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In this work we study an integrated problem of lot sizing and distribution with multiple items considering a network of multiple plants and customers, which are geographically dispersed, with direct deliveries from the plants to customers. In addition to decisions about production and distribution, it is necessary to make a decision about the level of flexibility in the network, i.e. which items can be produced in which plants. There is a clear trade-off between these decisions. On the one hand, a network with full flexibility where each plant can produce all kinds of items allows for lower transportation costs, but requires large investments in flexibility and frequent machine preparations. On the other hand, a network with limited flexibility, where each plant produces only a few items, will increase transportation costs but require a lower investment in flexibility. We modeled this problem as an extension of the batch sizing problem and analyzed the value of flexibility.
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