Stochastic models for shared production resources in supply chains

Expectations of customers regarding variety, customization, fast and reliable due dates of products have been increasing over time. Meeting this demand is a constant challenge for companies given their limited resources. Finding the balance between customers' requirements from one side and companies operations from the other has shown to be an arduous task; variabilities in either demands or operations could have significant negative consequences on companies' performances. These variabilities could cause the planning problems, creating production delays, long and unreliable due date lead times and straining relationships with customers. As a consequence, more and more companies are interested in finding mechanisms allowing them to produce more efficiently in an environment that is increasingly subject to variability. In this thesis we provide a new perspective on how to implement capacity allocation strategies in order to achieve the desired profits and high due-date adherence. Here we show how to model: (i) capacity sharing with lead time decisions, and (ii) capacity allocation with admission control decisions. In the first part of the thesis, we study a capacity sharing strategy allowing manufacturing operations for heterogeneous products to be pooled. The literature on the design of service systems revealed that, in a stochastic environment, pooling naturally leads to economies of scale, but heterogeneity can create variability. We investigate this trade-off in the case of a manufacturer assigning due dates to customers in order to guarantee a high service level. We develop a simulation and analytical study based on queueing theory in order to gain insights into the impact of pooling on the due date performance. With this work we show that heterogeneity does not necessarily lead to deterioration of performance, as previously reported in studies of service environments. We show that in case of increased product variety and utilization rate, the heterogeneity can be exploited in our advantage. Next, we demonstrate how companies can attain high due date performance by making collaborative decisions to pool their resources within supply chains. In particular, we find that capacity sharing leads to better overall performance than producing separately even for very high heterogeneity. However, the decision regarding the due-date setting and scheduling policy to implement can have a significant impact on the individual performance. Finally, our study reveals that the benefits of pooling in terms of the expected sojourn time obtained by a simple analytical treatment serve as a good prediction of the benefits of pooling on the due date performance in a wide range of situations. In the second part of the thesis, we propose a new capacity allocation scheme with admission control decisions for a company that processes orders from multiple demand streams. Given that the capacity may be insufficient to cater for all demands while meeting their promised due dates, the company has to decide whether to accept or reject incoming orders in order to maximize its profit. We formulate this problem as a multi-dimensional Markov Decision Process to gain insights into the optimal policy. The description and calculation of the optimal policy can be highly complex. Thus we provide a family of approximate formulations to reduce the dimension of the state space via aggregation. We compute bounds on the profit associated with the optimal order acceptance policy to measure the efficiency of the approximate formulations for large instances. We then demonstrate that the structure of the optimal policy is threshold based for almost every state of the system in case of stochastic order sizes. We propose threshold based policies in order to further reduce the complexity of the formulations. Our results show the superiority of the proposed formulations over known methods widely used in the literature. In particular, our policies provide near-optimal solutions quickly and stand out for their robust performance with respect to changes in operational conditions and with respect to differences between the actual and estimated demands.