Welcome to this article with the aim of helping you with 11 inventory management exercises using the Wilson method from the Operational Management subject of the BTS MCO.
If you would like to first review the course on the same theme, Inventory Management, I invite you to read my article Inventory Management: The 7 Key Points to Master and also the article Supply Management: The 3 essential principles.
In this section:
Application: SARL Nouvelle Vague
States :
SARL Nouvelle Vague is a company specializing in the sale of high-end surfboards. It is looking to optimize its inventory management and has hired you as a financial management expert to help it.
Here is some relevant information:
– Cost of placing an order: €100
– Annual demand: 2400 surfs
– Cost of Ownership: €2 per surf per year
– Standard deviation of daily demand: 2 surfs
– Safety coefficient: 2
– Delivery time (Lead time): 5 days
– Average daily demand: 10 surfs
Work to do :
1. Calculate the Optimal Lot.
2. Calculate the Safety Stock.
3. Calculate the Maximum Stock.
4. Calculate the Reorder Point.
5. How would you use this information to improve the company's inventory management?
Proposed correction:
1. The Optimal Lot = ?((2 x Cost of placement x Annual demand) ÷ Cost of Ownership) = ?((2 x €100 x 2400 surfs) ÷ €2) = 120 surfs.
2. Safety Stock = Standard Deviation of Demand x Safety Coefficient = 2 surfs x 2 = 4 surfs.
3. Maximum Stock = Optimal Lot + Safety Stock = 120 surfs + 4 surfs = 124 surfs.
4. Reorder Point = Lead time*Average daily demand + Safety stock = 5 days*10 surfs + 4 surfs = 54 surfs.
5. SARL Nouvelle Vague may use this information to determine when to place new orders and how many surfboards to order each time. It may also determine the maximum number of surfboards it must have in stock to meet demand while minimizing its costs.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Maximum stock = Optimal lot + Safety stock | This is the maximum amount of products you should have in stock. |
| Optimal Lot = ?((2 x Cost of Placement x Annual Demand) ÷ Cost of Ownership) | This is the quantity of products that is best ordered each time to minimize total costs. The formula takes into consideration the cost of ordering and the cost of carrying inventory. |
| Safety stock = Standard deviation of demand x Safety coefficient | This is the amount of product you keep in reserve to accommodate unforeseen variations in demand or delivery times. |
| Reorder point = Lead time*Average daily demand + Safety stock | This is the inventory level that should trigger a new order to replenish stocks. |
Application: Wilson Company
States :
Wilson Company is a distributor of car parts. The company sells both retail and wholesale. They have a large number of references and need to optimize their inventory management to minimize their costs. One of their references is a spare part for which the ordering cost is €150, the annual unit holding cost is €3 and their annual demand for this reference is 900 parts.
Work to do :
1. What is the formula for the Wilson Inventory Management exercise?
2. What is the economic order quantity for this reference?
3. What is the inventory carrying cost for this reference per year?
4. What is the cost of placing orders for this reference per year?
5. What is the total cost of managing inventory for this reference per year?
Proposed correction:
1. The Wilson inventory management formula, also called the Wilson formula or the economic lot formula, is as follows: Q = ?((2xDxC) / H) Where D is the annual demand, C is the ordering cost, and H is the annual unit holding cost.
2. To calculate the economic order quantity for this reference, we use the Wilson formula: Q = ?((2x900x150) / 3) = ?(270000) = 519,6. We will round up to 520 pieces.
3. The cost of holding the stock for this reference per year is calculated by multiplying the unit holding cost by the economic order quantity divided by two (because on average, we have half the economic quantity in stock): €3 x (520 / 2) = €780.
4. The cost of placing orders for this reference per year is determined by dividing the annual demand by the economic order quantity and multiplying by the order cost: (900 / 520) x €150 = €260,77.
5. The total cost of managing inventory for this reference per year is the sum of the holding and transfer costs: €780 + €260,77 = €1040,77.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Q = ?((2xDxC) / H) | Wilson's formula for calculating economic order quantity. |
| Annual cost of ownership = H x (Q / 2) | Formula for calculating the carrying cost of inventory per year. |
| Annual contracting cost = (D / Q) x C | Formula for calculating the cost of placing orders per year. |
| Total inventory management cost = Annual carrying cost + Annual handover cost | Formula to calculate the total cost of inventory management per year. |
Application: La Bonne Mie Bakery.
