van der J Jan Wal

Combining make to order and make to stock

In inventory control and production planning one is tempted to use one of two strategies: produce all demand to stock or produce all demand to order. The disadvantages are well-known. In the ‘make everything to order’ case (MTO) the response times may become quite long if the load is high, in the ‘make everything to stock’ case (MTS) one gets an enormous inventory if the number of different products is large.In this paper we study two simple models which combine MTO and MTS, and investigate the effect of combining MTO and MTS on the production lead times.ZusammenfassungIn Lagerhaltung und Produktionsplanung werden überwiegend zwei alternative Strategien betrachtet: Produktion auf Bestellung oder auf Vorrat. Die Nachteile sind bekannt. Die erste Strategie kann zu sehr langen Durchlaufzeiten führen, die zweite zu hohen Beständen, insbesondere bei großer Produktanzahl. In dieser Arbeit werden zwei Modelle betrachtet, in denen die beiden Betrachtungsweisen kombiniert werden.

Admission policies for a two class loss system

We consider the problem of dynamic admission control in a Markovian loss queueing system with two classes of customers with different service rates and revenues. We show that under certain conditions, customers of one class, which we call a preferred class, are always admitted to the system. Moreover, the optimal policy is of threshold type, and we establish that the thresholds are monotone under very restrictive conditions.

Equilibrium strategies for processor sharing and random queues with relative priorities

We consider a memoryless single-server queue in which users can purchase relative priority so as to reduce their expected waiting costs, which are linear with time. Relative priority is given in proportion to a price paid by customers present in the system. For two service disciplines, (weighted) processor sharing and (weighted) random entrance, we find the unique pure and symmetric Nash equilibrium price paid by the customers.

The design of robotic dairy barns using closed queueing networks

In this paper we present a closed queueing network model for a robotic milking barn. We use an approximative mean-value algorithm to evaluate important performance criteria such as the number of cows waiting, their waiting time and the utilization of the facilities in the barn. It is shown how the results from the queueing network analysis can support the discussion about the optimal design of the robotic barn.

Designing the optimal robotic milking barn by applying a queuing network approach

The design of various conventional dairy barns is based on centuries of experience, but there is hardly any experience with robotic milking barns (RMB). Furthermore, as each farmer has his own management practices, the optimal layout is ‘site dependent’. A new universally applicable design methodology has been developed, to overcome this lack of experience with RMBs and to facilitate the designing of their optimal layout. This model for optimizing facility allocation, based on cow behaviour, welfare needs, and facility utilization, uses queuing network theory, Markov process, and heuristic optimization. The methodology has been programmed into a software application, supporting the design process. On a particular farm, presented later as a case study, numerical results include: if the herd contains more than 50 cows, the forage-lane utilization is greater than 70% (or idle time is less than 30%). To meet animal-welfare demands, the herd size should not exceed 60 cows. Therefore, the herd should comprise 50–60 cows. In the second scenario examined, the average robot idle time was 25%, queue length was three cows, and each cow waited for about 3 min at the robot. It is still uncommon to apply techniques from queuing-network theory to livestock housing, and this study demonstrates their potential as practical design tools that meet both economic and animal welfare needs.

Admission policies for a two class loss system with general interarrival times

This paper considers the problem of dynamic admission control in a loss queueing system with two classes of jobs. The jobs require an exponential amount of service time with different means and bring different revenues, whereas the arrivals occur according to a general distribution. We establish the existence of optimal acceptance thresholds for both job classes and show that under certain conditions there exists a preferred class. We also provide an example to demonstrate that for a Markov modulated Poisson arrival process there may be states in which both classes are rejected.

Iterative bounds on the equilibrium distribution of a finite Markov chain

This article presents a new iterative method for computing the equilibrium distribution of a finite Markov chain, which has the significant advantage of providing good upper and lower bounds for the equilibrium probabilities. The method approximates the expected number of visits to each state between two successive visits to a given reference state. Numerical examples indicate that the performance of this method is quite good.

Aggregation and disaggregation in Markov decision models for inventory control

In this paper the possibility is investigated of using aggregation in the action space for some Markov decision processes of inventory control type. For the standard (s, S) inventory control model the policy improvement procedure can be executed in a very efficient way, therefore, aggregation in the action space is not of much use. However, in situations where the decisions have some aftereffect and, hence, the old decision has to be incorporated in the state, it might be rewarding to aggregate actions. Some variants for aggregation and disaggregation are formulated and analyzed. Numerical evidence is presented.

ON THE USE OF INFORMATION IN MARKOV DECISION PROCESSES

This paper gives a systematic treatment of results about the existence of various types of nearly-optimal strategies (Markov , stationary) in countable state total reward Markov decision processes. For example the following questions are considered: do there exist optimal stationary strategics, uniformly nearly-optimal stationary strategies or uniformly nearly-optimal Harkov strategies.

Markov-decision processes and ship-handling : an exercise in aggregation

Operational planning in a general purpose ship terminal is treated. The decisions to be taken concern the weekly manpower capacity and the assignment of manpower and equipment to ships. As a Markov decision problem the model is very big and aggregation is desirable. As a check simulation is used, which leads to an iterative aggregation-disaggregation approach.