You have been hired as a consultant by the Ontario Provincial Government to help identify "efficiencies". One potential area of cost reduction is to centralize the procurement of basic supplies across multiple school boards. Prior to conducting a detailed investigation of cost savings you have been asked to prepare a report to illustrate potential benefits by focusing on a single commodity.

One basic commodity that is procured by the individual boards is copy paper. This is a high use item and the usage and procurement details for each board are as follows (assume that the school year is 12 months and usage is relatively constant). The unit price of a box of paper is $60 and the annual holding cost for a box is $2.

Monthly usage Cost of placing an order (estimated fixed cost) Current Order size School Board A 500 boxes $1000 1500 boxes School Board B 200 boxes $800 400 boxes School Board C 300 boxes $900 300 boxes School Board D 400 boxes $1000 1600 boxes School Board E 600 boxes $1200 900 boxes School Board F 100 boxes $400 300 boxes School Board G 200 boxes $1000 200 boxes report for the government detailing your analysis and procurement recommendations. You will want to calculate the current state total purchasing costs using the given order quantities and compare them to the total purchasing costs leaving the decentralized order process in place but applying economic order quantities for each school board and to the total purchasing costs after establishing a centralized order process utilized an economic order quantity for this process as well. Clearly state all assumptions. If it was known that the lead time was 1 week, would this change your conclusion (consider fixed cost and order process)?

Within the centralized option, assume that lead time is actually 1 week and suppose that lead time demand follows a normal distribution and the standard deviation of lead time demand is 50 boxes. As copy paper is a critical commodity and centralizing this commodity does pose some supply risk, in making your recommendation to management, you are proposing to put some safety inventory in place to ensure that a service level of 95% order fulfillment to the schools is achieved. How does this impact your reorder point? Please explain in detail showing your calculations.

You are welcome to provide more tables or columns in your analysis, however the following tables and columns are required:

1. Known data table

2. The Annual Usage of Each School Board (school board, monthly usage of boxes, cost of placing an order, current order size, annual usage)

3. Total Annual Costs of Each School Board (school board, number of orders per year, annual order cost, average cycle inventory, annual holding cost, annual procurement cost, total annual cost) - Scenario 1 (Current state order)

4. ROP (Re-Order Point) of Each School Board (school board, yearly usage, ROP)

5. Total Annual Costs of Each School Board (school board, economic order quantity, number of orders per year, annual order cost, average cycle inventory, annual holding cost, annual procurement cost, total annual cost) - Scenario 2 (Decentralized)

6. Combined Costs for All School Boards (school boards A-G, monthly usage of boxes, cost of placing an order, annual usage, economic order quantity, number of orders per year, annual order cost, average cycle inventory, annual holding cost, annual procurement cost, total annual cost) - Scenario 3 (Centralized)

7. Total Annual Cost Comparison of the Scenarios (scenario, total annual cost)

Engineering & TechnologyIndustrial EngineeringOperations ManagementQUAL 8085

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The consultant's analysis showed that centralizing the procurement of copy paper could result in significant cost savings for the Ontario Provincial Government. By using economic order quantities and centralizing the procurement process, the government could reduce the total annual cost of procuring copy paper by up to 33% compared to the current state order process. The consultant also recommended the use of safety inventory to ensure a service level of 95% order fulfillment to the schools. Overall, the results suggest that centralizing the procurement of copy paper could be a highly effective way for the Ontario Provincial Government to improve efficiencies and reduce costs.

Step-by-step explanation

1. Report on the Procurement of Copy Paper for Ontario Provincial Government

Introduction:

The Ontario Provincial Government has hired a consultant to identify "efficiencies" and recommend cost-saving measures in the procurement of basic supplies across multiple school boards. The consultant has been asked to prepare a report that illustrates potential benefits by focusing on a single commodity, copy paper. This report aims to analyze the current procurement process of copy paper, identify potential cost-saving measures, and recommend the most effective procurement strategy.

Known Data:

The unit price of a box of paper is $60, and the annual holding cost for a box is $2. The usage and procurement details for each school board are given in the following table:

School Board Monthly Usage Cost of Placing an Order Current Order Size

A 500 boxes $1000 1500 boxes

B 200 boxes $800 400 boxes

C 300 boxes $900 300 boxes

D 400 boxes $1000 1600 boxes

E 600 boxes $1200 900 boxes

F 100 boxes $400 300 boxes

G 200 boxes $1000 200 boxes

2. The Annual Usage of Each School Board:

To calculate the annual usage of each school board, we multiply the monthly usage by 12:

School Board Monthly Usage Cost of Placing an Order Current Order Size Annual Usage

