Lot-Sizing is a crucial decision arises, in many classes and variants, in the production planning. The paper focuses on the single-stage, dynamic, multi-item capacitated lot-sizing problem (CLSP) with continuous setups. It classically deals with the issue of determining a production plan for items in terms of quantities and their timing over a discrete finite horizon. so as to satisfy a known variable demand in each period without incurring backloggs and minimize the setup, production and holding costs. A finite production capacity of a single resource is shared by all items produced in each period. The literature showed that this problem is NP-hard in feasibilty and optimality. A special heuristic method is developed for small products. The mathematical models consider backorder and under capacity costs. The problem is reduced to a capacity distribution under special propositions and solved in two phases by using the fixed charge transportation problem (FCTP.) The first phase aggregately distributes the capacity between periods while the second decomposes this distribution into separate periods lot-sizing problems solvable as a sequence of FCTPs.
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