DYNAMIC LOT-SIZING PROBLEMS: A Review on Model and Efficient Algorithm

Due to their importance in industry, dynamic demand lot-sizing problems are frequently studied.This study consider dynamic lot-sizing problems with recent advances in problem and modelformulation, and algorithms that enable large-scale problems to be effectively solved.Comprehensive review is given on model formulation of dynamic lot-sizing problems, especiallyon capacitated lot-sizing (CLS) problem and the coordinated lot-sizing problem. Bothapproaches have their intercorrelated, where CLS can be employed for single or multilevel/stage, item, and some restrictions. When a need for joint setup replenishment exists, thenthe coordinated lot-sizing is the choice. Furthermore, both algorithmics and heuristics solutionin the research of dynamic lot sizing are considered, followed by an illustration to provide anefficient algorithm

Modeling Industrial Lot Sizing Problems: A Review

In this paper we give an overview of recent developments in the field of modeling single-level dynamic lot sizing problems. The focus of this paper is on the modeling various industrial extensions and not on the solution approaches. The timeliness of such a review stems from the growing industry need to solve more realistic and comprehensive production planning problems. First, several different basic lot sizing problems are defined. Many extensions of these problems have been proposed and the research basically expands in two opposite directions. The first line of research focuses on modeling the operational aspects in more detail. The discussion is organized around five aspects: the set ups, the characteristics of the production process, the inventory, demand side and rolling horizon. The second direction is towards more tactical and strategic models in which the lot sizing problem is a core substructure, such as integrated production-distribution planning or supplier selection. Recent advances in both directions are discussed. Finally, we give some concluding remarks and point out interesting areas for future research

A comparison of two lot sizing-sequencing heuristics for the process industry

Production Models;produktie

An Integrated Strategy for a Production Planning and Warehouse Layout Problem: Modeling and Solution Approaches

We study a real-world production warehousing case, where the company always faces the challenge to find available space for their products and to manage the items in the warehouse. To resolve the problem, an integrated strategy that combines warehouse layout with the capacitated lot-sizing problem is presented, which have been traditionally treated separately in the existing literature. We develop a mixed integer linear programming model to formulate the integrated optimization problem with the objective of minimizing the total cost of production and warehouse operations. The problem with real data is a large-scale instance that is beyond the capability of optimization solvers. A novel Lagrangian relax-and-fix heuristic approach and its variants are proposed to solve the large-scale problem. The preliminary numerical results from the heuristic approaches are reported

Improved formulations, heuristics and metaheuristics for the dynamic demand coordinated lot-sizing problem

Coordinated lot sizing problems, which assume a joint setup is shared by a product family, are commonly encountered in supply chain contexts. Total system costs include a joint set-up charge each time period any item in the product family is replenished, an item set-up cost for each item replenished in each time period, and inventory holding costs. Silver (1979) and subsequent researchers note the occurrence of coordinated replenishment problems within manufacturing, procurement, and transportation contexts. Due to their mathematical complexity and importance in industry, coordinated lot-size problems are frequently studied in the operations management literature. In this research, we address both uncapacitated and capacitated variants of the problem. For each variant we propose new problem formulations, one or more construction heuristics, and a simulated annealing metaheuristic (SAM). We first propose new tight mathematical formulations for the uncapacitated problem and document their improved computational efficiency over earlier models. We then develop two forward-pass heuristics, a two-phase heuristic, and SAM to solve the uncapacitated version of the problem. The two-phase and SAM find solutions with an average optimality gap of 0.56% and 0.2% respectively. The corresponding average computational requirements are less than 0.05 and 0.18 CPU seconds. Next, we propose tight mathematical formulations for the capacitated problem and evaluate their performance against existing approaches. We then extend the two-phase heuristic to solve this more general capacitated version. We further embed the six-phase heuristic in a SAM framework, which improves heuristic performance at minimal additional computational expense. The metaheuristic finds solutions with an average optimality gap of 0.43% and within an average time of 0.25 CPU seconds. This represents an improvement over those reported in the literature. Overall the heuristics provide a general approach to the dynamic demand lot-size problem that is capable of being applied as a stand-alone solver, an algorithm embedded with supply chain planning software, or as an upper-bounding procedure within an optimization based algorithm. Finally, this research investigates the performance of alternative coordinated lotsizing procedures when implemented in a rolling schedule environment. We find the perturbation metaheuristic to be the most suitable heuristic for implementation in rolling schedules

