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

Loss of customer goodwill in the uncapacitated lot-sizing problem

Abstract Loss of customer goodwill in uncapacitated single level lot-sizing is studied with a mixed integer programming model extending the well-known Wagner-Whitin (WW) model. The objective is to maximize profit from production and sales of a single good over a finite planning horizon. Demand, costs, and prices vary with time. Unsatisfied demand cannot be backordered. It leads to the immediate loss of profit from sales. Previous models augment the total cost objective by this lost profit. The difference of the proposed model is that unsatisfied demand in a given period causes the demand in the next period to shrink due to the loss of customer goodwill. A neighborhood search and restoration heuristic is developed that tries to adjust the optimal lot sizes of the original no-goodwill-loss model to the situation with goodwill loss. Its performance is compared with the Wagner-Whitin solution, and with the commercial solver CPLEX 8.1 on 360 test problems of various period lengths

Supply Chain and Revenue Management for Online Retailing

This dissertation focuses on optimizing inventory and pricing decisions in the online retail industry. Motivated by the importance of great customer service quality in the online retail marketplace, we investigate service-level-constrained inventory control problems in both static and dynamic settings. The first essay studies multi-period production planning problems (with or without pricing options) under stochastic demand. A joint service-level constraint is enforced to restrict the joint probability of having backorders in any period. We use the Sample Average Approximation (SAA) approach to reformulate both chance-constrained models as mixed-integer linear programs (MILPs). Via computations of diverse instances, we demonstrate the effectiveness of the SAA approach, analyze the solution feasibility and objective bounds, and conduct sensitivity analysis. The approaches can be generalized to a wide variety of production planning problems. The second essay investigates the dynamic versions of the service-level-constrained inventory control problems, in which retailers have the flexibility to adjust their inventory policies in each period. We formulate two periodic-review stochastic inventory models (backlogging model and remanufacturing model) via Dynamic Programs (DP), and establish the optimality of generalized base-stock policies. We also propose 2-approximation algorithms for both models, which is computationally more efficient than the brute-force DP. The core concept developed in our algorithms is called the delayed marginal cost, which is proven effective in dealing with service-level-constrained inventory systems. The third essay is motivated by the exploding use of sales rank information in today's internet-based e-commerce marketplace. The sales rank affects consumers' shopping preference and therefore, is critical for retailers to utilize when making pricing decisions. We study periodic-review dynamic pricing problems in presence of sales rank, in which customers' demand is a function of both prices and sales rank. We propose rank-based pricing models and characterize the structure and monotonicity of optimal pricing policies. Our numerical experiments illustrate the potential of revenue increases when strategic cyclic policy is used.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144159/1/ycjiang_1.pd

The lot sizing problem: A tertiary study

This paper provides a survey of literature reviews in the area of lot sizing. Its intention is to show which streams of research emerged from Harris' seminal lot size model, and which major achievements have been accomplished in the respective areas. We first develop the methodology of this review and then descriptively analyze the sample. Subsequently, a content-related classification scheme for lot sizing models is developed, and the reviews contained in our sample are discussed in light of this classification scheme. Our analysis shows that various extensions of Harris' lot size model were developed over the years, such as lot sizing models that include multi-stage inventory systems, incentives, or productivity issues. The aims of our tertiary study are the following: firstly, it helps primary researchers to position their own work in the literature, to reproduce the development of different types of lot sizing problems, and to find starting points if they intend to work in a new research direction. Secondly, the study identifies several topics that offer opportunities for future secondary research