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BY PAUL ENGLE
INDUSTRIAL ENGINEER – VOLUME 44 NUMBER 9
You have been asked to optimize the size, location and inventory levels of a new warehouse. Your source of supply is offshore, with long lead-ties and variable shipping times based on seasonality and other factors. Customer demand varies by season and is sensitive to the business cycle. Forecasting demand is problematic. Management sets on-time delivery goals at 100 percent of customer request, including same-day deliveries from large accounts. How large and where should the warehouse be, how much inventory should be kept to maximize service levels and inventory turns and minimize cost?
While there are many approaches, Monte Carlo simulations sets ranges of and assign probabilities to certain outcomes. Monte Carlo simulations were used first in U.S. government atomic weapons research. Scientist attempted to predict radiation levels at a certain distance and level of shielding. An equation using probabilities and ties to a random number generator was run thousands of times and the outcomes analyzed. The simulation provided a range of outcomes and illustrated the distribution of possible outcomes. This helped determine the probabilities of certain events.
Your warehouse analysis provides a similar situation. Historical data could help model delivery times for products from offshore suppliers. Using seasonality or other attributes may provide a sound basis for developing a set of outcomes that, through much iteration, mimic reality. Once this distribution is known, the Monte Carlo simulation algorithm captures it. Random numbers are entered hundreds or thousands of times to produce a distribution of outcomes.
Apply the same approach to demand. No single method predicts demand precisely over time due to the many variables that affect customer behavior. Predicting a range of demands and assigning probabilities to each level might be more useful. Again, demand typically falls into a recognizable mathematical distribution of outcomes. Once this distribution has been established with historical data, it can be incorporated into the algorithm.
The planner gathers historical supply and demand data to determine a predictable distribution for inputs. Once these distributions are established, an algorithm is developed incorporating the distribution. Many random numbers are put into the algorithm, and the outcomes are logged. A clear picture of predicted behaviors emerges that lets the planner fine-tune the model and make informed decisions regarding warehouse size, location and stocking levels.
The planner still must determine acceptable cost and service levels. The algorithm may provide the basis for making these decisions. Unfortunately, supply chains and customer demands change constantly. Assumptions included in the algorithm might be valid no longer, making the warehouse too large or too small, in the wrong location and with the wrong levels of inventory. Monitoring historical behavior, identifying new trends early and comparing new data against the model is vital to avoid poor financial performance and service levels.
Monte Carlo can’t eliminate risk but it provides the planner with a basis for evaluating different supply chain strategies and backing up decisions with data.
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