Reducing order and inventory variability under stochastic lead-time and correlated demand

Logistic volatility is considered to be an important contributor to supply chain inefficiency. In this paper we investigate the amplification of order and inventory fluctuations in a state-space model with stochastic lead time, ARMA(p,q) demand and a proportional order-up-to policy. We derive the exact distribution functions for order and inventory. For i.i.d. Gaussian demand, we prove that the proportional outperforms the classical order-up-to policy in reducing inventory and order variances simultaneously. Numerical experiments are carried out to show the complex interaction between demand correlation and stochastic lead-time

A Finite Horizon Inventory Model: An Operational Framework

We present a simulation based decision support system to decide the inventory ordering policy in the context of a single commodity, multi pack, and finite horizon situation. The multiple objectives include (a) Minimizing the end of the season inventory, (b) Maximizing the operating profit, (c) Minimizing the peak working capital requirements during the season. Stochastic demand and positive lead time add to the complexity of the problem context. In addition multiple partners in the supply chain with distinct and conflicting set of objectives necessitate the need for a formal approach. The motivation for this model is based on a real life situation. The model addresses the decision choices faced by the distributor in a specific logistics chain. In this chain, a typical distributor has to balance between the stochastic nature of the demand and the attractive nature of financial incentives (order quantity based) proposed by the manufacturer. The problem can be formulated as a multi-period dynamic programming problem with stochastic demand with an objective to optimize the expected operating profit, subject to specific constraints on working capital requirement, service level, order fill rate and end of the season inventory. Such a formulation is hard to solve and does not lend itself to analyze several ordering policies. Based on simulation experiments, we propose an ordering policy which optimizes the overall objectives of supply chain partners and hence demonstrated the possibility of jointly managing the uncertain demand by supply chain partners. The model is simple and easy to use. It is implemented by using spreadsheet. It provides adequate flexibility to conduct what-if analysis. The model has a potential to be useful in a wide range of situations.

An Inventory Model for Deteriorating Commodity under Stock Dependent Selling Rate

Economic order quantity (EOQ) is one of the most important inventory policy that have to be decided in managing an inventory system. The problem addressed in this paper concerns with the decision of the optimal replenishment time for ordering an EOQ to a supplier. This Model is captured the affect of stock dependent selling rate and varying price. We developed an inventory model under varying of demand-deterioration-price of commodity when the relationship of supplier-grocery-consumer at stochastic environment. The replenishment assumed instantaneous with zero lead time. The commodity will decay of quality according to the original condition with randomize characteristics. First, the model is addressed to solve a problem phenomenon how long is the optimum length of cycle time. Then, an EOQ of commodity to be ordered by will be determined by model. To solve this problem, the first step is developed a mathematical model based on reference’s model, and then solve the model analytically. Finally, an inventory model for deteriorating commodity under stock dependent selling rate and considering selling price was derived by this research. Keywords: deterioration commodity, expected profit, optimal replenishment time stock dependent selling rate

Considering inventory distributions in a stochastic periodic inventory routing system

Dealing with the stochasticity of parameters is one of the critical issues in business and industry nowadays. Supply chain planners have difficulties in forecasting stochastic parameters of a distribution system. Demand rates of customers during their lead time are one of these parameters. In addition, holding a huge level of inventory at the retailers is costly and inefficient. To cover the uncertainty of forecasting demand rates, researchers have proposed the usage of safety stock to avoid stock-out. However, finding the precise level of safety stock depends on forecasting the statistical distribution of demand rates and their variations in different settings among the planning horizon. In this paper the demand rate distributions and its parameters are taken into account for each time period in a stochastic periodic IRP. An analysis of the achieved statistical distribution of the inventory and safety stock level is provided to measure the effects of input parameters on the output indicators. Different values for coefficient of variation are applied to the customers’ demand rate in the optimization model. The outcome of the deterministic equivalent model of SPIRP is simulated in form of an illustrative case

Approximating the Nonlinear Newsvendor and Single-Item Stochastic Lot-Sizing Problems When Data Is Given by an Oracle

The single-item stochastic lot-sizing problem is to find an inventory replenishment policy in the presence of discrete stochastic demands under periodic review and finite time horizon. A closely related problem is the single-period newsvendor model. It is well known that the newsvendor problem admits a closed formula for the optimal order quantity whenever the revenue and salvage values are linear increasing functions and the procurement (ordering) cost is fixed plus linear. The optimal policy for the single-item lot-sizing model is also well known under similar assumptions. In this paper we show that the classical (single-period) newsvendor model with fixed plus linear ordering cost cannot be approximated to any degree of accuracy when either the demand distribution or the cost functions are given by an oracle. We provide a fully polynomial time approximation scheme for the nonlinear single-item stochastic lot-sizing problem, when demand distribution is given by an oracle, procurement costs are provided as nondecreasing oracles, holding/backlogging/disposal costs are linear, and lead time is positive. Similar results exist for the nonlinear newsvendor problem. These approximation schemes are designed by extending the technique of K-approximation sets and functions.National Science Foundation (U.S.) (Contract CMMI-0758069)United States. Office of Naval Research (Grant N000141110056

