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20171026014218economic_order_quantity_and_safety_stock_microwave_inventory2.docx
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Microwave Inventory Case

Intelligent Microwaves, Inc.

Intelligent Microwaves, Inc. (IMI) produces a wide range of personal and commercial microwaves, including a heavy-duty microwave oven for use in restaurants and other heavy use environments. Their microwaves are considered to be very reliable and have many “intelligent” features that customers appreciate. Recently, however, competitive price pressures have cut into IMI’s profit margins and they are taking a look at their operations to try to find ways to reduce cost while maintaining or improving product quality and customer service. You have been asked to look at their production and distribution of their heavy-duty microwave oven.

IMI actually produces 6 models of the heavy-duty microwave but they are essentially the same except for the power supply and the language of the instructions that are on the microwave. These differentiating features result in the 6 models and are necessary to meet the requirements of different overseas customers. IMI has always produced each microwave model in batches large enough to satisfy one month’s worth (30 days) of average demand. Historical records indicate it takes them on average 30 days, with a standard deviation of 4 days to produce a batch and an average of 7 days, with a standard deviation of 2 days, to ship a batch of microwaves to the appropriate warehouse in the appropriate country. There is a setup cost of $1000 to get the production line prepared to produce any of the heavy-duty models. One microwave of any model is valued at $500. Through trial and error over the last few years, IMI has found that using a reorder point of 51 days of supply (51 times the average daily demand) has given them a reliable performance, only running out of microwaves about 2% of the time while waiting for a new shipment to arrive. IMI uses an inventory carrying charge of $.25 per dollar of inventory per year.

Intelligent Microwaves:

Production and Distribution of Heavy Duty Microwaves

6 models of Heavy Duty Microwaves

Produced in batches to satisfy one month’s (30 days) of average demand

Production time – mean= 30 days, std dev = 4 days

Ship time – mean 7 days, std dev 2 days

Setup cost of $1000 to prepare the production line for any batch = Order cost

Each microwave is valued at $500

Reorder point is 51 days of supply = 51 days * average daily demand

Has yielded a 2% probability of stockout

Inventory carrying cost is $0.25/dollar of inventory

Key formulas

Lead time = Production time + Ship time

Demand during lead time = Lead time * Average daily demand

Std Dev of demand during lead time =>

Safety stock = Reorder point – Demand during lead time

Safety stock = z * std dev of demand during lead time thus`

Z = safety stock / std dev of demand during lead time

Service level = NORMDIST(z)

Total cost = Annual Purchase Cost + Annual Ordering Cost + Annual Holding Cost

TC = DC + (D/Q)S + (Q/2 + SS)H where

(D=Demand, C=Cost/unit, Q = order qty, S=Order cost, H=Holding cost, SS = Safety Stock)

A Based on the Microwave Inventory Case answers to the following question in form of a report:

1. Calculate the current cost of IMI’s inventory practices using the CURRENT tab of the template provided.

2. What would be the potential benefits of selecting both the production batch sizes and the reorder points more scientifically? Do this by completing columns B through H of the ANALYSIS tab of the template provided. Using the concepts of Economic Order Quantity and Reorder Point, explain the difference between this model and IMI’s current practice.

3. What if IMI was able to fully standardize the heavy-duty model to the point where the language and power supply customizing features could be added in a modular fashion immediately before shipping to the warehouse that needs them? You consulted with the production superintendent, who indicated that this could be done, but that it would add one day to the ship time to add these customizing features to the standard microwave just prior to shipping.

Consider it this way. IMI maintains a warehouse right next to their factory and they store inventory for models A, B, C, D, E, and F. Therefore they have to maintain separate inventory for each of the models. If they standardize to a single model, it may take them a day to ship, but they only need to keep one type of microwave in their warehouse.

For this part use the SINGLE MODEL column of the ANALYSIS tab and consider the impact RISK POOLING has should IMI combine all models. Using the inventory concepts we discussed in class, explain to IMI why they might achieve some cost benefit by embracing the idea of replacing all of their models with a single model.

4. Assuming that you have now convinced IMI to standardize on a single model of microwave, investigate other opportunities that IMI may have to reduce costs or improve customer service. Look at the components of total cost (not limited to transportation time, order cost, supply or demand variability) and make a recommendation to IMI on where else they may want to focus their efforts. Justify your recommendations.

5. Perform a sensitivity analysis and evaluate potential additional benefits focusing in Economic Order Quantity and Safety Stock

6. On the spreadsheet add a column and consider:

· Reducing set-up times

· Reducing production or lead times?

· What about variances

B. Paper should be professionally structured, well-organized, insightful, start with an executive overview, and conclude by emphasizing the most important parts of the analysis.

Based on the spreadsheet summarized results and deliver in form or report.

· what you have discovered

· Draw conclusions and summarize findings

· In what other areas might you invest?