States :
A bakery called 'La Bonne Mie' keeps a variety of products in stock. One of their flagship products is pain au chocolat. They have the following information regarding pain au chocolat:
– Annual demand (D): 36 pains au chocolat.
– Cost of placing an order (S): €50.
– Storage cost per unit per year (H): €0,2.
– Standard deviation of demand during delivery time (?LT): 60 pains au chocolat.
– Order cycle in days (L): 30 days.
Work to do :
1. Calculate the economic order quantity (EOQ).
2. Calculate the number of orders per year.
3. Calculate safety stock.
4. If the bakery wants to maintain a 95% service level, how many additional units of pain au chocolat should it store in safety stock?
5. What is the total annual cost of holding and ordering for the bakery?
Proposed correction:
1. The economic order quantity (EOQ) is calculated as follows: EOQ = ?((2DS)/H) = ?((2*36*000)/50) = 0,2 pains au chocolat.
2. The number of orders per year is calculated as follows: N = D/QEC = 36 / 000 = 6 orders per year.
3. The safety stock is calculated as follows: SS = (D x ?LT) / ?L = (36 x 000) / ?60 = 30 / ?24 = 000 pains au chocolat.
4. For a service level of 95%, the bakery should increase its safety stock by 5%, i.e.: 4 x 386% = 5 pains au chocolat. That is a total of 219 pains au chocolat in the safety stock.
5. The total annual cost of holding and placing orders is: (N x S) + (QEC/2 x H) = (6 x 50) + (6/000 x 2) = 0,2 + 300 = €600.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Economic order quantity (EOQ) = ?((2DS)/H) | Wilson's formula for determining the economic order quantity (EOQ), where D represents annual demand, S is the cost of placing an order, H is the storage cost per unit per year. |
| Number of orders per year (N) = D/QEC | Form to determine the number of orders per year. |
| Safety stock (SS) = (D x ?LT) / ?L | Formula for determining safety stock. ?LT is the standard deviation of demand during the delivery time (LT) and L is the order cycle in days. |
Application: Boutique Chic
States :
Boutique Chic is a high fashion clothing retailer. They recently hired you, a financial management expert, to help keep their inventory afloat. Boutique Chic specializes in women's and men's clothing, all of which are manufactured in-house. The annual demand is 10 units for a particular item, the ordering cost is €000 per order, the unit cost is €75 per unit, and the storage cost is €5 per unit per year.
Work to do :
1. Calculate the optimal quantity of orders per year.
2. Calculate the number of orders placed each year.
3. Calculate the total annual cost of inventory management.
4. Determine the time between two commands.
5. What is the proportion of safety stock to average stocks?
Proposed correction:
1. For the calculation of the optimal order quantity, we use Wilson's formula: Q = ?(2 x D x S / H) where D is the annual demand, S is the ordering cost and H is the storage cost per unit. Therefore, Q = ?(2 x 10 x 000 / 75) = 0,25 units.
2. The number of orders per year is calculated by dividing the annual demand by the optimal order quantity (D/Q). So N = 10000 ÷ 20000 = 0,5 times per year, which means that two years are needed to place an order.
3. The total annual cost of inventory management can be calculated using the following formula: (Q/2) x H + (D/Q) x S. Therefore, CT = (20000/2) x 0,25 + (10000/20000) x 75 = €2500 + €37,5 = €2537,5.
4. The lead time between two orders can be calculated by dividing the number of days per year by the number of orders per year. Assuming that the year has 365 days, the lead time between two orders is therefore 365 ÷ 0,5 = 730 days.
5. The proportion of safety stock to average stocks was not provided in the statement, so it is not possible to give a precise answer. Generally, this proportion varies depending on the desired performance level and the risk of stock depletion.
