The Uncapacitatied Dynamic Single-Level Lot-Sizing Problem under a Time-Varying Environment and an Exact Solution Approach

Yiyong Xiao, Meng You, Xiaorong Zuo, Shenghan Zhou and Xing Pan
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Yiyong Xiao: School of Reliability and System Engineering, Beihang University, Beijing 100191, China
Meng You: School of Reliability and System Engineering, Beihang University, Beijing 100191, China
Xiaorong Zuo: School of Reliability and System Engineering, Beihang University, Beijing 100191, China
Shenghan Zhou: School of Reliability and System Engineering, Beihang University, Beijing 100191, China
Xing Pan: School of Reliability and System Engineering, Beihang University, Beijing 100191, China

Sustainability, 2018, vol. 10, issue 11, 1-14

Abstract: The dynamic lot-sizing problem under a time-varying environment considers new features of the production system where factors such as production setup cost, unit inventory-holding cost, and unit price of manufacturing resources may vary in different periods over the whole planning horizon. Traditional lot-sizing theorems and algorithms are no longer fit for these situations as they had assumed constant environments. In our study, we investigated the dynamic lot-sizing problem with deteriorating production setup cost, a typical time-varying environment where the production setup is assumed to consume more preparing time and manufacturing resources as the production interval lasts longer. We proposed new lot-sizing models based on the traditional lot-sizing model considering the changing setup cost as a new constraint, called uncapacitatied dynamic single-level lot-sizing under a time-varying environment (UDSLLS-TVE for short). The UDSLLS-TVE problem has a more realistic significance and higher research value as it is closer to reality and has higher computational complexity as well. We proposed two mathematical programming models to describe UDSLLS_TVE with or without nonlinear components, respectively. Properties of the UDSLLS-TVE models were extensively analyzed and an exact algorithm based on forward dynamic programming (FDP) was proposed to solve this problem with a complexity of O ( n 2 ). Comparative experiments with the commercial MIP solver CPLEX on synthesized problem instances showed that the FDP algorithm is a global optimization algorithm and has a high computational efficiency.

Keywords: lot-sizing problem; time-varying environment; deteriorating setup cost; dynamic programming; optimization (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2018
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