1. INVENTORY MANAGEMENT, JIT, AND BACKFLUSH COSTING
CHAPTER 20

2. TWO ISSUES IN INVENTORY MANAGEMENT
HOW MUCH TO ORDER
WHEN TO ORDER

3. HOW MUCH TO ORDER ECONOMIC ORDER QUANTITY
THERE ARE TWO COSTS RELATED TO THE ORDER SIZE
CARRYING COSTS and ORDER COSTS
CARRYING COSTS ARE THOSE INCURRED WITH HOLDING A UNIT OF INVENTORY FOR SOME TIME PERIOD (WE WILL USE A YEAR)
ORDER COSTS ARE THOSE INCURRED IN PLACING AN ORDER

4. CARRYING COSTS
CARRYING COSTS INCLUDE STORAGE, CAPITAL COST ON INVESTMENT, OBSOLESCENCE, ETC.
THE MORE THE INVENTORY, THE MORE THE CARRYING COSTS.
THE CARRYING COSTS ARE BASED ON THE AVERAGE INVENTORY

5. AVERAGE INVENTORY
Assume we know demand exactly and delivery time is constant, i.e., the same each time. Inventory balance would be:
The average inventory would be:
Number Q
time
The average inventory is Q/2.

6. ANNUAL CARRYING COSTS ANNUAL CARRYING COSTS WOULD BE THE PRODUCT OF:
THE COST OF CARRYING ONE UNIT OF INVENTORY FOR ONE YEAR AND
AVERAGE INVENTORY: Q/2

7. ORDER COSTS
ORDER COSTS INCLUDE EMPLOYEE TIME, PAPER WORK ON AN ORDER, TELEPHONE/FAX, ETC.
THE ANNUAL ORDER COSTS ARE THE PRODUCT OF
THE COST OF PLACING AN ORDER AND
THE NUMBER OF ORDER PLACED
THE NUMBER OF ORDERS PLACED IS:
ANNUAL DEMAND / Q

8. WHAT HAPPENS TO CARRYING COSTS AS Q INCREASES?$ Q
AS Q INCREASES, AVERAGE INVENTORY INCREASE

9. WHAT HAPPENS TO ORDER COSTS AS Q INCREASES?$ Q
AS Q INCREASES, THE NUMBER OF ORDERS DECLINES

10. WHAT IS THE OBJECTIVE? REMEMBER THIS
TO MINIMIZE THE CARRYING COSTS OR THE ORDER COSTS?
NEITHER
TRY TO MINIMIZE THE SUM OF THE TWO COSTS
TOTAL COSTS ARE CARRYING COSTS AND ORDER COSTS -
REMEMBER THIS

11. WHAT HAPPENS TO TOTAL COSTS AS Q INCREASES?$
total costs
carrying costs
order costs Q
AS Q INCREASES, TOTAL COSTS DECLINE AND THEN START RISING

12. COSTS EQUATIONS CARRYING COSTS =
(COST OF CARRYING ONE UNIT OF INVENTORY) x (Q/2)
ORDER COSTS =
(COST OF PLACING AN ORDER) X (EXPECTED DEMAND/Q)
TOTAL COSTS =
CARRYING COSTS + ORDER COSTS

13. MINIMIZE TOTAL COSTS D P 2 D P C/2 C
TO MINIMIZE TOTAL COSTS, TAKE THE FIRST DIRIVATIVE OF THE TOTAL COST EQUATION
LET D = ANNUAL DEMAND
C = COST TO CARRY ONE ITEM ONE YEAR
P = COST TO PLACE ONE ORDER
THEN
Q = =
D P
C/2
2 D P C

14. HOW TO REMEMBER FORMULA
AS DEMAND INCREASES, WHAT SHOULD HAPPEN TO Q?
IT SHOULD INCREASE
AS ORDER COSTS INCREASE WHAT SHOULD HAPPEN TO Q?
IT SHOULD INCREASE, YOU WANT TO ORDER LESS OFTEN
AS CARRYING COSTS INCREASE WHAT SHOULD HAPPEN TO Q?
IT SHOULD DECREASE, YOU WANT A SMALLER AVERAGE INVENTORY.

