Dimitrios G. Pandelis

OPTIMALITY OF INDEX POLICIES FOR STOCHASTIC SCHEDULING WITH SWITCHING PENALTIES

We investigate the impact of switching penalties on the nature of optimal scheduling policies for systems of parallel queues without arrivals. We study two types of switching penalties incurred when switching between queues: lump sum costs and time delays. Under the assumption that the service periods of jobs in a given queue possess the same distribution, we derive an index rule that defines an optimal policy. For switching penalties that depend on the particular nodes involved in a switch, we show that although an index rule is not optimal in general, there is an exhaustive service policy that is optimal.

Single vehicle routing problems with a predefined customer sequence, compartmentalized load and stochastic demands

We consider the problem of finding the optimal routing of a single vehicle that delivers K different products to N customers according to a particular customer order. The demands of the customers for each product are assumed to be random variables with known distributions. Each product type is stored in its dedicated compartment in the vehicle. Using a suitable dynamic programming algorithm we find the policy that satisfies the demands of the customers with the minimum total expected cost. We also prove that this policy has a specific threshold-type structure. Furthermore, we investigate a corresponding infinite-time horizon problem in which the service of the customers does not stop when the last customer has been serviced but it continues indefinitely with the same customer order. It is assumed that the demands of the customers at different tours have the same distributions. It is shown that the discounted-cost optimal policy and the average-cost optimal policy have the same threshold-type structure as the optimal policy in the original problem. The theoretical results are illustrated by numerical examples.

Fixed task zone chaining: worker coordination and zone design for inexpensive cross-training in serial CONWIP lines

This work introduces a new canonical model of worker cross-training, called a Fixed Task Zone Chain (FTZC), as a special type of zone-based cross-training and develops a methodology to employ it in U-shaped CONstant Work In Process (CONWIP) lines. The FTZC approach is intended to address lines with more stations than workers in environments where extensive cross-training is prohibitive. It incorporates a two-skill chain to cross-train one skill at each end of each zone; however, tasks at the interior of a zone are not cross-trained. A heuristic dynamic control policy is developed that maximizes the line’s throughput given a zone structure. Some useful properties of the optimal policy are provided as a basis for a heuristic control policy that yields high throughput. The performance of an FTZC system is contingent upon the choice of zone structure; therefore, the zone assignment (ZonA) algorithm is created to design the zone structure to achieve high throughput levels. Sufficient conditions which guarantee that the line is balanceable through ZonA are derived. Benchmarking over a test suite supports the effectiveness of the proposed heuristic worker control policy as well as the ZonA algorithm, and its performance is compared with other paradigms.

Finite and infinite-horizon single vehicle routing problems with a predefined customer sequence and pickup and delivery

We consider the problem of finding the optimal routing of a single vehicle that starts its route from a depot and picks up from and delivers K different products to N customers that are served according to a predefined customer sequence. The vehicle is allowed during its route to return to the depot to unload returned products and restock with new products. The items of all products are of the same size. For each customer the demands for the products that are delivered by the vehicle and the quantity of the products that is returned to the vehicle are discrete random variables with known joint distribution. Under a suitable cost structure, it is shown that the optimal policy that serves all customers has a specific threshold-type structure. We also study a corresponding infinite-time horizon problem in which the service of the customers is not completed when the last customer has been serviced but it continues indefinitely with the same customer order. For each customer, the joint distribution of the quantities that are delivered and the quantity that is picked up is the same at each cycle. The discounted-cost optimal policy and the average-cost optimal policy have the same structure as the optimal policy in the finite-horizon problem. Numerical results are given that illustrate the structural results.

Optimal use of excess capacity in two interconnected queues

We consider a two-stage tandem queueing network where jobs from station 1 join station 2 with a certain probability. Each job incurs a linear holding cost, different for each station. Each station is attended by a dedicated server, and there is an additional server that is either constrained to serve in station 1 or can serve in both stations. Assuming no switching or other operating costs for the additional server, we seek an allocation strategy that minimizes expected holding costs. For a clearing system we show that the optimal policy is characterized by a switching curve for which we provide a lower bound on its slope. We also specify a subset of the state space where the optimal policy can be explicitly determined.

