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

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

Improved Algorithms for a Lot-Sizing Problem with Inventory Bounds and Backlogging

This paper considers a dynamic lot-sizing problem with storage capacity limitation in which backlogging is allowed. For general concave production and inventory costs, we present an O(T2) dynamic programming algorithm where T is the length of the planning horizon. Furthermore, for fixed-charge and nonspeculative costs, we provide O(Tlog T) and O(T) algorithms, respectively. This paper therefore concludes that the time complexity to solve the bounded inventory lot-sizing problem with backlogging is the same as the complexity to solve the uncapacitated lot-sizing problem for the commonly used cost structure

Stochastic Clearing Systems With Markovian Inputs: Performance Evaluation and Optimal Policies

This thesis studies the stochastic clearing systems which are characterized by a non-decreasing stochastic input process {Y(t), t > 0}, where Y(t) is the cumulative quantity entering the system in [0, t], and an output mechanism that intermittently and instantaneously clears the system. Examples of such systems can be found in shipment consolidation, inventory backlog, lot sizing, shuttle bus dispatch, bulk service queues, and other stochastic service and storage systems. In our model, the input process is governed by an underlying discrete-time Markov chain such that, the distribution of the input in any given period depends on the underlying state in that period. The outstanding inputs in the system are recorded in strings to keep track of the ages, i.e., the time elapsed since their arrival, of each input. The decision of when to clear the system depends on a \clearing policy" which itself depends on the input quantities, ages, and the underlying state. Clearing the system will incur a fixed cost and a variable cost depending on the quantities cleared; a penalty is charged to the outstanding inputs in every period, and such penalty is non-decreasing in both the quantities and the ages of the inputs. We model the system as a tree structured Markov chain with Markovian input processes and evaluate the clearing policies with respect to the expected total costs over a finite horizon, the expected total discounted cost over an infinite horizon, as well as the expected average total cost per period over an infinite horizon. Relying on theories of Markov Decision Processes and stochastic dynamic programming, we then proceed to show some properties unique to the optimal clearing policies, and prove that a state-dependent threshold policy can be optimal under special conditions. We develop algorithms or heuristics to evaluate a given clearing policy and find the optimal clearing policy. We also use Matrix Analytic Methods to evaluate a given clearing policy and develop an efficient heuristic to find near-optimal clearing policies. Finally, we conduct extensive numerical analyses to verify the correctness, complexity, and optimality gap of our algorithms and heuristics. Our numerical examples successfully demonstrate the analytical results we proved