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pose now that the unit cost for every speaker is $11 if less than 10,000 speakers are produced, $10 if production falls between 10,000 and 80,000 speakers, and $9.50 if production exceeds 80,000 speakers. What is the optimal policy?

pose now that the unit cost for every speaker is $11 if less than 10,000 speakers are produced, $10 if production falls between 10,000 and 80,000 speakers, and $9.50 if production exceeds 80,000 speakers. What is the optimal policy?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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The company is interested in determining when to produce a batch of speakers , and how many speakers to produce to each batch. 

 

b. Suppose now that the unit cost for every speaker is $11 if less than 10,000 speakers are produced, $10 if production falls between 10,000 and 80,000 speakers, and $9.50 if production exceeds 80,000 speakers. What is the optimal policy?

A television manufacturing company produces its own speakers, which are used in the production of its television sets. The television sets are assembled on a continuous production line at a rate of 8,000 per month, with one speaker needed per set. The speakers are produced in batches because they do not warrant setting up a continuous production line, and relatively large quantities can be produced in a short time. Therefore, the speakers are placed into inventory until they are needed for assembly into television sets on the production line. Several costs must be considered: 1. Each time a batch is produced, a setup cost of $12,000 is incurred. This cost includes the cost of "tooling up," administrative costs, record keeping, and so forth. Note that the existence of this cost argues for producing speakers in large batches. 2. The unit production cost of a single speaker (excluding the setup cost) is $10, independent of the batch size produced. (In general, however, the unit production cost need not be constant and may decrease with batch size.) 3. The production of speakers in large batches leads to a large inventory. The estimated holding cost of keeping a speaker in stock is $0.30 per month. This cost includes the cost of capital tied up in inventory. Since the money invested in inventory cannot be used in other productive ways, this cost of capital consists of the lost return (referred to as the opportunity cost) because alternative uses of the money must be forgone. Other components of the holding cost include the cost of leasing the storage space, the cost of insurance against loss of inventory by fire, theft, or vandalism, taxes based on the value of the inventory, and the cost of personnel who oversee and protect the inventory. 4. Company policy prohibits deliberately planning for shortages of any of its components.
Transcribed Image Text:A television manufacturing company produces its own speakers, which are used in the production of its television sets. The television sets are assembled on a continuous production line at a rate of 8,000 per month, with one speaker needed per set. The speakers are produced in batches because they do not warrant setting up a continuous production line, and relatively large quantities can be produced in a short time. Therefore, the speakers are placed into inventory until they are needed for assembly into television sets on the production line. Several costs must be considered: 1. Each time a batch is produced, a setup cost of $12,000 is incurred. This cost includes the cost of "tooling up," administrative costs, record keeping, and so forth. Note that the existence of this cost argues for producing speakers in large batches. 2. The unit production cost of a single speaker (excluding the setup cost) is $10, independent of the batch size produced. (In general, however, the unit production cost need not be constant and may decrease with batch size.) 3. The production of speakers in large batches leads to a large inventory. The estimated holding cost of keeping a speaker in stock is $0.30 per month. This cost includes the cost of capital tied up in inventory. Since the money invested in inventory cannot be used in other productive ways, this cost of capital consists of the lost return (referred to as the opportunity cost) because alternative uses of the money must be forgone. Other components of the holding cost include the cost of leasing the storage space, the cost of insurance against loss of inventory by fire, theft, or vandalism, taxes based on the value of the inventory, and the cost of personnel who oversee and protect the inventory. 4. Company policy prohibits deliberately planning for shortages of any of its components.
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