Summary of Formulas Used:
| Optimal order quantity | Q = ?(2 x D x S / H) |
|---|---|
| Number of orders per year | N = D / Q |
| Total annual cost of inventory management | CT = (Q/2) x H + (D/Q) x S |
| Delay between two orders | Lead time = Number of days per year / Number of orders per year |
Application: SportsGear
States :
SportsGear, a company specializing in high-end sports equipment, uses the Wilson method for inventory management. Their flagship product is a pair of tennis rackets, for which they provide the following data:
– Annual demand: 2000 units
– Cost of placing an order: €50
– Storage cost per unit per year: €2
Work to do :
1. Determine the optimal batch size to order
2. How many times per year does the company need to place orders at this quantity level?
3. How much time elapses between two orders?
4. What is the total annual cost of orders?
5. What is the total annual storage cost?
Proposed correction:
1. Wilson's formula for determining lot size L is: L = ?((2xDxCd)/Cs), where D = annual demand, Cd = cost of placing an order, Cs = storage cost per unit per year. We therefore have L = ?((2x2000x50)/2) = 1000 units
2. The company must place a D/L order once a year, so 2000/1000 = 2 times a year.
3. The time between two orders is 365 / (D/L) days so 365 /2 = 182,5 days.
4. The total annual cost of orders is D/L * Cd, so 2000/1000 * 50 = €100.
5. The total annual storage cost is L/2 * Cs, so 1000/2 * 2 = €1000.
Summary of Formulas Used:
| Packages | Meaning |
|---|---|
| L = ?((2xDxCd)/Cs) | Optimal order batch size |
| D / L | Number of orders per year |
| 365 / (D/L) | Time between two orders |
| D/L * Cd | Total annual cost of orders |
| L/2 * Cs | Total annual storage cost |
Application: FinestThread
States :
FinestThread Textiles, a high-quality wool yarn manufacturer based in France, uses Wilson’s inventory management model to manage their yarn inventory. Management manager Patrick wants to review the efficiency of the existing model to ensure better inventory control and optimize costs.
Patrick has the following information:
– Annual yarn consumption is 12 kg.
– The cost of launching the order is €75.
– The cost of ownership (storage, obsolescence, insurance, etc.) is €1 per kg per year.
– The cost of purchasing the yarn is €20 per kg.
– The delivery time is systematically 2 weeks.
The applicable VAT rate is 20%.
Work to do :
1. Calculate the optimal order quantity using Wilson's formula.
2. What is the total annual cost of inventory management?
3. If the delivery time varies and can be up to 3 weeks, how does this affect the safety stock?
4. If Patrick decides to order less than the calculated optimal quantity, how will this affect inventory management costs?
5. How can variation in holding cost affect optimal order quantity and total inventory management cost?
Proposed correction:
1. The optimal order quantity (Q*) can be calculated by Wilson's formula: Q* = ?((2DS)/H) with D = annual consumption, S = order launch cost and H = carrying cost. Therefore, Q* = ?((2*12000*75)/1) = 1000 kg.
2. The total annual cost of inventory management (CT*) = D*CA + (Q*/2)*H + (D/Q*)*S = 12*000 + (20/1000)*2 + (1/12)*000 = €1000.
3. If the delivery time is up to 3 weeks, the safety stock should be increased to cover the risk of stock shortages during this period.
4. If Patrick decides to order a quantity lower than the calculated optimal quantity (Q < Q*), the number of annual orders will increase, thus increasing launch costs.
At the same time, there will be a decrease in the carrying cost due to the lower average inventory level. 5. If the carrying cost increases, the optimal order quantity Q* will decrease, in order to minimize these costs.
At the same time, the total cost of inventory management will increase due to higher carrying costs.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Q* = ?((2DS)/H) | Optimal order quantity |
| CT* = D*CA + (Q*/2)*H + (D/Q*)*S | Total annual cost of inventory management |
Application: OptimumTech Company
States :
OptimumTech is a manufacturer specializing in digital technologies. Each year, the company produces and sells thousands of items. Currently, OptimumTech uses a standard inventory replenishment system, but has found that it often has too much or too little inventory to meet demand. Management is considering implementing Wilson's inventory management method to optimize its process.
