**Author(s):**

**Dr. M. Theodore Farris II**

Dr. M. Theodore Farris II, Professor, University of South Alabama, Mobile, AL 36688, 334/460-6412.

Efforts to reduce cycle time through the channel have historically been secondary to schedule optimization and cost reduction. Cycle time reduction offers as much impact on inventory levels as schedule or cost changes. Measuring the impact of change in cycle time is difficult especially when cycle changes involve multiple functional organizations or companies. This article introduces flow models, a technique which offers a quick method to accurately estimate the relationships between cycle changes and inventory levels throughout the supply chain.

What Is A Flow Model? Flow modeling may be used to manage cycle time at all levels of the organization and across all members in the supply chain. Flow modeling identifies both the time and cost associated with a process. Multiplied by a scheduling vector, the flow model will emulate the entire process. The flow modeling technique offers valuable insights to many of the strategic and operational decisions critical to successful operation in a competitive environment, utilizes components from common business decisions, and may be utilized in both service industries and goods manufacturing.

**CREATING A FLOW MODEL**

The three steps in creating a flow model require gathering the following three variables:

- Total cycle time,
- Total cost, and,/li>
- Production schedule in terms of the daily going rate (DGR)

Step I: Identify Total Cycle Time. The first variable is the total lead time of a part or assembly from initial order to final delivery. Lead time can extend across the entire supply chain from the purchase of raw materials all the way to the final end consumer.

Step II: Identify Total Cost. Cumulative lead time diagrams are limited in quantitative value as they only reflect cycle days and not the value of the inventory. Many cycle time reduction efforts focus solely upon the number of days removed from the cycle without regard for the value added during the cycle period. This assumption limits cycle reduction gains by misdirecting reduction efforts and causing suboptimal results. It is imperative to consider the multi-dimensional attributes of each segment within the process.

(FIGURE ONE - A SIMPLIFIED FLOW MODEL is not available in this text only version.)

The total cost variable provides a more precise representation of cycle value. The model design graphically creates a two dimensional shape representing the inventory investment in a process. This relatively simple technique offers many opportunities to manage the overall business perspective. To develop a quick estimate, utilize a straight line (from point A to point B) to represent a consistent change in the value build-up.

Step III: Determine the Production Schedule. The flow model is initially based on a daily going production rate of one unit per day. It is comprised of a series of daily snapshots throughout the production cycle for manufacturing a single unit. A third dimension can be added to the model to adjust for a daily going rate larger than one by multiplying the variables along the Z-axis by the daily going rate. By adjusting for the daily going rate, the flow model takes a three dimensional shape.

(FIGURE TWO - THREE DIMENSIONAL FLOW MODEL is not available in this text only version.)

**KEY USES OF SIMPLIFIED FLOW MODELS**

Flow models may be used to estimate optimum inventory, identify inventory changes, measure inventory at risk, analyze postponement analysis, estimate the amount of inventory required, annualize inventory savings, and determine unit price reductions stemming from cycle changes.

**Determining Optimum Inventory**. "Optimum inventory" is defined as the total amount of inventory that must be loaded into a process to support the manufacture of one unit per day. Total optimum inventory may be estimated by determining the area inside the flow model. Each unit area will measure one value unit times one time unit and will represent one value unit of optimum inventory required to support the process.

Example:

For the diagrams in this article, the process requires 100 days to build $50 of product value. The optimal inventory required to support the manufacture of one unit per day is $2,500.

$50 unit cost x 100 days/2 = $2,500

The changes in the optimum inventory level required for a different production rate may be estimated by comparing values from each flow model after multiplying by the daily going rate.

Example: If the daily going rate is 50 units, the total optimal inventory that must be held is $125,000.

$2,500 per unit x 50 units per day = $125,000

An increase to a daily going rate to 75 units would result in an optimal total inventory requirement of $187,500, an increase in required inventory financing of $62,500.

$2,500 per unit x 75 units per day = $187,500

**Identify Inventory Changes**. Changes in inventory levels may be explained by investigating three basic variables; cost, schedule, and cycle times. Inventories will increase if there has been an increase in scheduled production, cost, or cycle times. Conversely, they will reduce if the schedule is cut back, costs drop, or cycle times are shortened. Flow models may be utilized to estimate the impact of multiple changes to schedule, cost, or cycle times. It may be adjusted to accommodate varying production rates. In short, it may be utilized as an effective tool to reflect changes to the process or business.

**Measuring Inventory at Risk**. When a buyer places an order commitment on a supplier, the buyer has an obligation to receive and pay for the completed order, or in the event of a cancellation, compensate the supplier. This obligation represents risk by the buyer. In the event of a cancellation, the buyer should expect to compensate the supplier only for the amount of value added. Extreme situations of 0% cancellation charge or a 100% cancellation charge are financially unfair to one of the parties. Disputes arise when attempting to determine equitable financial responsibilities.

The flow model provides a representation of the process to develop an estimate of the amount of value added at any point in the process. This measurement is called "inventory at risk" and is the maximum risk a buyer will incur in terms of inventory or cancellation charges in the event an order is canceled.

(FIGURE 3 - INVENTORY AT RISK is not available in this text only version.)

For on-going business relationships, use of the flow models" may be useful to help resolve disputes and ensure fair treatment of both parties.

Example: Utilizing Figure Three, the following chart can be derived.

