INVENTORY MANAGEMENT, JIT, AND BACKFLUSH COSTING CHAPTER 20

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

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

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

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.

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

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

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

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

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

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

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

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

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.

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

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

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

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

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.

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

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

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

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

TOTAL COSTS TREAT DISCOUNTS AS ADDITIONAL COSTS ORDER: 130: 150: TREAT DISCOUNTS AS COSTS REDUCTIONS (7.692 @ $50) + (65 @ $6) + (1,000 @ $0.50) = $1,275 (6.667 @ $50) + (75 @ $6) = $783 (7.692 @ $50) + (65 @ $6) = $775 (6.667 @ $50) + (75 @ $6) - 1,000 @ $0.50 = $283

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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