Projected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes

We consider the canonical periodic review lost sales inventory system with positive lead-times and stochastic i.i.d. demand under the average cost criterion. We introduce a new policy that places orders such that the expected inventory level at the time of arrival of an order is at a fixed level and call it the Projected Inventory Level (PIL) policy. We prove that this policy has a cost-rate superior to the equivalent system where excess demand is back-ordered instead of lost and is therefore asymptotically optimal as the cost of losing a sale approaches infinity under mild distributional assumptions. We further show that this policy dominates the constant order policy for any finite lead-time and is therefore asymptotically optimal as the lead-time approaches infinity for the case of exponentially distributed demand per period. Numerical results show this policy also performs superior relative to other policies

Certainty Equivalent Planning for Multi-Product Batch Differentiation: Analysis and Bounds

We consider a multi-period planning problem faced by a firm that must coordinate the production and allocations of batches to end products for multiple markets. Motivated by a problem faced by a biopharmaceutical firm, we model this as a discrete-time inventory planning problem where in each period the firm must decide how many batches to produce and how to differentiate batches to meet demands for different end products. This is a challenging problem to solve optimally, so we derive a theoretical bound on the performance of a Certainty Equivalent (CE) control for this model, in which all random variables are replaced by their expected values and the corresponding deterministic optimization problem is solved. This is a variant of an approach that is widely used in practice. We show that while a CE control can perform very poorly in certain instances, a simple re-optimization of the CE control in each period can substantially improve both the theoretical and computational performance of the heuristic, and we bound the performance of this re-optimization. To address the limitations of CE control and provide guidance for heuristic design, we also derive performance bounds for two additional heuristic controls -- (1) Re-optimized Stochastic Programming (RSP), which utilizes full demand distribution but limits the adaptive nature of decision dynamics, and (2) Multi-Point Approximation (MPA), which uses limited demand information to model uncertainty but fully capture the adaptive nature of decision dynamics. We show that although RSP in general outperforms the re-optimized CE control, the improvement is limited. On the other hand, with a carefully chosen demand approximation in each period, MPA can significantly outperform RSP. This suggests that, in our setting, explicitly capturing decision dynamics adds more value than simply capturing full demand information.http://deepblue.lib.umich.edu/bitstream/2027.42/116386/1/1296_Ahn.pd

Optimal Structural Results for Assemble-to-Order Generalized M-Systmes

Cataloged from PDF version of article.We consider an assemble-to-order generalized M-system with multiple components and multiple products, batch ordering of components, random lead times, and lost sales. We model the system as an in nite-horizon Markov decision process and seek an optimal control policy, which speci es when a batch of components should be produced and whether an arriving demand for each product should be satis ed. To facilitate our analysis, we introduce new functional characterizations for convexity and submodularity with respect to certain non-unitary directions. These help us characterize optimal inventory replenishment and allocation policies under a mild condition on component batch sizes via a new type of policy: lattice-dependent base-stock and lattice-dependent rationing

COMPUTER AIDED ASSEMBLY PLANNING USING MS EXCEL SOFTWARE – A CASE STUDY

The issue of planning assembly operations remains crucial decision-making area for many of manufacturing companies. It becomes particularly significant in case of small and medium enterprises that perform unit or small-scale production, where the option of applying specialized software is often very limited – both due to high purchase price, but also due to its applicability to single unit manufacturing, that is executed based on individual customer orders. The present article describes the possibility of applying the MS Excel spreadsheet in the planning of machine assembly processes. It emphasises, in particular, the method for using the spreadsheet in subsequent stages of the process, and the identification of possible causes that have impact on problems with the planning process. We performed our analysis on the basis of actual data from one of the machine industry enterprises that manufactures in central Poland

Convexity Properties and Comparative Statics for M/M/S Queues with Balking and Reneging

We use sample path arguments to derive convexity properties of an M/M/S queue with impatient customers that balk and renege. First, assuming that the balking probability and reneging rate are increasing and concave in the total number of customers in the system (head-count), we prove that the expected head-count is convex decreasing in the capacity (service rate). Second, with linear reneging and balking, we show that the expected lost sales rate is convex decreasing in the capacity. Finally, we employ a sample-path sub-modularity approach to comparative statics. That is, we employ sample path arguments to show how the optimal capacity changes as we vary the parameters of customer demand and impatience. We find that the optimal capacity increases in the demand rate and decreases with the balking probability, but is not monotone in the reneging rate. This means, surprisingly, that failure to account for customersâ reneging may result in over-investment in capacity. Finally, we show that a seemingly minor change in system structure, customer commitment during service, produces qualitatively different convexity properties and comparative statics.Operations Management Working Papers Serie

Base-stock policies for lost-sales models: Aggregation and asymptotics

This paper considers the optimization of the base-stock level for the classical periodic review lost-sales inventory system. The optimal policy for this system is not fully understood and computationally expensive to obtain. Base-stock policies for this system are asymptotically optimal as lost-sales costs approach infinity, easy to implement and prevalent in practice. Unfortunately, the state space needed to evaluate a base-stock policy exactly grows exponentially in both the lead time and the base-stock level. We show that the dynamics of this system can be aggregated into a one-dimensional state space description that grows linearly in the base-stock level only by taking a non-traditional view of the dynamics. We provide asymptotics for the transition probabilities within this single dimensional state space and show that these asymptotics have good convergence properties that are independent of the lead time under mild conditions on the demand distribution. Furthermore, we show that these asymptotics satisfy a certain ow conservation property. These results lead to a new and computationally efficient heuristic to set base-stock levels in lost-sales systems. In a numerical study we demonstrate that this approach performs better than existing heuristics with an average gap with the best base-stock policy of 0.01% across a large test-bed