15. EXAMPLE Q = 2 x 50 x 1,000 6 = 130 IT COSTS $50 TO PLACE AN ORDER
IT COSTS $6 TO HOLD ONE ITEM OF INVENTORY FOR A YEAR
WE WILL USE/ORDER 1,000 ITEMS DURING THE YEAR
CALCULATE THE EOQ
Q =
2 x 50 x 1,000 6
= 130

16. EXERCISE DETERMINE THE EOQ IF: ORDER COSTS ARE $25
CARRYING COSTS ARE $3
ANNUAL USE/DEMAND IS 600
Q = 100

17. OBSERVE
THE MINIMUM TOTAL COSTS ARE WHERE ORDER COSTS EQUAL CARRYING COSTS – under a weird cost structure, there may be an exception – BUT,
THE OBJECTIVE IS TO MINIMIZE THE TOTAL COSTS, NOT TO EQUALIZE THE TWO COSTS

18. WHAT TO DO ABOUT DISCOUNTS
THERE ARE TWO TYPES OF DISCOUNTS:
CASH DISCOUNTS --
THOSE RELATED TO EARLY PAYMENT
THESE DO NOT CONCERN INVENTORY
QUANTITY (PURCHASE) DISCOUNTS
THOSE RELATED TO THE QUANTITY PURCHASED
THESE DO CONCERN INVENTORY

19. AFFECT OF QUANTITY DISCOUNTS
EARLIER WE WERE CONCERNED WITH INVENTORY COSTS EXCEPT FOR THE COST OF THE GOODS THEMSELVES
QUANTITY DISCOUNTS EFFECT THE EOQ BECAUSE THE COSTS OF THE GOODS DECREASE AS THE ORDER SIZE INCREASES. BUT, THE DECREASE IS ON A DISCRETE, NOT CONTINUOUS, BASIS.

20. DIAGRAMATICALLY $
TOTAL COSTS Q
PRICE
BREAK
EOQ
W/O PB
PRICE BREAK

21. LOWEST COST Q
THE LOWEST COSTS WOULD BE AT A PRICE BREAK OR AT THE POINT WHERE EOQ IS COMPUTED WITHOUT REGARD TO PRICE BREAKS
BUT, OBVIOUSLY, THE LOWEST COSTS Q WOULD NOT BE AT A POINT BELOW THE EOQ WITHOUT REGARD TO PRICE BREAKS

22. TO DETERMINE THE EOQ WITH PRICE BREAKS
DETERMINE THE COSTS,
CARRYING COSTS,
ORDER COSTS, AND
THE COSTS OF GOODS
AT THE PRICE BREAKS AND AT THE EOQ WITHOUT REGARD TO PRICE BREAKS
THE LOWEST COSTS POINT SUMMING THOSE THREE COSTS IS THE ECONOMIC ORDER QUANTITY

23. EXAMPLE – CONTINUATION OF PRIOR EXAMPLE
THERE ARE PRICE BREAKS OF $0.50 FOR EACH UNIT FOR PURCHASES OF 50 OR MORE AND A DISCOUNT OF $1.00 FOR PURCHASES OF 150 OR MORE.
THE EOQ WILL BE 130 (AS COMPUTED BEFORE) OR 150, THE NEXT PRICE BREAK

24. TOTAL COSTS TREAT DISCOUNTS AS ADDITIONAL COSTS ORDER: 130: 150:
TREAT DISCOUNTS AS COSTS REDUCTIONS
$50) +
$6) +
$0.50) =
$1,275
$50) +
$6) =
$783
$50) +
$6) =
$775
$50) +
$6) -
$0.50 =
$283

25. EXERCISE – CONTINUATION OF PRIOR EXERCISE
THE PRICE BREAKS OF $0.50 FOR EACH UNIT FOR PURCHASES OF 50 OR MORE AND A DISCOUNT OF $1.00 FOR PURCHASES OF 150 OR MORE.
THE EOQ WILL BE 100 (AS COMPUTED BEFORE) OR 150, THE NEXT PRICE BREAK

26. TOTAL COSTS TREAT DISCOUNTS AS ADDITIONAL COSTS ORDER AT: 100: 150:
TREAT DISCOUNTS AS COSTS REDUCTIONS
(6X$25) +
($3X50) +
(600x$0.50) =
$600
(4X$25) +
($3X75) =
$325
(6X$25) +
($3X50) =
$300
(4X$25) +
($3X75) -
(600x$0.50) =
$25

27. NOW LET’S FIGURE OUT WHEN TO ORDER SAFETY STOCK
WE ARE FACING TWO COSTS
CARRYING COSTS AND
STOCK OUT COSTS
THE REORDER POINT ABOVE EXPECTED DEMAND/USE DURING THE REORDER PERIOD IS THE
SAFETY STOCK

