Refik Güllü

On the value of information in dynamic production/inventory problems under forecast evolution

In this article we explore how total system costs and inventory positions are affected when forecasts are incorporated explicitly in production/inventory systems. We assume that forecasts for demand of a certain item are available in each period, and they evolve from one period to the next in accordance with an additive evolution model. In order to analyze the effects of the forecasts on the production/inventory system we compare the optimal ordering policy and the expected costs of the model that keeps forecasts with that of a comparable standard inventory model. We show that under mild assumptions the former yields lower expected costs and inventory levels than the latter.

Analysis of an inventory system under supply uncertainty

In this paper, we analyze a periodic review, single-item inventory model under supply uncertainty. The objective is to minimize expected holding and backorder costs over a finite planning horizon under the supply constraints. The uncertainty in supply is modeled using a three-point probability mass function. The supply is either completely available, partially available, or the supply is unavailable. Machine breakdowns, shortages in the capacity of the supplier, strikes, etc., are possible causes of uncertainty in supply. We demonstrate various properties of the expected cost function, and show the optimality of order-up-to type policies using a stochastic dynamic programming formulation. Under the assumption of a Bernoulli-type supply process, in which the supply is either completely available or unavailable, and when the demand is deterministic and dynamic, we provide a newsboy-like formula which explicitly characterizes the optimal order-up-to levels. An algorithm is given that computes the optimal inventory levels over the planning horizon. Extensions and computational analysis are presented for the case where the partial supply availability has positive probability of occurrence.

A two-echelon allocation model and the value of information under correlated forecasts and demands

Abstract In this article we explore the effects of incorporating forecasts explicitly in a two-echelon allocation model which consists of a central depot and several retailers. In particular, we investigate the possible benefits on the system costs and inventory levels. The depot does not hold any inventory and the demand is observed only at the retailers. Under a general correlated demand-forecast structure we obtain the approximate system-wide order-up-to level and the expected system cost. In order to assess the value of information provided by keeping track of the forecasts, we construct a comparable inventory system operating under a standard demand model. We demonstrate that the standard demand model results in higher order-up-to levels and higher system costs.

Assessing the benefits of remanufacturing option under one-way substitution and capacity constraint

In this article, we investigate the profitability of remanufacturing option when the manufactured and remanufactured products are segmented to different markets and the production capacity is finite. A single period profit model under substitution is constructed to investigate the system conditions under which remanufacturing is profitable. We present analytical findings and computational results to show profitability of remanufacturing option under substitution policy subject to a capacity constraint of the joint manufacturing/remanufacturing facility.

A model to evaluate inventory costs in a remanufacturing environment

Abstract In this study we investigate possible benefits of remanufacturing in inventory-related costs. In order to examine the conditions on different system parameters that make the remanufacturing option cost attractive, the return ratio is considered as a decision variable. The production environment, where the manufacturing and remanufacturing require both common and separate operations, together with the suppliers operations for the new parts and useful lifetime of the product is modeled as a queuing network. A cost model is constructed under certain environmental assumptions. In this paper, the analysis of the model and computational study carried out are discussed.

Base stock policies for production/inventory problems with uncertain capacity levels

Abstract In this paper we consider a single item, stochastic demand production/inventory problem where the maximum amount that can be produced (or ordered) in any given period is assumed to be uncertain. Inventory levels are reviewed periodically. The system operates under a stationary modified base stock policy. The intent of our paper is to present a procedure for computing the optimal base stocl level of this policy under expected average cost per period criterion. This procedure would provide guidance as to the appropriate amount of capacity to store in the form of inventory in the face of stochastic demand and uncertain capacity. In achieving this goal, our main contribution is to establish the analogy between the class of base stock production/inventory policies that operate under demand/capacity uncertainty, and the G/G/1 queues and their associated random walks. We also present example derivations for some important capacity distributions.

Assessing the benefits of remanufacturing option under one-way substitution

In this study, we consider a segmented market for a product that can either be manufactured or remanufactured. It is assumed that the remanufactured products can be substituted by the new ones. A steady-state profit model is constructed under certain environmental assumptions on capacity requirements of operations, and revenue and cost schemes. Exact steady-state probabilities of the Markovian model constructed are solved via matrix geometric techniques. An extensive computational study is performed to investigate the conditions under which the utilization of remanufacturing option and the use of one-way substitution policy increase the average expected profit.

Optimal Lot-Sizing/Vehicle-Dispatching Policies Under Stochastic Lead Times and Stepwise Fixed Costs

We characterize optimal policies of a dynamic lot-sizing/vehicle-dispatching problem under dynamic deterministic demands and stochastic lead times. An essential feature of the problem is the structure of the ordering cost, where a fixed cost is incurred every time a batch is initiated (or a vehicle is hired) regardless of the portion of the batch (or vehicle) utilized. Moreover, for every unit of demand not satisfied on time, holding and backorder costs are incurred. Under mild assumptions we show that the demand of a period is satisfied from at most three distinct production (dispatching) epochs. We devise a dynamic programming algorithm to compute the production/dispatching quantities and times.

Analysis of an inventory system under backorder correlated deterministic demand and geometric supply process

Abstract In this article we propose a single item, periodic review model that investigates the effects of changes in the demand process that occur after stockout realizations. We investigate a system where the demands in successive periods are deterministic but affected by the backorder realizations. In order to capture the effects of changes in the demand process we use a geometric type supply availability. We analytically derive the necessary components for obtaining profit related performance measures and provide computational analysis.

Optimal allocation policies in a two-echelon inventory problem with fixed shipment costs

This study investigates the stock allocation problems in a two-echelon distribution system which consists of a central warehouse and two identical retailers. We restrict our attention to two-period order cycles where the period lengths are allowed to be different. Shipments from the supplier to the warehouse arrive at the beginning of the order cycle (i.e. at the beginning of the first period). In each order cycle, there are two shipment opportunities from the warehouse to the retailers: at the beginning of the first and the second periods. In each shipment realization a fixed shipment cost is incurred. In each period a random demand is observed at each retailer (which is assumed to follow a normal distribution). The overall two-stage problem is to determine the optimal allocation policies at the beginning of each period, so that the expected two-period inventory holding, shortage and the shipment costs will be minimum. In this work, we characterize the optimal policy for the second period allocation problem as a function of the stock levels of the retailers at the beginning of the second period, and the reserve stock held at the warehouse. Furthermore, we provide sufficient conditions for which realizing an allocation yields inferior expected costs over keeping the reserve stock at the warehouse. A simulation model is employed to find the optimal first period decision parameters.