Concept explainers
a)
Interpretation: Determine the ordering policy is recommended by the silver-Meal heuristic.
Concept Introduction: Silver-Meal heuristic mainly focused on the manufacture planning in the production companies. It determines that within the minimum cost level, the quantities of the products will be produced by the company.
a)
Answer to Problem 49AP
The order policy according to silver meal heuristic method is
Explanation of Solution
Given information: The anticipated demand for an inventory is as follows:
Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Demand | 22 | 34 | 32 | 12 | 8 | 44 | 54 | 16 | 76 | 30 |
The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.
The order policy of the inventory under silver meal method can be calculated as follows:
According to silver meal method the average cost per period C (T) is a function of the average holding and set up cost per period for T number of Periods. The production in period 1 is equal to the demand in that period 1 to incur the order cost K.
Hence
And
And general equation is
Once
Now, calculate the order policy using the above formula as follows:
Starting in period 1:
(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)
Starting from period 1
Stop the process since
Starting in period 3:
Stop the process since
Starting in period 6:
Stop the process since
Starting in period 9:
b)
Interpretation: Determine the ordering policy is recommended by the part period balancing heuristic.
Concept Introduction: one of the lot-sizing technique is to implementing the lowest-cost with the interconnection between costs of order and carrying cost for the inventory is generally known as Part period balancing.it is more effective for the product whose demand is unstable.
b)
Answer to Problem 49AP
The order policy according to the part period balancing heuristic method will be
is
Explanation of Solution
Given information: The anticipated demand for an inventory is as follows:
Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Demand | 22 | 34 | 32 | 12 | 8 | 44 | 54 | 16 | 76 | 30 |
The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.
The order policy according to part period balancing method can be calculated as follows:
In this method the order horizon that equates holding and setup cost over that period has to be calculated as follows:
(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)
Starting from period 1:
Period | Holding Cost |
2 | 110.5 |
3 | 318.5 |
Since the setup cost $200 is closer at period 4, stop and equate
Starting in period 3:
Period | Holding Cost |
2 | 25 |
3 | 65 |
4 | 520 |
Since the setup cost $200 is closer to 4 than 3, stop and equate
Starting in period 6:
Period | Holding Cost |
2 | 175.5 |
3 | 279.5 |
Since the setup cost $200 is closer to 3, stop and equate
Starting in period 8:
Period | Holding Cost |
2 | 247 |
Since the setup cost $200 is closer to 2, stop and equate
c)
Interpretation: Determine the ordering policy is recommended by the least unit cost heuristic.
Concept Introduction: Least unit cost heuristic technique is one of the time-varying demand pattern technique.one of the dynamic lot-sizing concept is that interrelated between the order cost and carrying cost of the inventory for the every lot size is defined as
Least Unit Cost (LUC).
c)
Answer to Problem 49AP
The order policy according to the least unit cost heuristic method will be
is
Explanation of Solution
Given information: The anticipated demand for an inventory is as follows:
Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Demand | 22 | 34 | 32 | 12 | 8 | 44 | 54 | 16 | 76 | 30 |
The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.
The order policy according to lease unit cost(LUC) method can be calculated as follows:
LUC divides the average cost per period C (T) by the total number of units demanded. Hence
And
And general equation is
Once
Starting from period 1
Stop the process since
Starting in period 3:
Stop the process since
Starting in period 5:
Stop the process since
Starting in period 8:
Stop the process since
d)
Interpretation: Determine the method resulted in the lowest-cost policy for the given problem.
Concept Introduction: Least unit cost method makes the present period of the demands and evaluates the period of the future. Adding the carrying cost for the setup and the period of the inventory cost, the least unit cost will be occur.
d)
Answer to Problem 49AP
The least expensive method is the least unit cost method with a total cost of
Explanation of Solution
Given information: The anticipated demand for an inventory is as follows:
Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Demand | 22 | 34 | 32 | 12 | 8 | 44 | 54 | 16 | 76 | 30 |
The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.
Comparison of the three methods can be calculated as follows:
Calculate the total cost of the inventory for the three months. The method which yields less cost is the lowest cost policy.
The total cost under silver meal method can be calculated as follows:
The method required is 4 set ups
The total set up cost is
The total holding cost is
The total cost
The total cost under silver-meal heuristic is
The total cost under least unit cost method can be calculated as follows:
The method required is 5 set ups
The total set up cost is
The total holding cost is
The total cost
The total cost under least unit cost method is
The total cost under part period balancing method can be calculated as follows:
The method required is 5 set ups
The total set up cost is
The total holding cost is
The total cost
The total cost under part period balancing method is
Want to see more full solutions like this?