28. CARRYING COSTS
SAFETY STOCK X COST OF CARRYING ONE UNIT OF INVENTORY FOR ONE YEAR
AS SAFETY STOCK INCREASES, CARRYING COSTS INCREASE $
SAFETY STOCK

29. STOCK OUT COSTS
EXPECTED STOCK-OUTS PER YEAR X COST OF BEING OUT OF STOCK BY ONE UNIT
EXPECTED ANNUAL STOCK-OUTS = EXPECTED UNITS OF STOCK-OUTS EACH TIME WE FACE A REORDER (STOCK-OUT POSSIBILITY) X NUMBER OF REORDERS PER YEAR (DEMAND/Q) $
SAFETY STOCK

30. OBJECTIVE MINIMIZE THE TOTAL COSTS:
THE SUM OF THE CARRYING COSTS AND STOCK-OUT COSTS

31. EXAMPLE THE E[COST OF A STOCKOUT] = $2
THE LEAD TIME (TIME BETWEEN PLACING AN ORDER AND RECEIVING THE GOODS) IS 45 DAYS
EXPECTED USE IN A 45 DAYS PERIOD
ASSUME WE WILL ORDER 7.7 TIMES PER YEAR
DEMAND
PROB.
E[D]
110
0.10 11
120
0.20 24
130
0.50 65
140 14
150
0.05
7.5
160 8

32. STOCK-OUT COSTS EXPECTED COSTS = 19.5 X $2 X 7.7 = $300.30
IF WE REORDER AT 110, THE POSSIBLE STOCK-OUTS AND THEIR PROBABILITIES ARE:
DEMAND
STOCK-OUT
P[SO]
E[SO]
120 10
0.20
2.0
130 20
0.50
10.0
140 30
0.10
3.0
150 40
0.05
160 50
2.5
19.5
EXPECTED COSTS = 19.5 X $2 X 7.7 = $300.30

33. IF WE REORDER AT 120, THE POSSIBLE STOCK-OUTS AND THEIR PROBABILITIES ARE:
DEMAND
STOCK-OUT
P[SO]
E[SO]
130 10
0.50
5.0
140 20
0.10
2.0
150 30
0.05
1.5
160 40
10.5
EXPECTED COSTS = 10.5 X $2 X 7.7 = $84.70

34. IF WE REORDER AT 130, THE POSSIBLE STOCK-OUTS AND THEIR PROBABILITIES ARE:
DEMAND
STOCK-OUT
P[SO]
E[SO]
140 10
0.10
1.0
150 20
0.05
160 30
1.5
3.5
EXPECTED COSTS = 3.5 X $2 X 7.7 = $53.90

35. IF WE REORDER AT 140, THE POSSIBLE STOCK-OUTS AND THEIR PROBABILITIES ARE:
DEMAND
STOCK-OUT
P[SO]
E[SO]
150 10
0.05
0.5
160 20
1.0
1.5
EXPECTED COSTS = 1.5 X $2 X 7.7 = $23.10

36. IF WE REORDER AT 150, THE POSSIBLE STOCK-OUTS AND THEIR PROBABILITIES ARE:
DEMAND
STOCK-OUT
P[SO]
E[SO]
160 10
0.05
0.5
EXPECTED COSTS = 0.5 X $2 X 7.7 = $7.70

37. CARRYING COSTS
WE WILL OVERSIMPLIFY THE ESTIMATION OF CARRYING COSTS AND ESTIMATE CARRYING COSTS RELATIVE TO EXPECTED DEMAND
IF WE REORDER AT 110, 120, OR 130 [EXPECTED DEMAND], WE WILL HAVE NO SAFETY STOCK AND THUS NO CARRYING COSTS

38. CARRYING COSTS AT 140 AND 150 REORDER POINTS
SAFETY STOCK
CARRYING COSTS PER UNIT
CARRYING COSTS
140 10 $6
$60
150 20
$120
160 30
$180

39. REORDERING AT 130 YIELDS THE LOWEST COSTS
TOTAL COSTS
REORDER POINT
STOCK-OUT COSTS
CARRYING COSTS
TOTAL COSTS
110
300.30
120
84.70
130
53.90
140
23.10
60.00
83.10
150
7.70
120.00
127.70
160
180.00
REORDERING AT 130 YIELDS THE LOWEST COSTS

40. EXERCISE - CONTINUATION
THE E[COST OF A STOCKOUT] = $3
THE LEAD TIME (TIME BETWEEN PLACING AN ORDER AND RECEIVING THE GOODS) IS 1 MONTH. EXPECTED USE PER MONTH:
ASSUME WE WILL ORDER 6 TIMES PER YEAR
DEMAND
PROB. 30
0.10 40
0.20 50
0.50 60 70
0.05 80

