Aggregate constrained inventory systems with independent multi-product demand: control practices and theoretical limitations

In practice, inventory managers are often confronted with a need to consider one or more aggregate constraints. These aggregate constraints result from available workspace, workforce, maximum investment or target service level. We consider independent multi-item inventory problems with aggregate constraints and one of the following characteristics: deterministic leadtime demand, newsvendor, basestock policy, rQ policy and sS policy. We analyze some recent relevant references and investigate the considered versions of the problem, the proposed model formulations and the algorithmic approaches. Finally we highlight the limitations from a practical viewpoint for these models and point out some possible direction for future improvements

Supply Chain Pricing, Risk-Return Analysis, and Online Resource Allocation

University of Minnesota Ph.D. dissertation. 2018. Major: Industrial and Systems Engineering. Advisor: Zizhuo Wang. 1 computer file (PDF); 139 pages.This dissertation studies a few models in two categories of operations management. The first part of the dissertation focuses on supply chain management related topics. We consider a supply chain model with one supplier and one retailer who acts as a newsvendor. The first model in this dissertation focuses on the supplier and the retailer's optimal policies in a multi-period newsvendor model. We derive the optimal pricing and ordering policies for demand with Increasing Generalized Failure Rate (IGFR) property and obtain comparative statics for the optimal prices. We discover that under certain conditions of the demand distribution, the supplier's optimal prices are increasing in time. Moreover, the price increments are increasing in the backorder cost and the optimal prices are increasing in the backorder cost as well. We also perform a distribution-free analysis of the multi-period newsvendor model and provide the structure of the worst-case distribution. In addition to the pricing and ordering decisions, we also analyze the risk-return trade-off in single-period newsvendor models using the mean-variance approach. We discuss the classic newsvendor model which uses the wholesale-price contract and two variations of the model, a spot market model and a revenue-sharing contract model. We derive the risk-return curve for the retailer and the corresponding distribution in closed-form for a two-point distribution and a three-point distribution in the classic model. When the demand follows a multi-point distribution or a continuous distribution, we provide a linear program to compute the risk-return curves and show the curves' upper bounds. An approximation algorithm is introduced to efficiently calculate the risk-return curve in the continuous distribution models. Introducing some variation to the basic model, we consider a supply chain setting with a spot market where unsatisfied demand can purchase from the supplier at the market price. The supplier's decisions are the wholesale price and the buffer inventory for the spot market. We derive the supplier's optimal decisions and study the supplier's risk-return trade-off under uniform and exponential distributions. Another problem that we consider is the risk-return analysis under a revenue-sharing model. We derive the supplier's optimal pricing policy and characterize the effect of φ on both the supplier and the retailer's decisions and risks. Numerical experiments are conducted to demonstrate the results. The second part of this thesis concerns resource allocation in an online setting, specifically, the online matching problems. Online matching problems are used as the backstage algorithm by search engines to match advertisements with each search. We focus on the online matching problem with concave return functions and a random permutation model. In this dissertation, we introduce two online learning algorithms to solve the associated matching problem. The main idea is to utilize the observed data in the allocation process and project it into the future. We begin with the one-time learning algorithm that only uses the data to compute an allocation rule once. This algorithm achieves near-optimal performance when input data satisfy certain conditions. To further improve the performance, we introduce a dynamic learning algorithm which updates the allocation rule at a geometric pace, at time εn, 2εn, 4εn and so on. This algorithm achieves near-optimal performance with fewer restrictions on the input data conditions. We compare the performance of the one-time learning algorithm, the dynamic learning algorithm, and the greedy algorithm in numerical experiments

Last Time Buy and Control Policies With Phase-Out Returns: A Case Study in Plant Control Systems

This research involves the combination of spare parts management and reverse logistics. At the end of the product life cycle, products in the field (so called installed base) can usually be serviced by either new parts, obtained from a Last Time Buy, or by repaired failed parts. This paper, however, introduces a third source: the phase-out returns obtained from customers that replace systems. These returned parts may serve other customers that do not replace the systems yet. Phase-out return flows represent higher volumes and higher repair yields than failed parts and are cheaper to get than new ones. This new phenomenon has been ignored in the literature thus far, but due to increased product replacements rates its relevance will grow. We present a generic model, applied in a case study with real-life data from ConRepair, a third-party service provider in plant control systems (mainframes). Volumes of demand for spares, defects returns and phase-out returns are interrelated, because the same installed base is involved. In contrast with the existing literature, this paper explicitly models the operational control of both failed- and phase-out returns, which proves far from trivial given the nonstationary nature of the problem. We have to consider subintervals within the total planning interval to optimize both Last Time Buy and control policies well. Given the novelty of the problem, we limit ourselves to a single customer, single-item approach. Our heuristic solution methods prove efficient and close to optimal when validated. The resulting control policies in the case-study are also counter-intuitive. Contrary to (management) expectations, exogenous variables prove to be more important to the repair firm (which we show by sensitivity analysis) and optimizing the endogenous control policy benefits the customers. Last Time Buy volume does not make the decisive difference; far more important is the disposal versus repair policy. PUSH control policy is outperformed by PULL, which exploits demand information and waits longer to decide between repair and disposal. The paper concludes by mapping a number of extensions for future research, as it represents a larger class of problems.spare parts;reverse logistics;phase-out;PUSH-PULL repair;non stationary;Last Time Buy;business case

