Mathematical programming heuristics for nonstationary stochastic inventory control

This work focuses on the computation of near-optimal inventory policies for a wide range of problems in the field of nonstationary stochastic inventory control. These problems are modelled and solved by leveraging novel mathematical programming models built upon the application of stochastic programming bounding techniques: Jensen's lower bound and Edmundson-Madanski upper bound. The single-item single-stock location inventory problem under the classical assumption of independent demand is a long-standing problem in the literature of stochastic inventory control. The first contribution hereby presented is the development of the first mathematical programming based model for computing near-optimal inventory policy parameters for this problem; the model is then paired with a binary search procedure to tackle large-scale problems. The second contribution is to relax the independence assumption and investigate the case in which demand in different periods is correlated. More specifically, this work introduces the first stochastic programming model that captures Bookbinder and Tan's static-dynamic uncertainty control policy under nonstationary correlated demand; in addition, it discusses a mathematical programming heuristic that computes near-optimal policy parameters under normally distributed demand featuring correlation, as well as under a collection of time-series-based demand process. Finally, the third contribution is to consider a multi-item stochastic inventory system subject to joint replenishment costs. This work presents the first mathematical programming heuristic for determining near-optimal inventory policy parameters for this system. This model comes with the advantage of tackling nonstationary demand, a variant which has not been previously explored in the literature. Unlike other existing approaches in the literature, these mathematical programming models can be easily implemented and solved by using off-the-shelf mathematical programming packages, such as IBM ILOG optimisation studio and XPRESS Optimizer; and do not require tedious computer coding. Extensive computational studies demonstrate that these new models are competitive in terms of cost performance: in the case of independent demand, they provide the best optimality gap in the literature; in the case of correlated demand, they yield tight optimality gap; in the case of nonstationary joint replenishment problem, they are competitive with state-of-the-art approaches in the literature and come with the advantage of being able to tackle nonstationary problems

Wide sense one-dependent processes with embedded Harris chains and their applications in inventory management

In this paper we consider stochastic processes with an embedded Harris chain. The embedded Harris chain describes the dependence structure of the stochastic process. That is, all the relevant information of the past is contained in the state of the embedded Harris chain. For these processes we proved a powerful reward theorem. Futher, we show how we can control these type of processes and give a formulation similar to semi-Markov decision processes. Finally we discuss a number of applications in inventory management.

Computing (R, S) policies with correlated demand

This paper considers the single-item single-stocking non-stationary stochastic lot-sizing problem under correlated demand. By operating under a nonstationary (R, S) policy, in which R denote the reorder period and S the associated order-up-to-level, we introduce a mixed integer linear programming (MILP) model which can be easily implemented by using off-theshelf optimisation software. Our modelling strategy can tackle a wide range of time-seriesbased demand processes, such as autoregressive (AR), moving average(MA), autoregressive moving average(ARMA), and autoregressive with autoregressive conditional heteroskedasticity process(AR-ARCH). In an extensive computational study, we compare the performance of our model against the optimal policy obtained via stochastic dynamic programming. Our results demonstrate that the optimality gap of our approach averages 2.28% and that computational performance is good

Measuring the variability in supply chains with the peakedness

This paper introduces a novel way to measure the variability of order flows in supply chains, the peakedness. The peakedness can be used to measure the variability assuming the order flow is a general point pro- cess. We show basic properties of the peakedness, and demonstrate its computation from real-time continuous demand processes, and cumulative demand collected at fixed time intervals as well. We also show that the peakedness can be used to characterize demand, forecast, and inventory variables, to effectively manage the variability. Our results hold for both single stage and multistage inventory systems, and can further be extended to a tree-structured supply chain with a single supplier and multiple retailers. Furthermore, the peakedness can be applied to study traditional inventory problems such as quantifying bullwhip effects and determining safety stock levels. Finally, a numerical study based on real life Belgian supermarket data verifies the effectiveness of the peakedness for measuring the order flow variability, as well as estimating the bullwhip effects.variability, peakedness, supply chain

Optimizing Inventory for Profitability and Order Fulfillment Improvement

Despite the extensive research on inventory management, few studies have investigated the optimization of inventory classification and control policies for maximizing the net present value of profit and order fulfillment performance. This dissertation aims to fill the gaps, and consists of two main essays. Essay One (Chapter 1) presents a new multi-period optimization model to explicitly address nonstationary demand, arbitrary review periods, and SKU-specific lead times, with the objective of maximizing the net present value of profit. A real-world application and computational experiments show that the optimal dynamic inventory classification and control decisions obtained from the model significantly reduce both safety stock and base stock levels compared to a multi-criteria inventory classification scheme and the traditional ABC approach. Essay Two (Chapter 2) examines two order-based fulfillment performance measures: the order fill rate, defined as the percentage of orders that are completely filled from available inventory; and the average customer-order fill rate, defined as the mean percentage of total units in a customer order that can be filled from on-hand inventory. Novel optimization models are developed to maximize the order fulfillment performance. Computational results indicate that a commonly used item-based measure in general does not adequately indicate order-based performance, and the tradeoffs between profit and order-based measures vary with inventory investment. This research contributes to the existing literature by providing new approaches to optimize inventory classification and control policies with various performance criteria. It also provides practitioners with a viable way to manage inventory with nonstationary demand, general review periods and lead times, and further allows companies to quantity the tradeoffs of different performance measures

Computation of order and volume fill rates for a base stock inventory control system with heterogeneous demand to investigate which customer class gets the best service

We consider a base stock inventory control system serving two customer classes whose demands are generated by two independent compound renewal processes. We show how to derive order and volume fill rates of each class. Based on assumptions about first order stochastic dominance we prove when one customer class will get the best service. That theoretical result is validated through a series of numerical experiments which also reveal that it is quite robust.Base stock policy; service measures; two customer classes; compound renewal processes

Myopic inventory policies using individual customer arrival information

We investigate optimality of myopic policies using the single-unit decomposition approach in inventory management. We derive, under certain conditions, closed-form replenishment decisions, which we call a base-probability policy. That is, the order associated with a given customer is placed if and only if its arrival probability within the lead-time is higher than a threshold.inventory management; base-stock policies; myopic policies;