Develop a lot-for-lot solution and calculate total relevant costs for the gross
ID: 368440 • Letter: D
Question
Develop a lot-for-lot solution and calculate total relevant costs for the gross requirements in the following table* Period Gross requirements20 1 23 4 5 6 7 89 10 11 12 40 0 70 3010 80 50 "Holding cost = $2.50/unitweek setup costs S200: lead time: 1 week; beginning inventory : 40 Develop a lot-for-lot solution (enter your responses as whole numbers). Period Gross requirements On-hand at beginning of period On-hand at end of period Order receipt Order release 1 2 3 4 5 6 78 9 10 11 12 20 40 40 70 30 10 80 50 40Explanation / Answer
The MRP table for Lot-for -Lot solution is presented below :
Beginning inventory : 40
Week
Lot size: Lot for Lot
Lead time: 1 week
1
2
3
4
5
6
7
8
9
10
11
12
Gross Requirement
20
0
40
0
40
70
30
0
10
80
0
50
On hand at beginning of period : 40
40
20
20
0
0
0
0
0
0
0
0
0
On hand at end of period
20
20
0
0
0
0
0
0
0
0
0
0
Planned order receipt
0
0
20
0
40
70
30
0
10
80
0
50
Planned order release
0
20
0
40
70
30
0
10
80
0
50
0
Following have been considered while developing above Lot-for-Lot solution :
i)On hand at beginning of period 1 = 40
On hand at beginning of period t+1 = On hand at end of period t
ii) On hand at end of period t = On hand at beginning of period t – Gross requirement for period t
( when On hand inventory at beginning of period t > Gross requirement for period t)
In such case, Planned order Receipt for period t = 0
iii) On hand at end of period t = 0 ( when On hand inventory at beginning of period t < Gross requirement for period t)
In such case ,
Planned order receipt for period t > Gross requirement for period t – On hand inventory at beginning of period t
iv) Since Lead time is 1 week ,
Planned order receipt for period t = Planned order Release for period t-1
Given are :
Holding cost = $2.50 per unit per week
Set up cost = $ 200 ( We presume set up cost is incurred EVERYTIME AN ORDER IS RELEASED)
Total quantity of inventory held for 1 week = 20 + 20 = 40
Therefore ,
Holding cost = $ 2.50 x 40 = $100
Total number of Planned Order Releases = 7
Therefore ,
Total Set up Cost = $200 / set up x 7 ( number of set ups ) = $1400
Thus total relevant cost
= Total inventory holding cost + Total set up cost
= $100 + $ 1400
= $ 1500
TOTAL RELEVANT COST FOR GROSS REQUIREMENTS = $1500
Beginning inventory : 40
Week
Lot size: Lot for Lot
Lead time: 1 week
1
2
3
4
5
6
7
8
9
10
11
12
Gross Requirement
20
0
40
0
40
70
30
0
10
80
0
50
On hand at beginning of period : 40
40
20
20
0
0
0
0
0
0
0
0
0
On hand at end of period
20
20
0
0
0
0
0
0
0
0
0
0
Planned order receipt
0
0
20
0
40
70
30
0
10
80
0
50
Planned order release
0
20
0
40
70
30
0
10
80
0
50
0
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