Roelof Kuik

Controlling inventories with stochastic item returns: A basic model

Abstract Environmental legislation and customer expectations increasingly force manufacturers to take back their products after use. Returned products may enter the production process again as input resources. Material management has to be modified accordingly. One of the areas concerned is inventory management. The present paper provides a step towards a systematic analysis of inventory control in the context of reuse. A basic inventory model is presented comprising Poisson demand and returns. For this model, an optimal control policy is derived and optimal control parameters are computed. Moreover, a numerical analysis is provided of the impact of the return-flow on the inventory system. Comparison with traditional ( s , Q )-inventory models is central throughout the analysis.

Batching decisions: structure and models

Abstract Batching decisions are one of managements instruments to impact performance of goods-flow systems. There is a vast body of literature on analysis and modeling of batching. This paper aims to provide a structure for batching decisions that can help in positioning batching research and models with respect to issues pertinent to goods-flow management. The basis of the structure is a distinction of batching issues as related to three decision levels: (i) process choice/design, (ii) activity planning (aggregate planning and activity programming), and (iii) activity control. Furthermore, the paper discusses some often heard criticisms of batching analysis. The paper concludes with a little speculation of the authors on the future directions of batching research.

On optimal inventory control with independent stochastic item returns

To a growing extent companies take recovery of used products into account in their material management. One aspect distinguishing inventory control in this context from traditional settings is an exogenous inbound material flow. We analyze the impact of this inbound flow on inventory control. To this end, we consider a single inventory point facing independent stochastic demand and item returns. This comes down to a variant of a traditional stochastic single-item inventory model where demand may be both positive or negative. Using general results on Markov decision processes we show average cost optimality of an (s,S)-order policy in this model. The key result concerns a transformation of the model into an equivalent traditional (s,S)-model without return flows, using a decomposition of the inventory position. Traditional optimization algorithms can then be applied to determine control parameter values. We illustrate the impact of the return flow on system costs in a numerical example.

Multi-level lot-sizing problem: Evaluation of a simulated-annealing heuristic

Abstract The multi-level lot-sizing problem (MLP) is the problem of determining production quantities in multi-stage production settings, such that the sum of set-up and holding costs is minimized. This type of problem is hard to solve to optimality thereby compelling one to use heuristic approaches. In this paper we investigate heuristics based on a stochastic search method. Experimental results concerning the quality and efficiency of these methods for the MLP are presented and compared to the quality and efficiency of heuristic methods which are based on applying single-level heuristics on a level-by-level basis.

LINEAR PROGRAMMING, SIMULATED ANNEALING AND TABU SEARCH HEURISTICS FOR LOTSIZING IN BOTTLENECK ASSEMBLY SYSTEMS

Multilevel lotsizing is one of the most challenging subjects in production planning, especially in the presence of capacity constraints. In this paper we investigate lotsizing heuristics for assembly production systems with a bottleneck. More specifically, we discuss heuristics based on Linear Programming (LP), and compare the performance of these heuristics with the performance of approaches based on simulated annealing and tabu search techniques.A comparison of the three heuristics on a set of test problems shows that simulated annealing and tabu search perform well compared to pure LP-based heuristics, but the effectiveness of the latter heuristics can be improved by combining them with elements from simulated annealing and tabu search.

Note on supply chain integration in vendor-managed inventory

In a recent paper Yao et al. present a single-buyer-single-supplier model to explore the effects of collaborative supply-chain initiatives such as vendor managed inventory (VMI). Several conclusions drawn from their model are arguable as (i) the model ignores the costs of shipments from the supplier to the buyer and (ii) the model times the incoming and outgoing flows at the supplier in a manner that overstates the inventory needed at the supplier.

Statistical search methods for lotsizing problems

This paper reports on our experiments with statistical search methods for solving lotsizing problems in production planning. In lotsizing problems the main objective is to generate a minimum cost production and inventory schedule, such that (i) customer demand is satisfied, and (ii) capacity restrictions imposed on production resources are not violated. We discuss our experiences in solving these, in general NP-hard, lotsizing problems with popular statistical search techniques like simulated annealing and tabu search. The paper concludes with some critical remarks on the use of statistical search methods for solving lotsizing problems.

The single-item discrete lotsizing and scheduling problem: optimization by linear and dynamic programming

Abstract This paper considers the single-item discrete lotsizing and scheduling problem (DLSP). DLSP is the problem of determining a minimal cost production schedule, that satisfies demand without backlogging and does not violate capacity constraints. We formulate DLSP as an integer programming problem and present two solution procedures. The first procedure is based on a reformulation of DLSP as a linear programming assignment problem, with additional restrictions to reflect the specific (setup) cost structure. For this linear programming (LP) formulation it is shown that, under certain conditions on the objective, the solution is all integer. The second procedure is based on dynamic programming (DP). Under certain conditions on the objective function, the DP algorithm can be made to run very fast by using special properties of optimal solutions.

Stochastic inventory control for product recovery management

Essentially, inventory management concerns the process of deciding on 1) how often to review stocks, 2) when to replenish stocks, and 3) how much to replenish. This basic focus of inventory management persists in the presence of item returns that can be recovered and then used for servicing demand. However, the details and complexities with which the three basic decisions manifest themselves can, and usually do, differ greatly due to the presence of recoverable-item flows. This, and the practical relevance of inventory management with recoverables, warrants the development of inventory theory that explicitly includes flows of recoverable items.

An exploration of models that minimize leadtime through batching of arrived orders

Abstract In the last decade interest in work-in-process inventory control has grown. Many papers deal with this topic by considering the manufacturing leadtime as the critical factor that determines the amount of work-in-process. Several authors studied the influence of a batching decision on the average manufacturing leadtime. To this end queueing models with batch arrivals and batch service times were analyzed. One of the underlying assumptions made in the analysis is that the arrival process of the batches can be approximated by a Poisson process for each choice of the batchsize. However, when the interarrival times of individual clients are negative exponentially distributed an Erland distribution may be more appropriate as distribution of the interarrival time of the batches at the production unit. In this paper we consider the single item case. A very tractable analytical approximation for the average leadtime when batches arrive according to an Erlang distribution will be derived. Expressions for the optimal batchsize and the associated minimal leadtime are calculated and compared to experimental values obtained by simulation experiments. The approximation appears to be good. Finally, the huge differences in outcomes between Poisson and Erlang arrivals of the batches are highlighted.