A 500 boxes $1000 1500 boxes 6000 boxes

B 200 boxes $800 400 boxes 2400 boxes

C 300 boxes $900 300 boxes 3600 boxes

D 400 boxes $1000 1600 boxes 4800 boxes

E 600 boxes $1200 900 boxes 7200 boxes

F 100 boxes $400 300 boxes 1200 boxes

G 200 boxes $1000 200 boxes 2400 boxes

3. Total Annual Costs of Each School Board - Scenario 1 (Current State Order):

To calculate the total annual costs of each school board under the current state order process, we need to calculate the following parameters:

Number of orders per year

Annual order cost

Average cycle inventory

Annual holding cost

Annual procurement cost

Total annual cost

Assumptions:

Demand is constant and known

Lead time is zero

No stockouts occur

Fixed ordering cost per order

To calculate the number of orders per year, we divide the annual usage by the current order size:

School Board Annual UsageCurrent Order Size Number of Orders per Year

A 6000 boxes 1500 boxes 4

B 2400 boxes 400 boxes 6

C 3600 boxes 300 boxes 12

D 4800 boxes 1600 boxes

4. Reorder Point (ROP) of Each School Board

The reorder point is the inventory level at which a new order is placed to replenish the stock. It is calculated as the lead time demand plus safety stock. The safety stock is the inventory held as a buffer against uncertainties in demand or lead time.

ROP = Lead time demand + Safety stock

Assuming a lead time of one week, the lead time demand can be calculated as follows:

Lead time demand = Monthly usage x Lead time in months

Lead time demand = Monthly usage x (1/12)

Lead time demand = Monthly usage / 12

The safety stock is calculated based on the desired service level and the standard deviation of lead time demand. Assuming a service level of 95% and a standard deviation of lead time demand of 50 boxes, the safety stock can be calculated using the following formula:

Safety stock = Z-score x Standard deviation of lead time demand x Square root of lead time in weeks

where Z-score is the number of standard deviations from the mean that corresponds to the desired service level. For a service level of 95%, the Z-score is 1.645.

Using these formulas, the ROP for each school board can be calculated and summarized in the following table:

School Board Yearly usage Lead time demand Safety stock ROP

A 6,000 500 118 618

B 2,400 200 63 263

C 3,600 300 94 394

D 4,800 400 126 526

E 7,200 600 189 789

F 1,200 100 32 132

G 2,400 200 63 263

5. Total Annual Costs of Each School Board - Scenario 2 (Decentralized)

Using the economic order quantity (EOQ) model, the optimal order quantity for each school board can be calculated as follows:

EOQ = Square root of (2 x Annual demand x Cost of placing an order / Holding cost per unit)

The annual demand is simply the yearly usage, and the holding cost per unit is $2 per box per year. The optimal order quantity and the resulting total annual cost can then be calculated and summarized in the following table:

School Board EOQ Number of orders per year Annual order cost Average cycle inventory Annual holding cost Annual procurement cost Total annual cost

A 565 11 $6,583282.5 $1,131$12,750 $20,464

B 282 9 $2,561141 $565 $5,640$8,766

C 424 9 $3,871212 $848 $5,664$10,383

D 565 9 $4,124282.5 $1,131$10,800 $16,055

6. Combined Costs for All School Boards (Scenario 3: Centralized Procurement)

Assuming the Ontario Provincial Government decides to centralize the procurement of copy paper, the combined costs for all school boards would be as follows:

School Board Monthly Usage Cost of Placing OrderAnnual UsageEconomic Order Quantity Number of Orders per Year Annual Order Cost Average Cycle Inventory Annual Holding Cost Annual Procurement Cost Total Annual Cost

A 500 $1000 6000 294 21 $17,640 147 $294 $5,958$24,891

B 200 $800 2400 100 24 $6,00050 $100 $2,399$8,499

C 300 $900 3600 173 21 $10,380 87 $174 $4,188$14,742

D 400 $1000 4800 235 21 $14,100 196 $392 $7,523$29,015

E 600 $1200 7200 353 21 $21,180 325 $650 $11,929 $39,759

F 100 $400 1200 49 24 $2,94012 $24 $1,200$4,164

G 200 $1000 2400 117 21 $7,02098 $196 $3,753$11,969

Total 2200 $6900 26400 153 $79,260 $1,836$46,950 $127,046

7. The total annual cost for centralized procurement is $127,046. This represents a significant cost savings of $54,356 compared to the current state order.

Total Annual Cost Comparison of the Scenarios

The total annual cost for each scenario is as follows:

Scenario Total Annual Cost

Current State $181,402

Decentralized $140,695

Centralized $127,046

As shown in the table, centralizing the procurement of copy paper results in the lowest total annual cost. Compared to the current state order, centralized procurement represents a cost savings of $54,356 or 30%.

Overall, the analysis suggests that centralizing the procurement of copy paper is a cost-effective solution for the Ontario Provincial Government. The use of an economic order quantity and safety inventory can help ensure that service levels are maintained while also minimizing costs. If the lead time was known to be 1 week, this would not change the conclusion, but it would impact

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