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
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Chapter 8 Solutions
Production and Operations Analysis, Seventh Edition
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