.00 per person with an annual service contract with STE. If STE's forecast is 3,100 searches next year, should STE continue to do the search in-house or accept the third-party offer? Use the Excel template Break-Even to determine the best decision. Round your answer for the breakeven quantity to the nearest whole number and round your answer for the amount of saving/loss to the nearest dollar. Breakeven quantity: searches Since the demand forecast of 3,100 searches is than the breakeven quantity, STE outsource the work. STE $ by outsourcing.arrow_forward(Please apply indifference point formula for this exercise) 1. The school cafeteria can make pizza for approximately $0.30 per slice. The cost of the kitchen use and cafeteria staff runs about $200 per day. The Pizza Den nearby will deliver whole pizzas for $9.00 each. The cafeteria staff cuts the pizza into eight (8) pieces and serves them in the usual cafeteria line. With no cooking duties, the staff can be reduced by half, for a fixed cost of $75 per day. Should the school cafeteria make or buy pizza? Calculations are needed to justify the answer. (Please apply the indifference point formula for this exercise). Excel spreadsheet would be great!.arrow_forward* 00 Miles is considering buying a new pickup truck for his lawn service firm. The economy in town seems to be growing, and he is wondering whether he should opt for a subcompact, compact, or full-size pickup truck. The smaller truck would have better fuel economy, but would sacrifice capacity and some durability. A friend at the Bureau of Economic Research told him that there is a 30% chance of lower gas prices in his area this year, a 20% chance of higher gas prices, and a 50% chance that gas prices will stay roughly unchanged. Based on this information, Miles has developed a decision table that indicates the profit amount he would end up with after a year for each combination of truck and gas prices. States of Nature Lower gas Gas prices Higher gas Alternatives prices unchanged prices Subcompact 19,000 000 Compact OGOʻST 000 Full size 000'9 Probability 0.3 0.5 0.2 MacBook Air 000 000 DD F7 08 F4 F5 6 %24 ) 9 | K. D.arrow_forward
- A machine was purchased one year ago. Presently, the market value is $16,000 and it declines by $3,000 every year. For the next 3 years, the maintenance costs are as follows: Year Maintenance costs 1 $890 $1,290 $1,690 2 3 What is the marginal cost of extending the service for the 3rd year? A. $2,690 В. $5,490 C. $4,690 D. $5,690arrow_forwardS7.25 B Zan Azlett and Angela Zesiger have joined forces to start A&Z Lettuce Products, a processor of packaged shredded lettuce for institutional use. Zan has years of food processing experience, and Angela has extensive commercial food preparation experience. The process will consist of opening crates of lettuce and then sorting, washing, slicing, preserving, and finally packaging the prepared lettuce. Together, with help from vendors, they think they can adequately estimate demand, fixed costs, revenues, and variable cost per 5-pound bag of lettuce. They think a largely manual process will have monthly fixed costs of $37,500 and variable costs of $1.75 per bag. A more mechanized process will have fixed costs of $75,000 per month with variable costs of $1.25 per 5-pound bag. They expect to sell the shredded lettuce for $2.50 per 5-pound bag. d) What is the revenue at the break-even quantity for the mechanized process? e) What is the monthly profit or loss of the manual process if…arrow_forwardA fully leased three-story suburban office building near Disneyworld had a total of 60,000 rentable square feet. Each of the three floors had an identical layout with two public bathrooms, an elevator lobby, and a public hallway that yielded a load factor per floor of 1.20. The lease form used for the building was written so that rent was paid by the tenants per usable square foot of rented floor space. If the total annual rental income for the building was $1.8 million, what was the monthly rent per usable square foot? a. $3.00 b. $3.60 c. $2.00 d. $2.40arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,MarketingMarketingISBN:9780357033791Author:Pride, William MPublisher:South Western Educational Publishing