Chapter 8 Solutions
Production and Operations Analysis, Seventh Edition
- A component used in a manufacturing facility is ordered from an outside supplier.Because the component is used in a variety of end products, the demand is high. Estimated demand (in thousands) over the next 10 weeks isWeek 1 2 3 4 5 6 7 8 9 10Demand 22 34 32 12 8 44 54 16 76 30The components cost 65 cents each and the interest rate used to compute the holding cost is 0.5 percent per week. The fixed order cost is estimated to be $200. (Hint:Express h as the holding cost per thousand units.)b. What ordering policy is recommended by the part period balancing heuristic?arrow_forwardThe demand for a certain article is 400 art/month. The ordering cost is $35 and the storage cost is $10/month. The purchase cost is $15 but if 70 items or more are purchased there is a discount andThey drop at $10. a) Obtain the optimal amount of inventory Yb) Obtain the total cost of inventoryc) Is it convenient to accept the discount?d) What is the cost of inventory with quantity m?arrow_forwardUnder the last-in, first-out (LIFO) inventory valuation method, a price index for inventory must be established for tax purposes. The quantity weights are based on year-ending inventory levels. Unit Price ($) Product EndingInventory Beginning Ending A 500 0.15 0.19 B 50 1.40 1.80 C 100 4.50 4.20 D 60 12.00 13.60 Use the beginning-of-the-year price per unit as the base-period price and develop a weighted aggregate index for the total inventory value at the end of the year. (Round your answer to the nearest integer.) I = ?? What type of weighted aggregate price index must be developed for the LIFO inventory valuation? -Paasche index -Laspeyres Indexarrow_forward
- 1. David and Beth Sheba run a health food store. Their top selling item is called Heavenly Kelp. The annual demand for this is 3200 units, and demand is constant throughout the year. The cost of placing an order is $100, while the holding cost per unit per year is $4. How many orders per year should be placed if they wish to minimize their total cost ? If you want to be eligible for partial credit, give an idea as to how you arrived at that number?arrow_forwardParasol Systems sells motherboards for personal computers. For quantities upthrough 25, the firm charges $350 per board; for quantities between 26 and 50,it charges $315 for each board purchased beyond 25; and it charges $285 eachfor the additional quantities over 50. A large communications firm expects torequire these motherboards for the next 10 years at a rate of at least 140 peryear. Order setup costs are $30 and holding costs are based on an 18 percentannual interest rate. What should be the size of the standing order?arrow_forwardThe Strong Tire Company uses the EPQ model to manufacture tires for all makes of cars. The Company can produce 320 tires daily. The set up cost for each production run is BD 100. The annual holding cost per tire is BD 5 and the Company operates 300 days a year. The annual demand for these tires is 57,600. Find the amount of inventory used to meet immediate demand during the production run. A. 480 B. 720 C. 1440 D. 840arrow_forward
- nder the last-in, first-out (LIFO) inventory valuation method, a price index for inventory must be established for tax purposes. The quantity weights are based on year-ending inventory levels. Unit Price ($) Product EndingInventory Beginning Ending A 500 0.17 0.19 B 50 1.60 1.80 C 100 4.50 4.20 D 40 12.00 13.20 Use the beginning-of-the-year price per unit as the base-period price and develop a weighted aggregate index for the total inventory value at the end of the year. (Round your answer to the nearest integer.) I = What type of weighted aggregate price index must be developed for the LIFO inventory valuation? Laspeyres IndexPaasche indexarrow_forwardInstructions There are four parts to this problem. Use Excel to perform the following. a. Use the economic order quantity formula (EOQ = SQRT((2SD/H)) to determine the optimal number of units that the company should order based on each assumed level of order based on each assumed level of order quantities provided in the data. b. Complete the table by calculating the number of orders per year, annual order cost, annual holding cost, and annual total cost. Highlight the minimum annual total cost using conditional formatting. Hint: The minimum cost should equal the cost at the EOQ you calculated in part a. c. Create a line chart that graphs annual order cost, annual holding cost, and annual total cost. The x-axis should be the quantity ordered. Include a chart legend, appropriate chart title, axes labels, and properly formatted amounts on the axes. d. Examine the chart and your responses to parts a and b. Indicate any relationships.arrow_forwardA distributor of large appliances needs to determine the order quantities and reorderpoints for the various products it carries. The following data refer to a specii c refrigeratorin its product line:Cost to place an orderHolding costCost of refrigeratorAnnual demandStandard deviation of demand during lead timeLead time$10020 percent of product cost per year$500 each500 refrigerators10 refrigerators7 daysConsider an even daily demand and a 365-day year.a. What is the economic order quantity?b. If the distributor wants a 97 percent service probability, what reorder point, R, shouldbe used?arrow_forward
- Rocky Mountain Tire Centre sells 20,000 tires of a particular type per year. The ordering cost for each order is $40, and the holding cost is 20% of the purchase price of the tires per year. The purchase price is $20. per tire if fewer than 500 tires are ordered, $18. Per tire if more than 500 but fewer than 1,000 tires are ordered and $17. per tire if 1,000 or more tires are ordered. Quantity Unit Price 1-499 $20. 500-999 $18. 1000 & over $17 Based on available information, lead time demand for CD-ROM drives averages 50 units (normally distributed), with a standard deviation of 5 drives. Management wants a 97% service level. What value of Z should be applied? How many drives should be carried as safety stock?arrow_forwardThe home appliance department of a large department store is using inventory models to controlthe replenishment of a particular model of Microwave ovens. The daily demand follows anormal distribution with a mean of 150 units and standard deviation of 16 units. The store pays$100 for each oven. Fixed costs of replenishment are $28. The accounting departmentrecommends a 20% annual holding cost rate. Assume that the average lead time is 5 days with astandard deviation of 1 day. Assume 365 days a year.Part A: What is the EOQ?Part B: What is the reorder point if the maximum chance of 5% of stock out (i.e. 95% servicelevel) is desired?Part C: What is the reorder point if a fill rate of 99% is required?Part D: Suppose management wants to simplify the process by setting the reorder point to“1000” units. Based on this policy, what is the implied chance of stock out?arrow_forwardi need D) The demand for a certain article is 400 art/month. The ordering cost is $35 and the storage cost is $10/month. The purchase cost is $15 but if 70 items or more are purchased there is a discount andThey drop at $10. a) Obtain the optimal amount of inventory Yb) Obtain the total cost of inventoryc) Is it convenient to accept the discount?d) What is the cost of inventory with quantity m?arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,