Matching Spatially Diversified Suppliers with Random Demands

A fundamental challenge in operations management is to dynamically match spatially diversified supply sources with random demand units. This dissertation tackles this challenge in two major areas: in supply chain management, a company procures from multiple, geographically differentiated suppliers to service stochastic demands based on dynamically evolving inventory conditions; in revenue management of ride-hailing systems, a platform uses operational and pricing levers to match strategic drivers with random, location and time-varying ride requests over geographically dispersed networks. The first part of this dissertation is devoted to finding the optimal procurement and inventory management strategies for a company facing two potential suppliers differentiated by their lead times, costs and capacities. We synthesize and generalize the existing literature by addressing a general model with the simultaneous presence of (a) orders subject to capacity limits, (b) fixed costs associated with inventory adjustments, and (c) possible salvage opportunities that enable bilateral adjustments of the inventory, both for finite and infinite horizon periodic review models. By identifying a novel, generalized convexity property, termed (C1K1, C2K2)-convexity, we are able to characterize the optimal single-source procurement strategy under the simultaneous treatment of all three complications above, which has remained an open challenge in stochastic inventory theory literature. To our knowledge, we recover almost all existing structural results as special cases of a unified analysis. We then generalize our results to dual-source settings and derive optimal policies under specific lead time restrictions. Based on these exact optimality results, we develop various heuristics and bounds to address settings with fully general lead times. The second part of this dissertation focuses on a ride-hailing platform's optimal control facing two major challenges: (a) significant demand imbalances across the network, and (b) stochastic demand shocks at hotspot locations. Towards the first major challenge, which is evidenced by our analysis of New York City taxi trip data, the dissertation shows how the platform's operational controls--including demand-side admission control and supply-side empty car repositioning--can improve system performance significantly. Counterintuitively, it is shown that the platform can improve the overall value through strategic rejection of demand in locations with ample supply capacity (driver queue). Responding to the second challenge, a demand shock of uncertain duration, we show how the platform can resort to surge pricing and dynamic spatial matching jointly, to enhance profits in an incentive compatible way for the drivers. Our results provide distinctive insights on the interplay among the relevant timescales of different phenomena, including rider patience, demand shock duration and drivers' traffic delay to the hotspot, and their impact on optimal platform operations

Stochastic Reorder Point-Lot Size (r,Q) Inventory Model under Maximum Entropy Principle

This paper takes into account the continuous-review reorder point-lot size (r,Q) inventory model under stochastic demand, with the backorders-lost sales mixture. Moreover, to reflect the practical circumstance in which full information about the demand distribution lacks, we assume that only an estimate of the mean and of the variance is available. Contrarily to the typical approach in which the lead-time demand is supposed Gaussian or is obtained according to the so-called minimax procedure, we take a different perspective. That is, we adopt the maximum entropy principle to model the lead-time demand distribution. In particular, we consider the density that maximizes the entropy over all distributions with given mean and variance. With the aim of minimizing the expected total cost per time unit, we then propose an exact algorithm and a heuristic procedure. The heuristic method exploits an approximated expression of the total cost function achieved by means of an ad hoc first-order Taylor polynomial. We finally carry out numerical experiments with a twofold objective. On the one hand we examine the efficiency of the approximated solution procedure. On the other hand we investigate the performance of the maximum entropy principle in approximating the true lead-time demand distribution

Applications of stochastic inventory control in market-making and robust supply chains

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 169-172).This dissertation extends the classical inventory control model to address stochastic inventory control problems raised in market-making and robust supply chains. In the financial market, market-makers assume the role of a counterpart so that investors can trade any fixed amounts of assets at quoted bid or ask prices at any time. Market-makers benefit from the spread between the bid and ask prices. but they have to carry inventories of assets which expose them to potential losses when the market price moves in an undesirable direction. One approach to reduce the risk associated with price uncertainty is to actively trade with other Market-Makers at the price of losing potential spread gain. We propose a dynamic programming model to determine the optimal active trading quantity., which maximizes the Market-Maker's expected utility. For a single-asset model. We show that a threshold inventory control policy is optimal with respect to both an exponential utility criterion and a mean-variance tradeoff objective. Special properties such as symmetry and monotonicity of the threshold levels are also investigated. For a multiple-asset model. the mean-variance analysis suggests that there exists a connected no-trade region such that the Market-Maker does not need to actively trade with other market-makers if the inventory falls in the no-trade region. Outside the no-trade region. the optimal way to adjust inventory levels can be obtained from the boundaries of the no-trade region. These properties of the optimal policy lead to practically efficient algorithms to solve the problem. The dissertation also considers the stochastic inventory control model in robust supply chain systems. Traditional approaches in inventory control first estimate the demand distribution among a predefined family of distributions based on data fitting of historical demand observations, and then optimize the inventory control policy using the estimated distributions. which often leads to fragile solutions in case the preselected family of distributions was inadequate. In this work. we propose a minimax robust model that integrates data fitting and inventory optimization for the single item multi-period periodic review stochastic lot-sizing problem. Unlike the classical stochastic inventory models, where demand distribution is known, we assume that histograms are part of the input. The robust model generalizes Bayesian model, and it can be interpreted as minimizing history dependent risk measures. We prove that the optimal inventory control policies of the robust model share the same structure as the traditional stochastic dynamic programming counterpart. In particular., we analyze the robust models based on the chi-square goodness-of-fit test. If demand samples are obtained from a known distribution, the robust model converges to the stochastic model with true distribution under general conditions.by Miao Song.Ph.D