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Microwave ModelABCDEF

Daily Demand:

Average122288359744

Std. Dev.171867192222

Current

Microwave Model A B C D E F Total
$ Value 500.00 500.00 500.00 500.00 500.00 500.00
Order Quantity 360 660 2640 1050 2910 1320
Reorder Point 612 1122 4488 1785 4947 2244
Holding Cost Factor 0.25 0.25 0.25 0.25 0.25 0.25
Fixed Cost Per Order 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00
Daily Demand:
Average 12 22 88 35 97 44
Std. Dev. 17 18 67 19 22 22
Ship Time (days):
Average 7 7 7 7 7 7
Std. Dev. 2 2 2 2 2 2
Production Time (days):
Average 30 30 30 30 30 30
Std. Dev. 4 4 4 4 4 4
Lead Time (days):
Average 37.00 37.00 37.00 37.00 37.00 37.00
Std. Dev. 4.47 4.47 4.47 4.47 4.47 4.47
Demand during Lead Time:
Average 444 814 3256 1295 3589 1628
Std. Dev. 117 147 567 195 454 238
Safety Stock:
Units 168 308 1232 490 1358 616
Safety Factor (Std. Devs.) 1.44 2.09 2.17 2.52 2.99 2.59
Inventory Performance:
Service Level 0.9254 0.9818 0.9852 0.9941 0.9986 0.9952 0.9800
Annual Holding Cost:
Cycle Stock 22500 41250 165000 65625 181875 82500 558750
Safety Stock 21000 38500 154000 61250 169750 77000 521500
Total 43500 79750 319000 126875 351625 159500 1080250
Anuual Fixed Order Cost 12166.6666666667 12166.6666666667 12166.6666666667 12166.6666666667 12166.6666666667 12166.6666666667 73000
Annual Total Cost 55666.6666666667 91916.6666666667 331166.666666667 139041.666666667 363791.666666667 171666.666666667 1153250
p038981: sqrt(sum of variances of ship time + production time)
p038981: Average daily demand * average lead time

Order Quantity

Microwave Model A B C D E F Total
$ Value 500.00 500.00 500.00 500.00 500.00 500.00
Order Quantity 265 358 717 452 753 507
Reorder Point 612 1122 4488 1785 4947 2244
Holding Cost Factor 0.25 0.25 0.25 0.25 0.25 0.25
Fixed Cost Per Order 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00
Daily Demand:
Average 12 22 88 35 97 44
Std. Dev. 17 18 67 19 22 22
Ship Time (days):
Average 7 7 7 7 7 7
Std. Dev. 2 2 2 2 2 2
Production Time (days):
Average 30 30 30 30 30 30
Std. Dev. 4 4 4 4 4 4
Lead Time (days):
Average 37.00 37.00 37.00 37.00 37.00 37.00
Std. Dev. 4.47 4.47 4.47 4.47 4.47 4.47
Lead Time Demand:
Average 444 814 3256 1295 3589 1628
Std. Dev. 117 147 567 195 454 238
Safety Stock:
Units 168 308 1232 490 1358 616
Safety Factor (Std. Devs.) 1.44 2.09 2.17 2.52 2.99 2.59
Inventory Performance:
Service Level 0.9254 0.9818 0.9852 0.9941 0.9986 0.9952 0.9800
Annual Holding Cost:
Cycle Stock 16545.3921077743 22402.5668172199 44805.1336344397 28256.6363886433 47040.5410258003 31682.0138248818 190732
Safety Stock 21000 38500 154000 61250 169750 77000 521500
Total 37545.3921077743 60902.5668172198 198805.13363444 89506.6363886433 216790.5410258 108682.013824882 712232
Anuual Fixed Order Cost 16545.3921077743 22402.5668172198 44805.1336344397 28256.6363886433 47040.5410258003 31682.0138248818 190732
Annual Total Cost 54090.7842155486 83305.1336344397 243610.267268879 117763.272777287 263831.082051601 140364.027649764 902965

Safety Stock

Microwave Model A B C D E F Total
$ Value 500.00 500.00 500.00 500.00 500.00 500.00
Order Quantity 360 660 2640 1050 2910 1320
Desired Service Level 0.9800 0.9800 0.9800 0.9800 0.9800 0.9800
Reorder Point 683 1116 4420 1695 4521 2117
Holding Cost Factor 0.25 0.25 0.25 0.25 0.25 0.25
Fixed Cost Per Order 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00
Daily Demand:
Average 12 22 88 35 97 44
Std. Dev. 17 18 67 19 22 22
Ship Time (days):
Average 7 7 7 7 7 7
Std. Dev. 2 2 2 2 2 2
Production Time (days):
Average 30 30 30 30 30 30
Std. Dev. 4 4 4 4 4 4
Lead Time (days):
Average 37.00 37.00 37.00 37.00 37.00 37.00
Std. Dev. 4.47 4.47 4.47 4.47 4.47 4.47
Lead Time Demand:
Average 444 814 3256 1295 3589 1628
Std. Dev. 117 147 567 195 454 238
Safety Stock:
Units 239 302 1164 400 932 489
Safety Factor (Std. Devs.) 2.05 2.05 2.05 2.05 2.05 2.05
Inventory Performance:
Service Level 0.9800 0.9800 0.9800 0.9800 0.9800 0.9800 0.9800
Annual Holding Cost:
Cycle Stock 22500 41250 165000 65625 181875 82500 558750
Safety Stock 29908.5245802184 37789.0938693328 145442.494813956 49949.3869522672 116542.255003939 61090.3588880882 440722
Total 52408.5245802184 79039.0938693328 310442.494813956 115574.386952267 298417.255003939 143590.358888088 999472
Anuual Fixed Order Cost 12166.6666666667 12166.6666666667 12166.6666666667 12166.6666666667 12166.6666666667 12166.6666666667 73000
Annual Total Cost 64575.191246885 91205.7605359995 322609.161480623 127741.053618934 310583.921670605 155757.025554755 1072472

