Optimizing Production Schedules with Min-Cost Flow Modeling
"Explore how small manufacturing companies can minimize costs by using min-cost flow modeling to determine production schedules. Dive into scenarios like non-matching supply/demand and learn how to adapt the model accordingly for efficient decision-making."
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MS&E 214 11/22 Discussion Section
Problems using MCF/Max-flow 1.Production problem 2.MCF with non-matching supply/demand 3.Matrix rounding example 4.Probability of failure (modelling)
Production problem A small computer manufacturing company forecasts the demand over the next n months to be di, i = 1, 2, . . . , n. In any month it can produce r units, using regular production, at a cost of b dollars per unit. By using overtime, it can produce additional units at c dollars per unit, where c > b. The firm can store units from month to month at a cost of s dollars per unit per month. Formulate the problem of determining the production schedule that minimizes cost. Show how this problem can be solved as a min-cost flow problem.
Non-matching supply/demand Class question: What if the total demand is not zero? Eg. what if it is bigger than 0, i.e. the demand is smaller or bigger than the supply ? Formal question: Consider a variant of the min-cost flow problem where any excess supply can be discarded at no cost (free- disposal)? Or at the cost of L per unit? How can you model this case as the standard min-cost flow considered in class?