Constructive solution methodologies to the capacitated newsvendor problem and surrogate extension

The newsvendor problem is a single-period stochastic model used to determine the order quantity of perishable product that maximizes/minimizes the profit/cost of the vendor under uncertain demand. The goal is to fmd an initial order quantity that can offset the impact of backlog or shortage caused by mismatch between the procurement amount and uncertain demand. If there are multiple products and substitution between them is feasible, overstocking and understocking can be further reduced and hence, the vendor\u27s overall profit is improved compared to the standard problem. When there are one or more resource constraints, such as budget, volume or weight, it becomes a constrained newsvendor problem. In the past few decades, many researchers have proposed solution methods to solve the newsvendor problem. The literature is first reviewed where the performance of each of existing model is examined and its contribution is reported. To add to these works, it is complemented through developing constructive solution methods and extending the existing published works by introducing the product substitution models which so far has not received sufficient attention despite its importance to supply chain management decisions. To illustrate this dissertation provides an easy-to-use approach that utilizes the known network flow problem or knapsack problem. Then, a polynomial in fashion algorithm is developed to solve it. Extensive numerical experiments are conducted to compare the performance of the proposed method and some existing ones. Results show that the proposed approach though approximates, yet, it simplifies the solution steps without sacrificing accuracy. Further, this dissertation addresses the important arena of product substitute models. These models deal with two perishable products, a primary product and a surrogate one. The primary product yields higher profit than the surrogate. If the demand of the primary exceeds the available quantity and there is excess amount of the surrogate, this excess quantity can be utilized to fulfill the shortage. The objective is to find the optimal lot sizes of both products, that minimize the total cost (alternatively, maximize the profit). Simulation is utilized to validate the developed model. Since the analytical solutions are difficult to obtain, Mathematical software is employed to find the optimal results. Numerical experiments are also conducted to analyze the behavior of the optimal results versus the governing parameters. The results show the contribution of surrogate approach to the overall performance of the policy. From a practical perspective, this dissertation introduces the applications of the proposed models and methods in different industries such as inventory management, grocery retailing, fashion sector and hotel reservation

Evolutionary multiobjective optimization of the multi-location transshipment problem

We consider a multi-location inventory system where inventory choices at each location are centrally coordinated. Lateral transshipments are allowed as recourse actions within the same echelon in the inventory system to reduce costs and improve service level. However, this transshipment process usually causes undesirable lead times. In this paper, we propose a multiobjective model of the multi-location transshipment problem which addresses optimizing three conflicting objectives: (1) minimizing the aggregate expected cost, (2) maximizing the expected fill rate, and (3) minimizing the expected transshipment lead times. We apply an evolutionary multiobjective optimization approach using the strength Pareto evolutionary algorithm (SPEA2), to approximate the optimal Pareto front. Simulation with a wide choice of model parameters shows the different trades-off between the conflicting objectives

Deep Inventory Management

We present a Deep Reinforcement Learning approach to solving a periodic review inventory control system with stochastic vendor lead times, lost sales, correlated demand, and price matching. While this dynamic program has historically been considered intractable, we show that several policy learning approaches are competitive with or outperform classical baseline approaches. In order to train these algorithms, we develop novel techniques to convert historical data into a simulator. We also present a model-based reinforcement learning procedure (Direct Backprop) to solve the dynamic periodic review inventory control problem by constructing a differentiable simulator. Under a variety of metrics Direct Backprop outperforms model-free RL and newsvendor baselines, in both simulations and real-world deployments

The Food Truck Problem, Supply Chains and Extensions of the Newsvendor Problem

Inventory control is important to ensuring sufficient quantities of items are available tomeet demands of customers. The Newsvendor problem is a model used in Operations Research to determine optimal inventory levels for fulfilling future demands. Our study extends the newsvendor problem to a food truck problem. We used simulation to show that the food truck does not reduce to a newsvendor problem if demand depends on exogenous factors such temperature, time etc. We formulate the food truck problem as a multi-product multi-period linear program and found the dual for a single item. We use Discrete Event Simulation to solve the stochastic version of the dual and found the optimal order to maximize the food vendors profit