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

Inventory management with advance capacity information

One of the important aspects of supply chain management is dealing with demand and supply uncertainty. The uncertainty of future supply can be reduced, if a company is able to obtain advance capacity information (ACI) on future supply/production capacity availability from its supplier. We address a periodic-review inventory system under stochastic demand and stochastic limited supply, for which ACI is available. We show that the optimal ordering policy is a state-dependent base stock policy characterized by a base stock level that is a function of ACI. We establish a link to inventory models using advance demand information (ADI) by developing a capacitated inventory system with ADI, and showing that the model is closely related to the proposed ACI model. Our numerical results reveal several managerial insights. In particular, we show that ACI is most beneficial when there exists sufficient flexibility to react to anticipated demand and supply capacity mismatches. Further, most of the benefits can be reached with only limited future visibility. We also show that the system parameters affecting the value of ACI interact in a complex way, and therefore need to be considered in an integrated manner

The impact of freight transport capacity limitations on supply chain dynamics

We investigate how capacity limitations in the transportation system affect the dynamic behaviour of supply chains. We are interested in the more recently defined, 'backlash' effect. Using a system dynamics simulation approach, we replicate the well-known Beer Game supply chain for different transport capacity management scenarios. The results indicate that transport capacity limitations negatively impact on inventory and backlog costs, although there is a positive impact on the 'backlash' effect. We show that it is possible for both backlog and inventory to simultaneous occur, a situation which does not arise with the uncapacitated scenario. A vertical collaborative approach to transport provision is able to overcome such a trade-off. © 2013 Taylor & Francis

The influence of demand variability on the performance of a make-to-stock queue

Variability, in general, has a deteriorating effect on the performance of stochastic inventory systems. In particular, previous results indicate that demand variability causes a performance degradation in terms of inventory related costs when production capacity is unlimited. In order to investigate the effects of demand variability in capacitated production settings, we analyze a make-to-stock queue with general demand arrival times operated according to a basestock policy. We show that when demand inter-arrival distributions are ordered in a stochastic sense, increased arrival time variability indeed leads to an augmentation of optimal base-stock levels and to a corresponding increase in optimal inventory related costs. We quantify these effects through several numerical examplesproduction/inventory; make-to-stock; base-stock; stochastic comparisons; GI/M/1, POLICIES; COSTS; SYSTEMS; LEAD

Aggregate constrained inventory systems with independent multi-product demand: control practices and theoretical limitations

In practice, inventory managers are often confronted with a need to consider one or more aggregate constraints. These aggregate constraints result from available workspace, workforce, maximum investment or target service level. We consider independent multi-item inventory problems with aggregate constraints and one of the following characteristics: deterministic leadtime demand, newsvendor, basestock policy, rQ policy and sS policy. We analyze some recent relevant references and investigate the considered versions of the problem, the proposed model formulations and the algorithmic approaches. Finally we highlight the limitations from a practical viewpoint for these models and point out some possible direction for future improvements

Developing a closed-form cost expression for an (R,s,nQ) policy where the demand process is compound generalized Erlang.

We derive a closed-form cost expression for an (R,s,nQ) inventory control policy where all replenishment orders have a constant lead-time, unfilled demand is backlogged and inter-arrival times of order requests are generalized Erlang distributedInventory control; Compound renewal process; Generalized Erlang distribution;

The capacitated multi-echelon inventory system with serial structure. 1. The 'push ahead'-effect

This paper considers a multi-echelon, periodic review inventory model with discrete demand. We assume finite capacities on various production/order sizes and backordering of excess demand. We show that under the average cost criterion the optimal order strategy may be characterized by a so-called 'push ahead'-effect. Further we shall find that a modified base-stock policy approximates the optimal policy quite well