Building blocks for supply chain management - a study of inventory modelling

This thesis presents a study of stochastic models of continuous review of inventory systems of perishable and non-perishable products, as well as inventory systems operating in random environment. It contains five chapters. The first chapter is introductory in nature, containing the motivation for the study and the techniques required for the analysis of respective models described in the remaining chapters. Chapter 2 provides a model of perishable product inventory system operating in a random environment. For the sake of simplicity, the stochastic environment is considered to alternate randomly over time between two states 0 and 1 according to an alternating renewal process. When the environment is in state k, the items in inventory have a perishable rate ìk, the demand rate is ëk and the replenishment cost is CRk. The performance of various measures of the system evolution are obtained, assuming instantaneous replenishment at the epoch of the first demand after the stock-out and associating a Markov renewal process with the inventory level. In Chapter 3, a continuous review single product perishable inventory model is considered. Items deteriorate in two phases and then perish. Independent demands occur at constant rates for items in phase I and in phase II. Demand that occurs for an item in phase I during its stock-out period is satisfied by an item in phase II with some probability. However a demand for an item in phase II occurring during its stock-out period is lost. The reordering policy is an adjustable (S,s) policy with the lead-time following an arbitrary distribution. Identifying the stochastic process as a renewal process, the probability distribution of the inventory level at any arbitrary instant of time is obtained. The expressions for the mean stationary rates of demands lost, demands substituted, perished units and scrapped units are also derived. A numerical example is considered to highlight the results obtained. Chapter 4 is a study of a two-commodity inventory system under continuous review. The maximum storage capacity for the i-th item is Si (i=1, 2). The demand points for each commodity are assumed to form an independent Poisson process, with unit demand for one item and bulk demand for the other. The order level is fixed as si for the i-th commodity (i=1, 2) and the ordering policy is to place an order for Qi (= Si – si , i = 1,2) items for the i-the commodity when both the inventory levels are less than or equal to their respective reorder levels. The lead-time is assumed to be exponential. The joint probability distribution for both commodities is obtained in both transient and steady state cases. Various measures of systems performance and the total expected cost rate in the steady state are derived. The results are illustrated with numerical examples. Chapter 5 provides an analysis of a continuous review of two-product system with two types of demands and with individual (S,s) ordering policy. The lead-time distribution of product 1 is arbitrary and that of product 2 exponential. Two types of demands occur at constant rates either for both products or for product 2 alone. Expressions for the stationary distribution of the inventory level are obtained by identifying the underlying stochastic processes as a semi-regenerative process. The mean stationary rates of the lost demands, the demands that are satisfied and the number of reorders are obtained and these measures are used to provide an expression for the cost rate. The main objective of this thesis is to improve the state of art of continuous review inventory systems. The salient features of the thesis are summarized below: (a) Consideration of (i) The impact of the stochastic environment on inventory systems; (ii) The interactions existing among the products in multi-product systems; (iii) Individual and joint-ordering policies; (b) Discussion of inventory systems with perishable products; (c) Effective use of the regeneration point technique to derive expressions for various system measures; (d) Illustration of the various results by extensive numerical work; (e) Relevant optimization problemsThesis (PhD (Industrial Engineering))--University of Pretoria, 2006.Industrial and Systems Engineeringunrestricte

An Integrated Single Vendor-Buyer Stochastic Inventory Model with Partial Backordering under Imperfect Production and Carbon Emissions

This paper develops an integrated single vendor single buyer inventory model with imperfect quality and environmental impact. The demand during lead time is assumed to be stochastic and follows the normal distribution. An integrated system with controllable lead time and logarithmic investment to reduce the defective percentage is discussed in this model.100% error-free screening process is adopted by the buyer to separate defective and non-defective items. We assume that shortages are allowed and are partially backordered at the buyer’s end. Logistics management is the component of supply chain management that focusses on how and when to get raw materials, intermediate products and finished goods from their respective origins to their destinations.Thus, transportation play a major role in supply chain. As transportation increases, it affects the weather by the matter of carbon emission.The fixed and variable carbon emission cost for both vendor and buyer is considered. The prime motive is to determine the optimal policies regarding optimal order quantity, reorder point, lead time and the number of lots delivered in a production run by minimizing the expected total cost of the system. Finally, a numerical example is provided to demonstrate the model