Metin Çakanyildirim

Random lead times and expedited orders in (Q,r) inventory systems

This paper considers inventory models of the order-quantity/order-point type, or (Q,r) models. In general the control parameters (Q and r) depend on both the demand process and the replenishment lead time. Although many studies have treated lead time as constant, focusing solely on demand, a (Q,r) model with stochastic lead time could be a building block in Supply Chain Management. Variability in lead times between successive stages is often what disturbs supply chain coordination.In a two stage system with a constant demand rate, we will concentrate on lead time as a random variable, and develop two probabilistic models. In the first, lead T is exogenous. Lead time is made endogenous in the second stochastic model through an “expediting factor” τ, the constant of proportionality between random variables T (the expedited lead time) and T (ordinary lead time): T = τT. For expedited orders (τ 1. The second model thus has three decision variables (Q, r, τ).For each model, we show that the expected cost per unit time is jointly convex in the decision variables and obtain the global minimizer. Numerical examples are given. Sensitivity analyses are conducted with respect to the cost parameters, and suggestions are made for future research.

A Multiperiod Newsvendor Problem with Partially Observed Demand

We consider a newsvendor problem with partially observed Markovian demand. Demand is observed if it is less than the inventory. Otherwise, only the event that it is larger than or equal to the inventory is observed. These observations are used to update the demand distribution from one period to the next. The state of the resulting dynamic programming equation is the current demand distribution, which is generally infinite dimensional. We use unnormalized probabilities to convert the nonlinear state transition equation to a linear one. This helps in proving the existence of an optimal feedback ordering policy. So as to learn more about the demand, the optimal order is set to exceed the myopic optimal order. The optimal cost decreases as the demand distribution decreases in the hazard rate order. In a special case with finitely many demand values, we characterize a near-optimal solution by establishing that the value function is piecewise linear.

Network externalities, layered protection and IT security risk management

This paper considers two important issues related to security risk management. First, the presence of network externalities in security risks. Second, the distinction of general (network) and system-specific protection measures. We found the optimal allocation of security resources (investments) in protecting every system in an organization. The results show that the consideration of network externalities and layered protection changes the risk mitigation decisions significantly. In addition, accurate estimation of system risk plays a critical role in the success of risk management. Otherwise, the use of a uniform baseline protection approach may be more desirable when the misjudgment of relative system risks is likely to occur.

SeDFAM: semiconductor demand forecast accuracy model

In the semiconductor industry, many critical decisions are based on demand forecasts. However, these forecasts are subject to random error. In this paper, we lay out a scheme estimating the variance and correlation of forecast errors (without altering given forecasts) and modeling the evolution of forecasts over time. Our scheme allows correlations across time, products and technologies. It also addresses the case of nonstationary errors due to ramps (technology migrations). It can be used to simulate chip demands for production planning/capacity expansion studies.

Optimal capacity expansion for multi-product, multi-machine manufacturing systems with stochastic demand

We consider a discrete-time capacity expansion problem involving multiple product families, multiple machine types, and non-stationary stochastic demand. Capacity expansion decisions are made to strike an optimal balance between investment costs and lost sales costs. Motivated by current practices in the semiconductor and other high-tech industries, we assume that only minimal amounts of finished-goods inventories are held, due to the risk of obsolescence. We assume that when capacity is in short supply, management desires to ensure that a minimal service level for all product families is obtained. Our approach uses a novel assumption that demand can be approximated by a distribution whose support is a collection of rays emanating from a point and contained in real multi-dimensional space. These assumptions allow us to solve the problem as a max-flow, min-cut problem. Computational experiments show that large problems can be solved efficiently.

Capacity-driven acceptance of customer orders for a multi-stage batch manufacturing system: models and algorithms

An automotive parts manufacturer produces a wide variety of parts in a job shop environment. Many of the manufacturing operations have substantial setups. When a client phones in an order, the manufacturer must decide quickly whether or not it has the capacity required to accept the order. We develop a simplified formulation of the order acceptance problem. We formulate the discrete-time version as an integer program. The problem is NP-hard, but in 51 out of 51 test problems the LP relaxation is tight. For larger problems we test several heuristics. Three of the heuristics look promising: simulated annealing, a genetic algorithm, and a linear-programming-based heuristic.

Continuous review inventory models where random lead time depends on lot size and reserved capacity

The processing time of large orders is, in many industries, longer than that of small orders. This renders supply lead times in such settings to be increasing in the order size. Yet that pattern is not reflected in existing inventory control models, especially those allowing for random lead times. This work aims at rectifying the situation. Our setting is an order-quantity/reorder-point model with backordering, where the shortage penalty is incurred per unit per unit time. The processing time of each unit is random; the processing time of a lot is correlated with its size. For the case where lead time is proportional to the lot size, we obtain a closed-form solution. That is, unlike the classical (Q,r) model (where lead time is independent of lot size), no iterations are required here. We also analyze a case where the processing time exhibits economies of scale in the lot size. Finally, we consider a situation where a customer can secure shorter processing times by reserving capacity at the supplier’s manufacturing facility.

Reverse bullwhip effect in pricing

Price variability is one of the major causes of the bullwhip effect. This paper analyzes the impact of procurement price variability in the upstream of a supply chain on the downstream retail prices. Procurement prices may fluctuate over time, for example, when the supply chain players deploy auction type procurement mechanisms, or if the prices are dictated in market exchanges. A game theory framework is used here to model a serial supply chain. Sequential price game scenarios are investigated to show that there is an increase in retail price variability and an amplified reverse bullwhip effect on prices (RBP) under certain demand conditions.

Two-dimensional cargo overbooking models

This paper introduces two-dimensional (weight and volume) overbooking problems arising mainly in the cargo revenue management, and compares them with one-dimensional problems. It considers capacity spoilage and cargo offloading costs, and minimizes their sum. For one-dimensional problems, it shows that the optimal overbooking limit does not change with the magnitude of the booking requests. In two-dimensional problems, the overbooking limit is replaced by a curve. The curve, along with the volume and weight axes, encircles the acceptance region. The booking requests are accepted if they fall within this region. We present Curve (Cab) and Rectangle (Rab) models. The boundary of the acceptance region in the Cab (resp. Rab) model is a curve (resp. rectangle). The optimal curve for the Cab model is shown to be unique and continuous. Moreover, it can be obtained by solving a series of simple equations. Finding the optimal rectangle for the Rab model is more challenging, so we propose an approximate rectangle. The approximate rectangle is a limiting solution in the sense that it converges to the optimal rectangle as the booking requests increase. The approximate rectangle is numerically shown to yield costs that are very close to the optimal costs.

On the Optimal Control of Partially Observed Inventory Systems

This paper introduces recent developments in the analysis of inventory systems with partial observations. The states of these systems are typically conditional distributions, which evolve in infinite dimensional spaces over time. Our analysis involves introducing unnormalized probabilities to transform nonlinear state transition equations to linear ones. With the linear equations, the existence of the optimal feedback policies are proved for two models where demand and inventory are partially observed. In a third model where the current inventory is not observed but a past inventory level is fully observed, a sufficient statistic is provided to serve as a state. The last model serves as an example where a partially observed model has a finite dimensional state. In that model, we also establish the optimality of the basestock policies, hence generalizing the corresponding classical models with full information.