OQ and SS

Microwave Model A B C D E F Total
$ Value 500.00 500.00 500.00 500.00 500.00 500.00
Order Quantity 265 358 717 452 753 507
Desired Service Level 0.9800 0.9800 0.9800 0.9800 0.9800 0.9800
Reorder Point 683 1116 4420 1695 4521 2117
Holding Cost Factor 0.25 0.25 0.25 0.25 0.25 0.25
Fixed Cost Per Order 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00
Daily Demand:
Average 12 22 88 35 97 44
Std. Dev. 17 18 67 19 22 22
Ship Time (days):
Average 7 7 7 7 7 7
Std. Dev. 2 2 2 2 2 2
Production Time (days):
Average 30 30 30 30 30 30
Std. Dev. 4 4 4 4 4 4
Lead Time (days):
Average 37.00 37.00 37.00 37.00 37.00 37.00
Std. Dev. 4.47 4.47 4.47 4.47 4.47 4.47
Lead Time Demand:
Average 444 814 3256 1295 3589 1628
Std. Dev. 117 147 567 195 454 238
Safety Stock:
Units 239 302 1164 400 932 489
Safety Factor (Std. Devs.) 2.05 2.05 2.05 2.05 2.05 2.05
Inventory Performance:
Service Level 0.9800 0.9800 0.9800 0.9800 0.9800 0.9800 0.9800
Annual Holding Cost:
Cycle Stock 16545.3921077743 22402.5668172199 44805.1336344397 28256.6363886433 47040.5410258003 31682.0138248818 190732
Safety Stock 29908.5245802184 37789.0938693328 145442.494813956 49949.3869522672 116542.255003939 61090.3588880882 440722
Total 46453.9166879927 60191.6606865527 190247.628448396 78206.0233409105 163582.796029739 92772.37271297 631454
Anuual Fixed Order Cost 16545.3921077743 22402.5668172198 44805.1336344397 28256.6363886433 47040.5410258003 31682.0138248818 190732
Annual Total Cost 62999.308795767 82594.2275037725 235052.762082835 106462.659729554 210623.337055539 124454.386537852 822187

Standard

Microwave Model A B C D E F Standard
$ Value 500.00 500.00 500.00 500.00 500.00 500.00 500.00
Order Quantity 265 358 717 452 753 507 1319
Desired Service Level 0.9800 0.9800 0.9800 0.9800 0.9800 0.9800 0.9800
Reorder Point 683 1116 4420 1695 4521 2117 14243
Holding Cost Factor 0.25 0.25 0.25 0.25 0.25 0.25 0.25
Fixed Cost Per Order 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00
Daily Demand:
Average 12 22 88 35 97 44 298
Std. Dev. 17 18 67 19 22 22 80.1935159474
Ship Time (days):
Average 7 7 7 7 7 7 8
Std. Dev. 2 2 2 2 2 2 2
Production Time (days):
Average 30 30 30 30 30 30 30
Std. Dev. 4 4 4 4 4 4 4
Lead Time (days):
Average 37.00 37.00 37.00 37.00 37.00 37.00 38.00
Std. Dev. 4.47 4.47 4.47 4.47 4.47 4.47 4.47
Lead Time Demand:
Average 444 814 3256 1295 3589 1628 11324
Std. Dev. 117 147 567 195 454 238 1421
Safety Stock:
Units 239 302 1164 400 932 489 2919
Safety Factor (Std. Devs.) 2.05 2.05 2.05 2.05 2.05 2.05 2.05
Inventory Performance:
Service Level 0.9800 0.9800 0.9800 0.9800 0.9800 0.9800 0.9800
Annual Holding Cost:
Cycle Stock 16545.3921077743 22402.5668172199 44805.1336344397 28256.6363886433 47040.5410258003 31682.0138248818 82451
Safety Stock 29908.5245802184 37789.0938693328 145442.494813956 49949.3869522672 116542.255003939 61090.3588880882 364907
Total 46453.9166879927 60191.6606865527 190247.628448396 78206.0233409105 163582.796029739 92772.37271297 447358
Anuual Fixed Order Cost 16545.3921077743 22402.5668172198 44805.1336344397 28256.6363886433 47040.5410258003 31682.0138248818 82451
Annual Total Cost 62999.308795767 82594.2275037725 235052.762082835 106462.659729554 210623.337055539 124454.386537852 529808
p038981: one more day for site customization