Computational procedures for stochastic multi-echelon production systems

This paper is concerned with the numerical evaluation of multi-echelon production systems. Each stage requires a fixed predetermined leadtime; furthermore, we assume a stochastic, stationary end-time demand process. In a previous paper, we have developed an analytical framework for determining optimal control policies for such systems under an average cost criterion.\ud \ud The current paper is based on this analytical theory but discusses computational aspects, in particular for serial and assembly systems. A hierarchical (exact) decomposition of these systems can be obtained by considering echelon stocks and by transforming penalty and holding costs accordingly. The one-dimensional problems arising after this decomposition however involve incomplete convolutions of distribution functions, which are only recursively defined. We develop numerical procedures for analysing these incomplete convolutions; these procedures are based on approximations of distribution functions by mixtures of Erlang distributions. Combining the analytically obtained (exact) decomposition results with these numerical procedures enables us to quickly determine optimal order-up-to levels for all stages. Moreover, expressions for the customer service level of such a multi-stage are obtained, yielding the possibility to determine policies which minimize average inventory holding costs, given a service level constraint

On multi-stage production/inventory systems under stochastic demand

This paper was presented at the 1992 Conference of the International Society of Inventory Research in Budapest, as a tribute to professor Andrew C. Clark for his inspiring work on multi-echelon inventory models both in theory and practice. It reviews and extends the work of the authors on periodic review serial and convergent multi-echelon systems under stochastic stationary demand. In particular, we highlight the structure of echelon cost functions which play a central role in the derivation of the decomposition results and the optimality of base stock policies. The resulting optimal base stock policy is then compared with an MRP system in terms of cost effectiveness, given a predefined target customer service level. Another extension concerns an at first glance rather different problem; it is shown that the problem of setting safety leadtimes in a multi-stage production-to-order system with stochastic lead times leads to similar decomposition structures as those derived for multi-stage inventory systems. Finally, a discussion on possible extensions to capacitated models, models with uncertainty in both demand and production lead time as well as models with an aborescent structure concludes the paper

The development of cross-border economic relationships between firms in border regions

Central question of this paper is what effects a state border has on the development of cross-border economic relationships in border regions. First the geographical spread of these relationships is analysed. Next a theoretical model is proposed to explain the pattern and the decision-process of bilateral international economic relationships. The model is mainly based on four theories: 1. the transaction costs approach on cross border economic relations under the condition of uncertainty. 2. The 'psychic distance' approach, which considers internationalization as an incremental learning process. The speed of the internationalization of a firm is determined by the experiential knowledge about the foreign country. 3. The network-approach, which considers (international) markets as networks. Firms are linked in patterns of cooperation and affiliation. Cooperation and not efficiency of transactions determine the behaviour of firms. 4. The socio-psychological approach of relations and social identity, which stresses the role of cognitive and affective aspects of cross-border relationships. These theories have lead to the model of INTERnational Formation of Autonomous Cooperation between Entrepreneurs (INTERFACE). The INTERFACE model distinguishes between different phases of relationship-building, namely contact, attraction (the choice for the partner), interaction (the negotiation about the conditions), transaction (the realization of the agreement/contract) and relationship. This relationship-development model is used to describe the process of the development of cross-border economic relationships and to explain the number and success of cross-border economic relationships. The model is empirically tested for a large sample of firms in two Dutch-Belgian border regions. The study is part of a dissertation on the development of cross-border economic relationships. The findings of the model suggests that the action-space of the firms, in terms of informal embeddedness and economic relationships, is spatially limited by the presence of the border. The factors of similarity and trust between the partners are found to be the most important determinants of success of cross-border economic relationships. The dimensions of expectations on the discrepancy in business conventions, the expectations on the success of economic relations in the neighbouring country and the strictness of the financial-economic terms of the relationship play a major role in determining the number of cross-border economic relationships. This is defined as the 'mental distance' effect of borders

Effect of commonality on spare parts provisioning costs for capital goods

Machines at customers have to be provided with spare parts upon failure. Consider a number of groups of machines, for each of which a target aggregate fill rate or target average response time (waiting time) should be met. Between groups, commonality exists, i.e., some parts occur in the material breakdown structure of machines in multiple groups. Instead of using separate stocks per group of machines, we study the potential benefits of exploiting commonality by using a shared stock for all groups together. For this purpose, we formulate a multi-item single-site spare parts inventory model, with the objective to minimize the spare parts provisioning costs, i.e., inventory holding and transportation costs, under the condition that all service level constraints are met. We develop a heuristic solution procedure using a decomposition approach as in Dantzig-Wolfe decomposition, in order to obtain both a heuristic solution and a lower bound for the optimal costs. In a case study and a numerical experiment, we show that significant reductions in spare parts provisioning costs can be obtained by using shared stocks. Furthermore, we show how the size of the potential benefits behaves as a function of the number of groups, the percentage of commonality and the occurrence of commonality in cheap or expensive items

Near-optimal heuristics to set base stock levels in a two-echelon distribution network

We consider a continuous-review two-echelon distribution network with one central warehouse and multiple local stock points, each facing independent Poisson demand for one item. Demands are fulfilled from stock if possible and backordered otherwise. We assume base stock control with one-for-one replenishments and the goal is to minimize the inventory holding and backordering costs. Although this problem is widely studied, only enumerative procedures are known for the exact optimization. A number of heuristics exist, but they ??nd solutions that are far from optimal in some cases (over 20% error on realistic problem instances). We propose a heuristic that is computationally e??cient and ??nds solutions that are close to optimal: 0.1% error on average and less than 3.0% error at maximum on realistic problem instances in our computational experiment

Incomplete convolutions in production and inventory models

In this paper, we study incomplete convolutions of continuous distribution functions, as they appear in the analysis of (multi-stage) production and inventory systems. Three example systems are discussed where these incomplete convolutions naturally arise. We derive explicit, nonrecursive formulae for these convolutions, for the relevant case in which the underlying distributions are (mixtures of) Erlang distributions with the same scale parameter. Numerical results for one example system, the multi-stage serial inventory system, are presented to show the effectiveness of these formulae

Reducing costs of repairable spare parts supply systems via dynamic scheduling

We study a system consisting of one repair shop and one stockpoint, where spare parts of repairables are kept on stock to serve an installed base of systems. Part requests are met from stock if possible, and backordered otherwise. Our objective is to determine initial stock levels and a policy for scheduling repair jobs such that holding and backorder cost are minimized. We propose two dynamic scheduling rules, compare their performance with the static priority rule, and show that even when stock levels and static priorities have been optimized simultaneously, dynamic scheduling rules often reduce total cost by more than 10%

A-posteriori symbol probabilities and log-likelihood ratios for coherently detected π/4-DE-QPSK

In this letter, coherent detection of p/4-DE-QPSK is considered, but our analysis also holds for common DE-QPSK. It is shown that maximum a-posteriori (MAP) sequence detection can be regarded as an approximation, based on selecting dominant exponentials, of MAP symbol detection. A better approximation, relying on piecewise-linear fitting of the logarithm of the hyperbolic cosine, is proposed. This approximation results in a performance very close to optimal symbol detection. For the case where the symbols are produced by convolutional encoding and Gray mapping, the log-likelihood ratios are investigated. Again a simple approximation based on selecting dominant exponentials and an improved approximation relying on piecewise-linear fits, are discussed. As in the uncoded case the improved approximation gives a performance quite close to ideal. While the particular examples considered show modest gains in performance, this letter provides a way of improving performance when needed