We develop new algorithmic approaches to compute provably near-optimal policies for multi-period stochastic lot-sizing inventory models with positive lead times, general demand distributions and dynamic forecast updates. The policies that are developed have worst-case performance guarantees of 3 and typically perform very close to optimal in extensive computational experiments. The newly propos...

We study a single product inventory system with nonnegative setup cost in which the demand is a continuous random variable but orders are restricted to be integer valued. Optimal policies, when there are no setup costs, have a nice form. However, we show that, when the setup costs are nonzero, optimal policies may have a very counterintuitive form without any particular structure. We obtain a b...

Introduction. We study a class of capacitated stochastic lot-sizing inventory control problems with stochastic, non-stationary and correlated demands that evolve over time. Economies of scale and capacity constraints exist in many practical scenarios. However, models with fixed ordering costs and capacity constraints are typically computationally intractable, and even the structure of the optim...

This paper studies stochastic inventory problems with unbounded Markovian demands, ordering costs that are lower semicontinuous, and inventory/backlog (or surplus) costs that are lower semicontinuous with polynomial growth. Finite horizon problems, stationary and nonstationary discounted cost in nite horizon problems, and stationary long-run average cost problems are addressed. Existence of opt...

This study analyzes an inventory control problem of a company in stochastic demand environment under carbon emissions regulations. In particular, a continuous review inventory model with multiple suppliers is investigated under carbon taxing and carbon trading regulations. We analyze and compare the optimal (Q,R) policies with order splitting under two ordering policies: sequential ordering and...

This paper examines the cost-reduction effect of “postponed” routing decisions in a two-echelon supply chain. When a delivery vehicle leaves the warehouse with system replenishment quantities, it sequentially makes routing decisions to choose the next retailer to visit. To measure this effect this paper studies combined vehicle routing and inventoryallocation policies designed to minimize total...

We consider periodic review perishable inventory systems with a fixed product lifetime. Unsatisfied demand can be either lost or backlogged. The objective is to minimize the long-run average holding, penalty, and outdating cost. optimal policy for these notoriously complex computationally intractable because of curse dimensionality. Hence, various heuristic replenishment policies are proposed i...

In this work, we discuss the effect of risk measure selection in the determination of inventory policies. We consider an inventory system characterized by the loss function of Luciano et al. [2003. VaR as a risk measure for multi-period static inventory models. International Journal of Production Economics 81–82, 375–384]. We derive the optimization problems faced by risk neutral, quadratic uti...

The theory on multi-echelon production/inventory systems is a core theory within supply chain management. It provides useful insights for design of supply chains and may be used for tactical and operational planning decisions. The multi-echelon theory started with the seminal paper of Clark and Scarf in 1960. In this tutorial, we describe for which systems optimal policies are known, which key ...