The stochastic economic lot sizing problem for non-stop multi-grade production with sequence-restricted setup changeovers

We study a variant of the stochastic economic lot scheduling problem (SELSP) encountered in process industries, in which a single production facility must produce several different grades of a family of products to meet random stationary demand for each grade from a common finished-goods (FG) inventory buffer that has limited storage capacity. When the facility is set up to produce a particular grade, the only allowable changeovers are from that grade to the next lower or higher grade. Raw material is always available, and the production facility produces continuously at a constant rate even during changeover transitions. All changeover times are constant and equal to each other, and demand that cannot be satisfied directly from inventory is lost. There is a changeover cost per changeover occasion, a spill-over cost per unit of product in excess whenever there is not enough space in the FG buffer to store the produced grade, and a lost-sales cost per unit short whenever there is not enough FG inventory to satisfy the demand. We model the SELSP as a discrete-time Markov decision process (MDP), where in each time period the decision is whether to initiate a changeover to a neighboring grade or keep the set up of the production facility unchanged, based on the current state of the system, which is defined by the current set up of the facility and the FG inventory levels of all the grades. The goal is to minimize the (long-run) expected average cost per period. For problems with more than three grades, we develop a heuristic solution procedure which is based on decomposing the original multi-grade problem into several 3-grade MDP sub-problems, numerically solving each sub-problem using value iteration, and constructing the final policy for the original problem by combining parts of the optimal policies of the sub-problems. We present numerical results for problem examples with 2–5 grades. For the 2- and 3-grade examples, we numerically solve the exact MDP problem using value iteration to obtain insights into the structure of the optimal changeover policy. For the 4- and 5-grade examples, we compare the performance of the decomposition-based heuristic (DBH) solution procedure against that obtained by numerically solving the exact problem. We also compare the performance of the DBH method against the performance of three simpler parameterized heuristics. Finally, we compare the performance of the DBH and the exact solution procedures for the case where the FG inventory storage consists of a number of separate general-purpose silos capable of storing any grade as long as it is not mixed with any other grade.

Optimal control of flexible servers in two tandem queues with operating costs

We consider two-stage tandem queuing systems with dedicated servers in each station and flexible servers that can serve in both stations. We assume exponential service times, linear holding costs, and operating costs incurred by the servers at rates proportional to their speeds. Under conditions that ensure the optimality of nonidling policies, we show that the optimal allocation of flexible servers is determined by a transition-monotone policy. Moreover, we present conditions under which the optimal policy can be explicitly determined.

Optimal stochastic scheduling of two interconnected queues with varying service rates

We consider two-stage tandem queueing systems attended by two specialized and one flexible server, where all servers have time varying rates. Assuming exponential processing times and linear holding costs, we derive properties of server allocation policies that minimize expected costs over an infinite time horizon.

Markov decision processes with multidimensional action spaces

We study controlled Markov processes where multiple decisions need to be made for each state. We present conditions on the cost structure and the state transition mechanism of the process under which optimal decisions are restricted to a subset of the decision space. As a result, the numerical computation of the optimal policy may be significantly expedited.

REAL-TIME PRODUCTION SCHEDULING IN A MULTI-GRADE PET RESIN PLANT UNDER DEMAND UNCERTAINTY

Abstract We deal with the real-time production scheduling of a continuous-process multi-grade PET resin plant. The process is surcharged by sequence-dependent changeovers, sequential processing with production and space capacity, and mixed and flexible finite intermediate storage. The management called us to develop a time responsive production scheduling tool that copes with demand uncertainty, urgent orders and increased lead times. We adopt simulation as a methodology approach and create a tool based on tangible control rules and simple production engineering methods that make dynamic analysis tractable. Our goal is to maximize the aggregate fill rate, taking into consideration the number of required equipment transitions which cause undesirable variations in base resin properties. The model is tested under a real-world six-month demand instance and ten other hypothetical scenarios. The results are compared with those of the optimal solution derived from a preexisting Mixed Integer Linear Programming model that considers short-term demand as known.