The information for last year is as follows:
– Annual consumption: 60 units
– Cost of placing an order: €200
– Annual storage cost: €15 per unit
Work to do :
1. Calculate the optimal number of orders to place in the year using Wilson's formula.
2. Find the optimal quantity to order at each replenishment.
3. Determine the total cost of inventory management using the results obtained previously.
4. Estimate the time between two orders in days.
5. Analyze the impact of a 10% increase in annual consumption and a 5% decrease in the cost of placing an order on the quantity to be ordered at each replenishment and on the number of orders to be placed in the year.
Proposed correction:
1. The optimal number of orders to place in the year is calculated using Wilson's formula:
N = ?(2DS/H), where D = annual demand, S = cost of placing an order and H = annual storage cost per item.
N = ?(2×60,000×200÷15)
N? 113 orders in the year.
2. The optimal quantity to order at each replenishment is calculated as follows:
Q = D/N
Q = 60,000 ÷ 113
Q? 531 units
3. The total cost of inventory management is the sum of the cost of placing orders and the cost of storing the items, therefore:
C = DS + HQ/2
C = 113×200 + 15×531/2
C = 22,600 + 3,980
C = €26,580
4. The time between two orders in days is calculated as follows:
T = 365/N
T = 365/113
T ? 3,23 days between two orders.
5. If annual consumption increases by 10% and the cost of placing an order decreases by 5%, we have:
D' = 60,000 x 1.1 = 66,000
S' = 200 x 0.95 = 190
H = 15
N' = ?(2D'S'/H)
N' ? 120 orders in the year.
Q' = D'/N'
Q' ? 550 units
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| N = ?(2DS/H) | Wilson's formula for the optimal number of orders per year |
| Q = D/N | Formula for the optimal quantity to order at each replenishment |
| C = DS + HQ/2 | Formula for Total Cost of Inventory Management |
| T = 365/N | Formula for time between two orders in days |
| D' = D x 1.1, S' = S x 0.95 | Adjustment formulas for increased consumption and decreased ordering cost |
Application: Le Wilson Supermarket
States:
Le Wilson supermarket would like to optimize its rice stock management. They sell about 10 bags per year, the cost of placing an order is €000, the cost of holding a bag in its stock for a year is €150.
Work to do :
1. Calculate the economic order quantity of rice for Wilson supermarket.
2. If the supermarket does not follow this recommendation and orders a quantity of 3000 bags at a time, how much will this cost in total annual costs?
3. If the supermarket follows the recommendation and orders an economical order quantity, how many orders will the supermarket have to place per year?
4. Respecting the economic order quantity, what will be the average stock over a year?
5. What is the total annual cost respecting the economic order quantity?
Proposed correction:
1. The formula for calculating the economic order quantity (EOQ) is: ?((2 * D * S)÷H) where D is the annual demand, S is the cost of placing an order and H is the annual unit holding cost. Applying this formula we obtain: ?((2 * 10 * 000)÷150) = ?2 ? 1 bags.
2. To calculate the total annual costs if the order quantity is 3000 bags at a time, we use the formula: (D÷Q)*S + (Q÷2)*H. Therefore, (10 ÷ 000) * 3000 + (150 ÷ 3000) * 2 = €2.
3. The supermarket will need to place approximately (D/Q) orders per year. So, (10 ÷ 000) ? 1. So, the supermarket will need to place approximately 225 orders per year.
4. The average stock over a year for a balanced cycle is calculated by (Q÷2). Therefore, (1 ÷ 225) = 2 bags.
5. The total annual cost respecting the economic order quantity is (D/Q)*S + (Q/2)*H. Therefore, (10 ÷ 000) * 1 + (225 ÷ 150) * 1 ? €225.
Summary of the formulas used:
| Packages | Explanations |
| QEC = ?((2 * D * S)/H) | Economic order quantity |
| Total cost = (D/Q)*S + (Q/2)*H | Total annual cost |
| Number of orders = D/Q | Number of annual orders |
| Average stock = Q/2 | Average stock over a year for a balanced cycle |
Application: Gastronomy Delight
States :
The company Gastronomie Délice is a business that sells high-end food products. Antoine, the manager, wants to improve his company's inventory management. One of its flagship products is the "Château Noblesse" wine. Antoine has collected the following information for this product:
– The order cost is €60.
