Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)
Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)
12th Edition
ISBN: 9781259580093
Author: William J Stevenson
Publisher: McGraw-Hill Education
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Chapter 13, Problem 14P

A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8 per stone for quantities of 600 stones or more, $9 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 200 days per year. Usage rate is 25 stones per day, and ordering costs are $48.

a. If Carrying costs are $2 per year for each stone, find the order quantity that will minimize total annual cost.

b. If annual carrying costs are 30 percent of unit cost, what is the optimal order size?

c. If lead time is six working days, at what point should the company reorder?

a)

Expert Solution
Check Mark
Summary Introduction

To determine: The Optimal order quantity that minimizes the total cost.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 14P

The Optimal order quantity that minimizes the total cost is 600 stones.

Explanation of Solution

Given information:

D=25stones/day×200days/year=5,000stones/yearS=$48

Number of Stones Price per Stone (P)
1-399 $10
400-599 $9
600+ $8

Formula:

Q=2DSH

TC=(Q2)H+(DQ)S+PD

Calculation of Economic Order Quantity:

H=$2

Q=2×5000×482=490stones

The economic order quantity is calculated by dividing the product of 2 and 5,000 and 48 with 2 and taking square root which gives the resultant value as 490 stones.

Calculation of total cost:

TC490=(4902)2+(5,000490)48+9(5,000)=$45,979.80

TC600=(6002)2+(5,000600)48+8(5,000)=$41,000

The optimal order quantity is 600 stones which is the minimal total cost.

Hence, the optimal order quantity is 600 stones.

b)

Expert Solution
Check Mark
Summary Introduction

To determine: The Optimal order size.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 14P

The Optimal order size is 600 stones.

Explanation of Solution

Given information:

D=25stones/day×200days/year=5,000stones/yearS=$48

Number of Stones Price per Stone (P)
1-399 $10
400-599 $9
600+ $8

Formula:

Q=2DSH

TC=(Q2)H+(DQ)S+PD

Calculation of optimum order size:

  • P=$8

Q=2×5,000×480.30×8=447stones

The economic order quantity is calculated by dividing the product of 2 and 5,000 and 48 with the product of 0.30 and 8, square root is taken which gives the resultant value as 447 stones which is not feasible.

  • P=$9

Q=2×5,000×480.30×9=422stones

The economic order quantity is calculated by dividing the product of 2 and 5,000 and 48 with the product of 0.30 and 9, square root is taken which gives the resultant value as 422 stones which is feasible.

Calculation of total cost:

TC422=(4222)(0.30×9)+(5,000422)48+9(5,000)=$46,138.42

TC600=(6002)(0.30×8)+(5,000600)48+8(5,000)=$41,120

The optimal order quantity is 600 stones which is the minimal total cost.

Hence, the optimal order quantity is 600 stones.

c)

Expert Solution
Check Mark
Summary Introduction

To determine: The reorder point.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 14P

The reorder point is 150 stones.

Explanation of Solution

Given information:

D=25stones/day×200days/year=5,000stones/yearS=$48

Number of Stones Price per Stone (P)
1-399 $10
400-599 $9
600+ $8

Calculation of reorder point:

ROP=25stones/day×6days=150stones

The reorder point is calculated by multiplying 25 stones/day with 6 days which gives 150 stones.

Hence, the reorder point is 150 stones.

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Chapter 13 Solutions

Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)

Ch. 13 - What is meant by the term service level? Generally...Ch. 13 - Describe briefly the A-B-C approach to inventory...Ch. 13 - The purchasing agent for a company that assembles...Ch. 13 - Explain how a decrease in setup time can lead to a...Ch. 13 - What is the single-period model, and under what...Ch. 13 - Can the optimal stocking level in the...Ch. 13 - Prob. 17DRQCh. 13 - What trade-offs are involved in each of these...Ch. 13 - Who needs to be involved in inventory decisions...Ch. 13 - How has technology aided inventory management? How...Ch. 13 - To be competitive, many fast-food chains began to...Ch. 13 - As a supermarket manager, how would you go about...Ch. 13 - Sam is at the post office to mail a package. After...Ch. 13 - Give two examples of unethical conduct involving...Ch. 13 - Prob. 1PCh. 13 - a. The following table contains figures on the...Ch. 13 - A bakery buys flours in 25-pound bags. The bakery...Ch. 13 - A large law firm uses an average of 40 boxes of...Ch. 13 - Garden Variety Flower Shop uses 750 clay pots a...Ch. 13 - A produce distributor uses 800 packing crates a...Ch. 13 - A manager receives a forecast for next year....Ch. 13 - A food processor uses approximately 27,000 glass...Ch. 13 - The Friendly Sausage Factory (FSF) can produce hot...Ch. 13 - A chemical firm produces sodium bisulfate in...Ch. 13 - A company is about to begin production of a new...Ch. 13 - Prob. 12PCh. 13 - A mail-order house uses 18,000 boxes a year....Ch. 13 - A jewelry firm buys semiprecious stones to make...Ch. 13 - A manufacturer of exercise equipment purchases the...Ch. 13 - A company will begin stocking remote control...Ch. 13 - A manager just received a new price list from a...Ch. 13 - A newspaper publisher uses roughly 800 feet of...Ch. 13 - Given this information: Expected demand during...Ch. 13 - Given this information: Lead-time demand = 600...Ch. 13 - Demand for walnut fudge ice cream at the Sweet...Ch. 13 - The injection molding department of a company uses...Ch. 13 - A company uses 85 circuit boards a day in a...Ch. 13 - One item a computer store sells is supplied by a...Ch. 13 - The manager of a car wash received a revised price...Ch. 13 - A small copy center uses five 500-sheet boxes of...Ch. 13 - Ned's Natural Foods sells unshelled peanuts by the...Ch. 13 - Regional Supermarket is open 360 days per year....Ch. 13 - A service station uses 1,200 cases of oil a year....Ch. 13 - Caring Hospital's dispensary reorders doses of a...Ch. 13 - A drugstore uses fixed-order cycles for many of...Ch. 13 - Prob. 32PCh. 13 - Prob. 33PCh. 13 - Demand for jelly doughnuts on Saturdays at Don's...Ch. 13 - A public utility intends to buy a turbine as part...Ch. 13 - Skinner's Fish Market buys fresh Boston bluefish...Ch. 13 - A small grocery store sells fresh produce, which...Ch. 13 - Demand for devil's food whipped-cream layer cake...Ch. 13 - Prob. 39PCh. 13 - Demand for rug-cleaning machines at Clyde's...Ch. 13 - A manager is going to purchase new processing...Ch. 13 - A Las Vegas supermarket bakery must decide how...Ch. 13 - Offwego Airlines has a daily flight from Chicago...Ch. 13 - UPD Manufacturing produces a range of health care...Ch. 13 - Prob. 1.2CQCh. 13 - Prob. 2.1CQCh. 13 - Grill Rite is an old-line company that started out...Ch. 13 - SARAH LUBBERS AND CHRIS RUSCHE, GRAND VALLEY STATE...Ch. 13 - SARAH LUBBERS AND CHRIS RUSCHE, GRAND VALLEY STATE...Ch. 13 - Prob. 4.3CQCh. 13 - SARAH LUBBERS AND CHRIS RUSCHE, GRAND VALLEY STATE...Ch. 13 - Prob. 4.5CQCh. 13 - Prob. 1OTQCh. 13 - Prob. 2OTQCh. 13 - Prob. 3OTQCh. 13 - Prob. 4OTQ
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