Mathematics in the Supply Chain

[no abstract available

Comparison of different approaches to multistage lot sizing with uncertain demand

We study a new variant of the classical lot sizing problem with uncertain demand where neither the planning horizon nor demands are known exactly. This situation arises in practice when customer demands arriving over time are confirmed rather lately during the transportation process. In terms of planning, this setting necessitates a rolling horizon procedure where the overall multistage problem is dissolved into a series of coupled snapshot problems under uncertainty. Depending on the available data and risk disposition, different approaches from online optimization, stochastic programming, and robust optimization are viable to model and solve the snapshot problems. We evaluate the impact of the selected methodology on the overall solution quality using a methodology-agnostic framework for multistage decision-making under uncertainty. We provide computational results on lot sizing within a rolling horizon regarding different types of uncertainty, solution approaches, and the value of available information about upcoming demands

Optimal lot-sizing, pricing, and product intergenerational lifestyle decisions for the case of disruptive innovations in fashion

The objective of this dissertation is to determine production schedules, production quantities, selling prices, and new product introduction timing to fulfill deterministic price-dependent demand for a series of products in such a way as to maximize profit per period. In order to accomplish the above task, some main assumptions are made. First, it is assumed that the series of products being considered are associated with sequential non-disruptive innovations in technology as well as disruptive innovations in fashion. That is to say, the products represent subsequent generations in the same family of products in an industry that experiences repeated minor technological innovations and in which product success is due in part to fashionability (Fisher, 1997). Second, it is assumed that the planning horizon is sufficiently long and product lifecycles are sufficiently short that several generations of the product family are planned. Third, it is assumed that the producer is following a solo-product roll strategy (Billington, Lee, & Tang, 1998). This means that the inventory of one product iteration is exhausted at the same time that the next product iteration is introduced and ready for sale. Fourth, it is assumed that demand for each product iteration is governed by a modified version of the Bass (1969) diffusion model that incorporates price. Fifth, it is assumed that the various demand and cost characteristics being considered do not change from one product iteration to the next. Sixth, it is assumed that no backlog of demand is maintained and that any unmet demand is lost. Seventh, it is assumed that the manufacturer is a monopolist or at least the dominant member of a market that is made up of it and smaller competitors that are not large enough to affect the market in a meaningful way. The formulated profit maximization problem uses the Thomas (1970) model which in turn depends in its solution on theorems first presented by Wagner and Whitin (1958a). An extensive numerical study that aims at examining the sensitivity of the planned product lifecycle length and profit per period to changes in model parameters is performed using software developed especially for that purpose. The results of the analysis reveal that the above two measures are more sensitive to changes in market-oriented parameters than to changes in operations-oriented parameters. Managerial implications of the research findings are discussed

Periodic Review, Push Inventory Policies for Remanufacturing

Sustainability has become a major issue in most economies, causing many leading companies to focus on product recovery and reverse logistics. This research is focused on product recovery, and in particular on production control and inventory management in the remanufacturing context. We study a remanufacturing facility that receives a stream of returned products according to a Poisson process. Demand is uncertain and also follows a Poisson process. The decision problems for the remanufacturing facility are when to release returned products to the remanufacturing line and how many new products to manufacture. We assume that remanufactured products are as good as new. In this paper, we employ a "push" policy that combines these two decisions. It is well known that the optimal policy parameters are difficult to find analytically; therefore, we develop several heuristics based on traditional inventory models. We also investigate the performance of the system as a function of return rates, backorder costs and manufacturing and remanufacturing lead times; and we develop approximate lower and upper bounds on the optimal solution. We illustrate and explain some counter-intuitive results and we test the performance of the heuristics on a set of sample problems. We find that the average error of the heuristics is quite low.inventory;reverse logistics;remanufacturing;environment;heuristics

Multi-level production planning with raw-material perishability and inventory bounds

