The dynamic lot-sizing problem with convex economic production costs and setups

Abstract

a b s t r a c tIn this work the uncapacitated dynamic lot-sizing problem is considered. Demands are deterministic and production costs consist of convex costs that arise from economic production functions plus set-up costs. We formulate the problem as a mixed integer, non-linear programming problem and obtain structural results which are used to construct a forward dynamic-programming algorithm that obtains the optimal solution in polynomial time. For positive setup costs, the generic approaches are found to be prohibitively time-consuming; therefore we focus on approximate solution methods. The forward DP algorithm is modified via the conjunctive use of three rules for solution generation. Additionally, we propose six heuristics. Two of these are single-stepSilver-Meal and EOQ heuristics for the classical lot-sizing problem. The third is a variant of the Wagner-Whitin algorithm. The remaining three heuristics are two-step hybrids that improve on the initial solutions of the first three by exploiting the structural properties of optimal production subplans. The proposed algorithms are evaluated by an extensive numerical study. The two-step Wagner-Whitin algorithm turns out to be the best heuristic.

A polynomial time algorithm for convex cost lot-sizing problems

“…The work by Kian et al [7] is also closely related to ours, as they analyzed a single-stage, uncapacitated economic lot-sizing problem with fixed setup costs and variable costs in each period that are convex in the production quantity (taking the form of a polynomial function of the production quantity). They derived several key optimality conditions for this problem class, as well as a dynamic programming solution algorithm that is exponential in the length of the time horizon.…”

“…Kian et al [7] study the uncapacitated dynamic lot-sizing problem with convex costs that take the form of a polynomial function of the production quantities. They provide a forward dynamic program to solve the version of the problem with fixed charges, which they modify in order to solve the problem with zero fixed charges, where they state the complexity of this algorithm as O(T 2 ).…”

An extension for dynamic lot-sizing heuristics

“…In a current study, Baciarello, D'Avino, Onori, and Schiraldi (2013) presented a comparison of basic lot-sizing heuristics (among them PP, SM, and GR) in a computational study using the results of WW as benchmark. A recent comparison of dynamic lot-sizing algorithms, including SM and WW, for the special case of convex production costs and setups, can be found in Kian, Gürler, and Berk (2014). From the literature review, we can deduce that most studies compared and tested the same popular heuristics, such as LUC, SM, or GR, while other heuristics and possible extensions have mainly been overlooked (Simpson, 2001).…”

Production process parameter optimization with a new model based on a genetic algorithm and ABC classification method

“…The structures of the production costs are made of the costs of labor, tooling costs, machine tool costs, and the costs of the refrigerant and lubricant. 10 For large-scale modern machining production line processes, machining parameters (such as cutting speed, depth of the cut, feed rate) have an impact that is significantly important when it comes to reliability (tool life cycle), product quality (roughness of the product surface), production costs, and productivity. A disadvantage of machining production line processes is that these parameters are conservatively chosen based on the experience of workers, and although all the conditions are fulfilled, tools and machines are not being fully used, that is, the production cost may be reduced.…”