– The storage cost per bottle per year is €3.
– The annual demand is 1200 bottles.
– The supplier offers a delivery time of 7 days.
– The Gastronomie Delice company is open 300 days a year.
Work to do :
1. Calculate the total cost of managing the inventory of “Château Noblesse” wine using Wilson’s formula.
2. Calculate the number of orders to be placed during the year.
3. Calculate the quantity to order for each order.
4. Calculate the safety stock level.
5. Determine the replenishment period.
Proposed correction:
1. Wilson's formula: Total cost = sqrt((2 x Annual demand x Ordering cost) ÷ Storage cost). Therefore, Total cost = sqrt((2 x 1200 x 60) ÷ 3) = €800.
2. Number of orders = Annual demand ÷ Quantity to order. However, we need the quantity to order. We use Wilson's formula for this: Quantity to order = sqrt((2 x Annual demand x Order cost) ÷ Storage cost). Thus, Quantity to order = sqrt((2 x 1200 x 60) ÷ 3) = 400 bottles. We can therefore calculate the number of orders: Number of orders = 1200 ÷ 400 = 3.
3. We have already calculated the quantity to order for the second question, so the quantity to order in each order is 400 bottles.
4. Safety stock level = Demand during delivery time. Knowing that the daily demand is 1200 ÷ 300 = 4 bottles, the safety stock level = 4 x 7 = 28 bottles.
5. Replenishment period = Time between two orders. Knowing that the company is open 300 days a year and that there are 3 orders per year, the replenishment period = 300 ÷ 3 = 100 days.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| sqrt((2 x Annual Demand x Ordering Cost) ÷ Storage Cost) | Wilson's Formula for Total Cost and Order Quantity |
| Annual demand ÷ Quantity to order | Formula to calculate the number of orders |
| Request during delivery time | Formula for calculating safety stock level |
| Time between two orders | Formula for calculating the replenishment period |
Application: Weather vane
States :
Girouette is a company specializing in the sale of decorative items. In order to minimize inventory costs, the company has adopted the Wilson inventory management method.
The data relating to the article "Scented candle" are as follows:
– Annual demand for the item “Scented candle”: 4 units
– Cost of placing an order: €100
– Annual unit cost of ownership: €2,50
Work to do :
1- Calculate the optimal quantity of items to order each time (Q*) using Wilson's formula.
2- Calculate the optimal number of annual orders (N) to place.
3- Determine the total annual cost of orders (C).
4- What is the benefit of the Wilson method for the Girouette company?
5- What are the risks incurred by the company by using this method?
Proposed correction:
1- To calculate the optimal quantity of items to order each time (Q*), we use Wilson's formula: Q* = ?((2 x D x S) ÷ H) where D is the annual demand, S is the cost of placing an order, and H is the unit holding cost. Therefore Q* = ?((2 x 4 x 000 ) ÷ 100) ? 2,50 units.
2- The optimal number of annual orders (N) is calculated by dividing the annual demand by the optimal quantity to order: N = D ÷ Q* or 4000 ÷ 1142 ? 3,5 or 4 orders per year after rounding up to the next unit.
3- The total annual cost of orders (C) is given by: C = (D/Q*)xS + (Q*/2)xH or (4000/1142) x 100 + (1142/2) x 2,50 ? €400 + €1 or €426.
4- The interest of the Wilson method for the company is that it allows to determine the optimal quantity of products to order for each supply in order to minimize stock management costs (ordering costs and stock holding costs).
5- Among the risks that the company runs by adopting this method, we can notably cite a possible stock shortage if demand is higher than forecast, or overstocking if demand is lower than forecast. The Wilson method is in fact based on a demand forecast that may prove to be inaccurate.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Q* = ?((2 x D x S) ÷ H) | Optimal quantity to order every time |
| N = D ÷ Q* | Optimal number of annual orders |
| C = (D/Q*)xS + (Q*/2)xH | Total annual cost of orders |
What are these corrections? You have the right formulas but not the right answers.
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