Days Before Product Completion |
Value of Work Completed |

12 |
88% |

44 |
56% |

62 |
38% |

Fifty-six percent of the product's value has been completed forty-four days before product completion.

A 50 unit order (valued at $50 per finished unit) canceled 44 days before the order was to be completed would translate into a maximum cancellation charge of $1,400.

50 units x $50 unit cost x 56% value-added = $1,400

**Postponement Analysis**. Flow models may be used for postponement analysis when rescheduling delivery dates. Upon notification of postponement, it is assumed the supplier will remove the product from his process and hold it until it is time to reinsert it into the process to coincide with the new delivery date. (The alternative is for the supplier to complete manufacturing the product and hold the higher valued finished product for later delivery. Unless there are technical limitations preventing the interruption in the process, it is not advisable to continue to add value to the product as this will result in higher inventory carrying charges.) The flow model is useful in estimating the value of inventory and holding charges to be incurred. Holding charges may be estimated to cover the period of time the unfinished product will likely be held.

Example: Analysis should be conducted to compare the cancellation charge of $1,400 with the cost to carry partially completed production in inventory until a later date.

The 50 units (valued at $50 per finished unit) are presently valued at $28 each. With an annual inventory carrying charge of 25%, the maximum cost to carry these partially completed parts in inventory is $37.50 per month.

50 x $28 x 25% x 1/12 = $29.17 carry cost per month

Obsolescence issues aside, the partially completed units could be held by the supplier for up to 48 months before it would make financial sense to cancel the order.

Calculating One-Time Inventory Reduction. A change in cycle time will result in a one-time reduction in the level of inventory carried to support the process. The savings will be in the form of excess inventory assets that may be reduced over time. Graphically, a reduction in cycle time shifts the value-added line toward the origin of the graph as shown in Figure Four.

(FIGURE 4 - SUMMARY OF IMPROVEMENTS is not available in this text only version.)

The one-time reduction in inventory can be estimated by subtracting the area under the revised value add line in Figure Four from the area under the original compression curve. The amount of the reduction represents the amount of capital that will become available for an alternative use.

Example: The original flow model required $125,000 in inventory to support a DGR of 50 units valued at $50. After cycle improvements, only $87,500 in inventory is required.

100 days x $50 unit cost x 50 DGR/2 = $125,000

70 days x $50 unit cost x 50 DGR/2 = $87,500

The difference between the areas under the curves is $37,500. This is the one time reduction in inventory due to cycle improvements.

Calculating Annual Savings in Carrying Costs. In addition to the one time reduction in inventory, there will be a reduction in the annual costs to carry the inventory that was previously tied up in the process. After excessive inventories are eliminated, the annual savings may be estimated by multiplying charges associated with carrying this inventory by the one time savings in inventory estimated above.

Example: One time savings in inventory due to cycle reductions (as determined in the previous example) was $37,500. At an annual cost to carry inventory of 25%, there would be $9,375 in annual savings.

$37,500 x 25% = $9,375 annual savings

Calculating Unit Price Reduction. The costs of carrying inventory are included in the final unit price of the product. Reduction in inventory carrying charges may be reflected in a lower unit price. The annual inventory cost savings should be spread over all of the units produced annually. Unit price reductions may be shared between buyer and supplier. The buyer benefits from a lower unit price. The supplier benefits from increased profitability and a more competitive price.

Example: Per unit inventory carrying cost in the process can be estimated by taking the total inventory carrying cost and dividing by the total units produced. For the example, $125,000 of inventory is maintained in the original process. At a 25% annual carrying charge, this amounts to $31,250 in annual inventory carrying charges per year which is spread over the annual production quantities. Assuming a DGR of 50 and 250 work days in a year, the cost per unit to carry inventory is $2.50 per $50 finished unit.

($125,000 x 25%)/(50 DGR x 250 working days) = $2.50

After the cycle reduction of previous examples, the annual $9,375 savings translates to a price reduction of 75 cents per unit.

$9,375/(50 DGR x 250 working days) = $0.75 cost reduction per unit

Calculating Reduction in "Inventory At Risk." When the value-added line moves toward the origin, inventory at risk is reduced. The average inventory at risk with the original curve is 50% of the unit price. The benefits quantified from the examples are shown in Table One.

Example:

The area under the original flow model identified $125,000 of inventory is contained in the process to support a DGR of 50 units. The new process requires only $87,500 in the process. Compared against the original flow model curve, this represents an average reduction in risk of 30%. Note that the last 30 days for the new curve have zero inventory but are included to measure the reduction in the average risk.

($125,000/50 DGR)/100 days = $25.00 risk/unit

($87,500/50 DGR)/100 days = $17.50 risk/unit

TABLE 1

RISK COMPARISON

Before | After | Change | |

Process time | 100 days | 70 days | reduced by 30 days |

Process inventory | $125,000 | $87,500 | saved $37,500 |

Annual inventory carry cost | $31,250 | $21,875 | saved $9,375 |

Product cost | $50.00 | $39.25 | reduced $0.75 |

Average risk | $25.00 | $17.50 | reduced 30% |

**SUMMARY**

Flow modeling may be utilized as a tool to help focus management direction. Utilized correctly, it can be beneficial to all members in the supply chain. Flow models allow the user to quickly estimate the relationship between inventory and changes in cycle and it incorporates cost, schedule, and cycle time variables.