Integrated production-distribution systems : Trends and perspectives

During the last two decades, integrated production-distribution problems have attracted a great deal of attention in the operations research literature. Within a short period, a large number of papers have been published and the field has expanded dramatically. The purpose of this paper is to provide a comprehensive review of the existing literature by classifying the existing models into several different categories based on multiple characteristics. The paper also discusses some trends and list promising avenues for future research

Managing Limited Retail Space for Basic Products: Space Sharing vs. Space Dedication

In this paper, we study the problem of managing limited retail shelf or storage space for basic products by considering two inventory management strategies: space dedication and space sharing. When space is dedicated to each product, there is more flexibility in planning as different products can be replenished independently. In contrast, when space is shared across different products, there is potential for saving space; however, replenishment has to be coordinated across products and this leads to additional costs due to the lack of flexibility in replenishing each product individually. We model this problem as a non-linear mixed integer program and develop an effective heuristic and an upper bound for each strategy. We introduce three different but consistent criteria to compare each strategy. Through an extensive computational study, we identify the most relevant factors that impact the relative benefit of space sharing over space dedication. In addition, we show that space sharing with an optimal replenishment scheduling program can on average reduce space consumption by 31%

Lot-Sizing of Several Multi-Product Families

Production planning problems and its variants are widely studied in operations management and optimization literature. One variation that has not garnered much attention is the presence of multiple production families in a coordinated and capacitated lot-sizing setting. While its single-family counterpart has been the subject of many advances in formulations and solution techniques, the latest published research on multiple family problems was over 25 years ago (Erenguc and Mercan, 1990; Mercan and Erenguc, 1993). Chapter 2 begins with a new formulation for this coordinated capacitated lot-sizing problem for multiple product families where demand is deterministic and time-varying. The problem considers setup and holding costs, where capacity constraints limit the number of individual item and family setup times and the amount of production in each period. We use a facility location reformulation to strengthen the lower bound of our demand-relaxed model. In addition, we combine Benders decomposition with an evolutionary algorithm to improve upper bounds on optimal solutions. To assess the performance of our approach, single-family problems are solved and results are compared to those produced by state-of-the-art heuristics by de Araujo et al. (2015) and Süral et al. (2009). For the multi-family setting, we first create a standard test bed of problems, then measure the performance of our heuristic against the SDW heuristic of Süral et al. (2009), as well as a Lagrangian approach. We show that our Benders approach combined with an evolutionary algorithm consistently achieves better bounds, reducing the duality gap compared to other single-family methods studied in the literature. Lot-sizing problems also exist within a vendor-managed-inventory setting, with production-planning, distribution and vehicle routing problems all solved simultaneously. By considering these decisions together, companies achieve reduced inventory and transportation costs compared to when these decisions are made sequentially. We present in Chapter 3 a branch-and-cut algorithm to tackle a production-routing problem (PRP) consisting of multiple products and customers served by a heterogeneous fleet of vehicles. To accelerate the performance of this algorithm, we also construct an upper bounding heuristic that quickly solves production-distribution and routing subproblems, providing a warm-start for the branch-and-cut procedure. In four scenarios, we vary the degree of flexibility in demand and transportation by considering split deliveries and backorders, two settings that are not commonly studied in the literature. We confirm that our upper bounding procedure generates high quality solutions at the root node for reasonably-sized problem instances; as time horizons grow longer, solution quality degrades slightly. Overall costs are roughly the same in these scenarios, though cost proportions vary. When backorders are not allowed (Scenarios 1 and 3), inventory holding costs account for over 90% of total costs and transportation costs contribute less than 0.01%. When backorders are allowed (Scenarios 2 and 4), most of the cost burden is shouldered by production, with transportation inching closer to 0.1% of total costs. In our fifth scenario for the PRP with multiple product families, we employ a decomposition heuristic for determining dedicated routes for distribution. Customers are clustered through k-means++ and a location-alloction subproblem based on their contribution to overall demand, and these clusters remain fixed over the entire planning horizon. A routing subproblem dictates the order in which to visit customers in each period, and we allow backorders in the production-distribution routine. While the branch-and-cut algorithm for Scenarios 1 through 4 quickly finds high quality solutions at the root node, Scenario 5's dedicated routes heuristic boasts high vehicle utilization and comparable overall costs with minimal computational effort