This thesis focuses on studying one of the most important and fundamental links in supply chain management: production planning. A considerably common assumptions in most of the production planning research literature is that the intermediate items involved in the production process have unlimited lifespans, meaning they can be stored and used indefinitely. In real life applications, whether referring to physical exhaustion, loss of functionality, or obsolescence, most items deteriorate over time and cannot be stored infinitely without enforcing specific constraints on a set of crucial production planning decisions. This is specially the case for multi-level production structures. In the thesis, we first introduce the fundamental characteristics in production planning modeling and discuss some of the common elements and assumptions used to model complex production planning problems. We also present an overview of the production planning research evolution. Our attention is then focused on the most relevant modeling approaches for perishability in production planning available in the research literature. We present lot-sizing problems that incorporate raw-material perishability and analyze how these considerations enforce specific constraints on a set of fundamental decisions. Three variants of the two-level lot-sizing problem are studied: with fixed raw-material shelf-life, with raw-material functionality deterioration, and with functionality and volume deterioration. We propose mixed-integer programming formulations for each of these variants and perform computational experiments with sensitivity analyses, showing the added value of explicitly incorporating perishability considerations into production planning problems. Using a Silver-Meal-based rolling-horizon algorithm, we develop a sequential approach to solve the studied problems and compare the results with our proposed formulations. We then shift our attention to study the multi-item, multi-level lot-sizing problem with raw-material perishability and batch ordering, inspired by an application in advanced composite manufacturing processes. We proposed a mixed-integer programming formulation for the problem and perform computational experiments with sensitivity analyses, demonstrating its potentials for practical applications in planning composite production. Finally, we address the study of production planning involving inventory bounds. This characteristic is shown to be related to the perishable raw-material considerations and constitutes another fundamental aspect of this family of problems. We study the multi-item uncapacitated lot-sizing problem with inventory bounds, presenting a new mixed-integer programming formulation for the case of non-speculative (Wagner-Whitin) cost structure using a special set of variables to determine the production intervals for each item. We then reformulate the problem using a variable-splitting technique that allows for a Dantzig-Wolfe decomposition. The Dantzig-Wolfe principle exploits the structure of the problem by decomposing it into two sub-problems: one relating to the production decisions per item and another that relates to the inventory decisions per period. We propose a Column Generation algorithm for solving the Dantzig-Wolfe reformulation. Computational experiments are performed to evaluate the proposed formulations and algorithms on a set of benchmark instances. This research presents important contributions on a variety of fields related to production planning that had only been partially studied in the literature. It also opens important research paths for the integration of different types of raw-material perishability in multi-level product structures processes, with the study of finished product inventory bounds

An application of capacitated lot-sizing model in petroleum sector

Cataloged from PDF version of article.In this thesis, we study capacitated lot-sizing problem with special feature, applicable to the petroleum refinery sector. In our model, the end-products should be stored in item-specific and capacitated storage tanks during pre-determined lead-time. Our aim is to find the optimum production schedule resulting minimum total cost whilst satisfying customer demand. To solve this problem in a reasonable amount of time, we propose a branch-and-cut algorithm. We perform experiments based on the data gathered from Turkish Petroleum Refineries Corporation. In order to evaluate our algorithm, we compare the results of our algorithm and the solution results of the optimization software.Nurlu, Nuri BarışM.S

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

Periodic Review, Push Inventory Policies for Remanufacturing

Sustainability has become a major issue in most economies, causing many leading companies to focus on product recovery and reverse logistics. This research is focused on product recovery, and in particular on production control and inventory management in the remanufacturing context. We study a remanufacturing facility that receives a stream of returned products according to a Poisson process. Demand is uncertain and also follows a Poisson process. The decision problems for the remanufacturing facility are when to release returned products to the remanufacturing line and how many new products to manufacture. We assume that remanufactured products are as good as new. In this paper, we employ a "push" policy that combines these two decisions. It is well known that the optimal policy parameters are difficult to find analytically; therefore, we develop several heuristics based on traditional inventory models. We also investigate the performance of the system as a function of return rates, backorder costs and manufacturing and remanufacturing lead times; and we develop approximate lower and upper bounds on the optimal solution. We illustrate and explain some counter-intuitive results and we test the performance of the heuristics on a set of sample problems. We find that the average error of the heuristics is quite low