41. CALCULATE EXPECTED DEMAND
PROB.
E[D] 30
0.10 3 40
0.20 8 50
0.50 25 60 6 70
0.05
3.5 80 4

42. STOCK-OUT COSTS EXPECTED COSTS = 19.5 X $3 X 6 = $351
IF WE REORDER AT 30, THE POSSIBLE STOCK-OUTS AND THEIR PROBABILITIES ARE:
DEMAND
STOCK-OUT
P[SO]
E[SO] 40 10
0.20
2.0 50 20
0.50
10.0 60 30
0.10
3.0 70
0.05 80
2.5
19.5
EXPECTED COSTS = 19.5 X $3 X 6 = $351

43. IF WE REORDER AT 40, THE POSSIBLE STOCK-OUTS AND THEIR PROBABILITIES ARE:
DEMAND
STOCK-OUT
P[SO]
E[SO] 50 10
0.50
5.0 60 20
0.10
2.0 70 30
0.05
1.5 80 40
10.5
EXPECTED COSTS = 10.5 X $3 X 6 = $186

44. IF WE REORDER AT 50, THE POSSIBLE STOCK-OUTS AND THEIR PROBABILITIES ARE:
DEMAND
STOCK-OUT
P[SO]
E[SO] 60 10
0.10
1.0 70 20
0.05 80 30
1.5
3.5
EXPECTED COSTS = 3.5 X $3 X 6 = $63

45. IF WE REORDER AT 60, THE POSSIBLE STOCK-OUTS AND THEIR PROBABILITIES ARE:
DEMAND
STOCK-OUT
P[SO]
E[SO] 70 10
0.05
0.5 80 20
1.0
1.5
EXPECTED COSTS = 1.5 X $3 X 6 = $27

46. IF WE REORDER AT 70, THE POSSIBLE STOCK-OUTS AND THEIR PROBABILITIES ARE:
DEMAND
STOCK-OUT
P[SO]
E[SO] 80 10
0.05
0.5
EXPECTED COSTS = 0.5 X $3 X 6 = $9

47. CARRYING COSTS
WE WILL OVERSIMPLIFY THE ESTIMATION OF CARRYING COSTS AND ESTIMATE CARRYING COSTS RELATIVE TO EXPECTED DEMAND
IF WE REORDER AT 30, 40, OR 50 [EXPECTED DEMAND], WE WILL HAVE NO SAFETY STOCK AND THUS NO CARRYING COSTS

48. CARRYING COSTS AT 60, 70 AND 80 REORDER POINTS
SAFETY STOCK
CARRYING COSTS PER UNIT
CARRYING COSTS 60 10 $3
$30 70 20
$60 80 30
$90

49. REORDERING AT 60 YIELDS THE LOWEST COSTS
TOTAL COSTS
REORDER POINT
STOCK-OUT COSTS
CARRYING COSTS
TOTAL COSTS 30
351 40
186 50 63 60 27 57 70 9 69 80 90
REORDERING AT 60 YIELDS THE LOWEST COSTS

50. MATERIALS REQUIREMENTS PLANNING (MRP) AND JUST-IN-TIME (JIT)
MRP IS A “PUSH-THROUGH” INVENTORY SYSTEM
JIT IS A “DEMAND-PULL” INVENTORY SYSTEM

51. MRP & JIT
MRP IS A TYPICAL INVENTORY SYSTEM WHERE INVENTORY IS MAINTAINED IN RELATION TO FORECASTED NEEDS
JIT IS A SYSTEM WHERE GOODS ARE PRODUCED AS THEY ARE NEEDED
UNDER JIT, INVENTORY CARRYING COSTS ARE MINIMIZED, BUT
WHAT HAPPENS IF THERE IS A BREAK IN PRODUCTION/SUPPLY?

52. BACKFLUSH COSTING IF AN INVENTORY ACCOUNT, E.G., RAW MATERIALS
WORK-IN-PROCESS
FINISHED GOODS
IS IMMATERIAL,
THEN IT IS ELIMINATED FROM THE RECORDS, I.E., COSTS FLOW PAST THAT ACCOUNT

53. DIAGRAMATICALLY OR OR OR MATERIALS WIP FG COGS CONVERSION COSTS
PURCHASES
WIP FG
COGS
CONVERSION
COSTS OR
PURCHASES FG
COGS
CONVERSION
COSTS OR
PURCHASES
COGS
CONVERSION
COSTS