In this paper, we address the problem of admission control and sequencing in a production system that produces two classes of products. The first class of products is made-to-stock, and the firm is contractually obliged to meet demand for this class of products. The second class of products is made-to-order, and the firm has the option to accept (admit) or reject a particular order. The problem is motivated by suppliers in many industries who sign contracts with large manufacturers to supply them with a given product and also can take on additional orders from other sources on a make-to-order basis. We model the joint admission control/sequencing decision in the context of a simple two-class M/M/1 queue to gain insight into the following problems: 1. How should a firm decide (a) when to accept or reject an additional order, and (b) which type of product to produce next? 2. How should a firm decide what annual quantity of orders to commit to when signing a contract to produce the make-to-stock products?

We consider a periodic review inventory system with two priority demand classes, one deterministic and the other stochastic. The deterministic demand must be met immediately in each period. However, the units of stochastic demand that are not satisfied during the period when demand occurs are treated as lost sales. At each decision epoch, one has to decide not only whether an order should be placed and how much to order, but also how much demand to fill from the stochastic source. The firm has the option to ration inventory to the stochastic source (i.e., not satisfy all customer demand even though there is inventory in the system). We first characterize the structure of the optimal policy. We show that, in general, the optimal order quantity and rationing policy are state dependent and do not have a simple structure. We then propose a simple policy, called (s, k, S) policy, where s and S (ordering policy) determine when and how much to order, while k (rationing policy) specifies how much of the stochastic demand to satisfy. We report the results of a numerical study, which shows that this simple policy works extremely well and is very easy to compute.

We consider the optimal control of two parallel servers in a two-stage tandem queuing system with two flexible servers. New jobs arrive at station 1, after which a series of two operations must be performed before they leave the system. Holding costs are incurred at rate h1 per unit time for each job at station 1 and at rate h2 per unit time for each job at station 2.The system is considered under two scenarios; the collaborative case and the noncollaborative case. In the prior, the servers can collaborate to work on the same job, whereas in the latter, each server can work on a unique job although they can work on separate jobs at the same station. We provide simple conditions under which it is optimal to allocate both servers to station 1 or 2 in the collaborative case. In the noncollaborative case, we show that the same condition as in the collaborative case guarantees the existence of an optimal policy that is exhaustive at station 1. However, the condition for exhaustive service at station 2 to be optimal does not carry over. This case is examined via a numerical study.

We consider the problem of quoting customer lead times in a manufacturing environment under a variety of modeling assumptions. First, we examine the case where capacity is infinite. For this case, we derive a closed-form expression for the optimal lead time quote. Second, we consider the case where capacity is finite and the firm processes jobs in first-come-first-served (FCFS) order. We prove the optimality of different forms of control limit policies for the situations where the lead time is dictated by the market and where firms are able to compete on the basis of lead time. Finally, we consider the case where the firm may choose to schedule jobs in other than FCFS order and give conditions under which the optimal due-date-quoting/order-scheduling policy will process jobs in earliest due date (EDD) order.lead times, queueing models, sequencing and scheduling

In this paper, we address the optimal joint control of inventory and transshipment for a firm that produces in two locations and faces capacity uncertainty. Capacity uncertainty (e.g., due to downtime, quality problems, yield, etc.) is a common feature of many production systems but its effects have not been explored in the context of a firm that has multiple production facilities. We first characterize the optimal production and transshipment policies and show that uncertain capacity leads the firm to ration the inventory that is available for transshipment to the other location and characterize the structure of this rationing policy. Then we characterize the optimal production policies at both locations which are defined by state-dependent produceup-to thresholds. We also describe sensitivity of the optimal production and transshipment policies to problem parameters and, in particular, explain how uncertain capacity can lead to counterintuitive behavior, such as produce-up-to limits decreasing for locations that face stochastically higher demand. We finally explore, through a numerical study, when applying the optimal policy is most likely to yield significant benefits compared to simple policies. In particular, we consider two simple straw policies: 1) a policy that disallows transshipment and 2) a policy that disallows rationing and forces the two locations to transship inventory to satisfy the other location's shortage.