Traditional Economic Lot Size (ELS) calculations determine the optimal lot size to balance the costs of holding inventory with the costs of setting up or changing over production lines (see How Much is Enough without being Too Much). One significant shortfall of ELS is that it assumes demand is constant and the cost of inventory is directly proportional to the number of units produced. However, that is rarely true in practice.
Many consumer items (such as food) have a fixed shelf life and variable demand. In this situation, obsolescence costs are not directly proportional to production lot size. At lower lot sizes, the risk of obsolescence may be negligible. As lot size increases beyond a certain point, expected obsolescence costs increase faster. With a little more math, ELS can be adapted for this situation.
An ELS Implementation Tale
Let me tell you about my imaginary friend Jorge. Jorge is a planner for Foodie Mega-Baking Company that sells products in multiple channels. He plans a production line that makes high-volume branded items and recently started making some lower-volume private-label items also. Some of the products have unique ingredients, so Jorge sets production schedules six weeks in advance.
Jorge used to schedule a minimum of one eight-hour shift for each item, at the insistence of the plant manager. But after they had been making the private label items for a while, Foodie Mega-Baking started having problems with obsolescence.
Even though the products have a shelf life of six to eighteen months, private-label customers require their products to have 75% or even 90% of the shelf life remaining when they take delivery from Foodie Mega-Baking. As a result, product that has a year shelf life might have a “ship life” of only a few weeks before Foodie Mega-Baking needs to offer a discount to get the customer to accept the product. These costs were starting to get out of control, so Jorge convinced the plant manager to run as little as four hours on the low-volume items, but no more often than once a month.
The plant manager continued to complain about the number of changeovers Jorge was scheduling. Then, when Jorge read my blog on Economic Lot Sizes (ELS), he decided to use the ELS calculations to set lot sizes for each item. Here is an example of one of his low-volume private label items:
- Historical monthly sales range from 0 cases to 3500 cases, averaging 800 cases per month with a standard deviation of 900 cases.
- It takes 30 minutes to change the packaging line from the branded item to run this item, which costs $810 in direct labor, utilities, and inefficiencies.
- Inventory is stored in a 3PL that charges $20 per pallet per month, so storage charges are proportionate to the production lot size.
- Holding costs are estimated at $0.40 per case per month, including storage charges, inventory shrinkage, opportunity cost, and historical liquidations of aged products.
Using these values, Jorge determined the optimal lot size to be 1800 cases (see figure 1), which is about a six-hour run. Jorge and the plant manager were happy that they found a way to minimize the total costs. Until Jorge read my blog on demand variability.
ELS with Variable Demand
After Jorge read my blog on demand variability, he realized that the cost of obsolescence would not be linear. The probability of obsolescence and expected value of the resulting liquidations would increase non-linearly as production lot size increased. He realized that he would have to separate the estimated cost of obsolescence from other holding costs and graph them separately.
The product has an 18-month shelf life. The customer requires 75% remaining when they pick up product from Foodie Mega-Baking’s warehouse, leaving ship life of 136 days. If product is older than this, Foodie is normally able to liquidate the product at a discount that is $4 per case below Foodie’s cost.
Jorge calculated the mean and standard deviation based on three years of sales history for each item. Then he calculated Alpha and Beta factors to come up with the gamma distribution shown in figure 2.
Then Jorge graphed the expected value of obsolescence at $4 per case together with the traditional ELS lines for setup cost and carrying cost. The minimum value of these three added together occurs at 1,122 cases, which is the new Economic Lot Size as shown in figure 3.
Jorge also noticed that the cost per case was within a dollar of optimal for a range from 1,090 cases to 1,155 cases. Jorge likes to schedule in round quantities, and he knows the plant is tends to run a little more than the schedule, so he now schedules 1,100 cases at a time.
Recently, Jorge realized that even after optimizing costs with ELS, the company was still having to liquidate an average of 55 cases from every run. He raised this as a new continuous improvement opportunity and Foodie Mega-Baking started working on a two-pronged approach to reduce this waste. They are now investigating opportunities to reduce setup time so they can reduce the minimum run. They are also working with the customer to develop a collaborative planning process so customer will reduce the amount of shelf life they require upon delivery.
I am sure you realize that Jorge is not a real person. Any resemblance to a real person is unintentional. However, this scenario is very realistic, drawn from my experience with several food manufacturers.
Objections to ELS
ELS and its sister Economic Order Quantity (EOQ) are out of favor in many circles today. Some say they are based on assumptions that no longer valid in today’s world. That is generally true of EOQ for purchased items where the fixed setup costs are typically negligible. However, ELS still has a place as production lines often have significant changeover costs, and these become more critical for production lines that are near or at maximum capacity.
One objection is that ELS assumes inventory carrying cost is directly proportional to lot size. If you have excess storage capacity, a fixed headcount, and no obsolescence, then the only cost proportional to lot size is the opportunity cost of money invested in inventory. However, if you are storing product in a 3PL, you may have a storage cost per pallet that is directly proportional to the amount of inventory. As demonstrated above, if you have product with a fixed shelf life, then expected obsolescence cost is non-linear and increases with increasing lot size.
Another objection to ELS comes when demand is variable and “lumpy” so the actual inventory varies from projections each month. This is true of most food and CPG products, but in a situation where a 3PL charges per pallet for storage each month it will average out over multiple cycles. If you have a situation where incremental storage costs are incurred only when overflow storage is needed, then a calculation of expected value for overflow storage might look like the calculations shown above for expected obsolescence (based on expected value of outside storage).
Others say that the newer optimization tools or Demand Driven planning make ELS obsolete. But in practice, optimization tools typically assume that the demand forecast is accurate. They may not have the computing power to dynamically calculate the expected value of obsolescence for variable demand for changing starting conditions. The total cost curve for ELS with demand distribution typically has a range where the cost is close to the minimum and does not change much. The upper end of this range could be used as target maximum inventory for inventory optimization tools and for “Top of Green” in Demand Driven MRP.
ELS assumes capacity is available whenever needed to run the next incremental production quantity. In practice, production timing varies due to line capacity and sequencing to minimize changeovers. I will discuss that further in an upcoming blog.
Another valid concern is that using a gamma distribution for demand obsolescence requires a reliable basis for estimating the demand distribution. However, in times like this current pandemic, history is unreliable as a predictor of future demand. My next blog will propose a method for estimating the gamma distribution function when history is not valid.
Conclusion
I hope I have demonstrated here that there are still applications for a modified ELS method that accounts for the risk of obsolescence with demand variability. I have personally used ELS with a gamma demand distribution for food products with variable demand, a finite shelf life, variable 3PL storage costs, and significant changeover costs between formulas and pack sizes. If you have also applied ELS in situations with variable demand, please comment below about your experience