Bajis Dodin

Bounding the Project Completion Time Distribution in PERT Networks

We consider the PERT model of a project composed of activities whose durations are random variables with known distributions. For the situations in which the activity durations are completely independent, we present a new method for obtaining a probability distribution function that bounds the exact probability distribution of the project completion time from below. The bounding distribution can be used to obtain an upper bound on the mean completion time of the project. We also prove and illustrate that this bounding distribution is better tighter than any of the existing lower bounds, implying that the corresponding upper bound on the mean completion time is tighter than any of the existing upper bounds.

A random activity network generator

Exact and heuristic procedures are often developed to obtain optimal and near-optimal solutions to decision problems modeled as activity networks. Testing the accuracy and efficiency of these procedures requires the use of activity networks with various sizes, structures, and parameters. The size of the network is determined by its number of nodes and arcs, where the structure is chosen from the set of all structures for the specified network size. The network parameters depend on the nature of the decision problem. Often, it is desirable for test problems to be generated at random from the space of all feasible networks. This paper deals with the problem of generating the size and structure of the network at random from the space of all feasible networks. It develops a theory which guarantees the randomness of the network structure. The theory is the basis for two methods. One can be used to generate dense networks, where the other is used to generate nondense networks. The methods, which are practical a...

Approximating the distribution functions in stochastic networks

Abstract In this paper an analytical procedure to approximate the distribution functions in stochastic networks is presented. The procedure is efficient in the sense of its accuracy and its computational requirements. Contrary to the existing approximating procedures, it can be applied to large networks. Examples and computational experiences involving large networks are provided.

Tabu Search in Audit Scheduling

In this paper, we present a heuristic procedure based on tabu search (TS) and intelligent memory structures for solving this problem. The TS method starts with a feasible schedule generated by a greedy forward dispatching procedure, then through a series of intensification and diversification steps it improves on the initial schedule. The improvement in the value of the objective function is observed interactively. The search can be terminated as the improvement in the value of the objective function stabilizes. Application of the TS method to different audit scheduling problems has consistently improved the value of the cost minimization objective function.

Integrated Project Scheduling and Material Planning with Variable Activity Duration and Rewards

Integrating project scheduling and material ordering adds more realism to project scheduling and considers additional trade-offs that could lead to reductions in the overall project costs. In this paper we review the evolution of the integrated problem, and investigate the impact of treating the activity duration as a decision variable on the activities schedule and materials plan. The effects of introducing rewards (penalties) for early (late) completion as well as materials quantity discounts on the project schedule and cost are also considered. These additions provide scheduling flexibility that might lead to further reduction in the projects total cost or makespan. Considering the various project costs, we found that there exists an optimal schedule that either start as early as possible (at time zero) or completes as late as possible. We also show that if the project starts at time zero, then its duration cannot be longer than that for the case where the schedule ends as late as possible. It is also shown that the material ordering policy does not follow the Wagner and Whitin model when activity duration is variable or in the presence of quantity discounts. These results have led to modeling and solving the problem in a more efficient manner. Extensive computational work shows the validity of the model and the solution approach.

Audit Scheduling with Overlapping Activities and Sequence Dependent Setup Costs

Abstract Audit firms are faced with the complex job of scheduling auditors to audit tasks. The scheduling becomes more complex as the firm needs to consider real life issues in determining an optimal schedule. Among these issues are the setup times and costs emanating from changing the assignments of the auditors and the lead and lag relationships between the audit tasks. Audit scheduling with overlapping activities and sequence-dependent setup cost has not been treated in literature. This paper presents a formulation and a solution approach for this audit scheduling problem. First, the problem is represented by an activity network with lead/lag relationships. Then the network is analyzed to determine the early and late finish times of activities. An integer linear program (ILP), which uses the early and late finish times of activities to reduce the number of decision variables, is formulated. A four-auditor two-engagement example is used to illustrate the ILP model and its solution. The results indicate that incorporating the setup cost and the overlapping of activities yields lower cost schedules leading to sizable savings in the cost of audits. The proposed treatment is of merit in providing realistic schedules that can be easily implemented

Stochastic networks and the extreme value distribution

Abstract This paper extends the extreme value theory to the problem of approximating the probability distribution of the duration of the longest path in stochastic networks and its parameters. It is demonstrated that the distribution function of the longest path can be more adequately represented by an extreme value distribution rather than by the normal distribution in most cases of interest. In particular, extreme value theory is used to derive estimates for the mean and the variance of the distribution. These estimates are compared with the simulated mean and variance as well as with estimates obtained by other estimating procedures. The new estimates are shown to be closer to the simulated mean and variance. Conditions that help determine which theory, normal or extreme value, is more applicable for a certain network are also provided.

Application of production scheduling methods to external and internal audit scheduling

Abstract This paper deals with the problem of labor staffing in a service organization. The specific problem is the scheduling of auditors to audit tasks in a complex real life audit environment. We extend the methods of production scheduling to solve such a complex problem and apply these methods to a real life audit scheduling case. Each audit engagement is broken into a set of interrelated tasks and modeled as an activity network. The networks of the individual engagements are combined into a larger activity network. Even though the analysis of the large network answers certain managerial questions it does not answer the specific scheduling questions: when will each audit task start? who is the auditor? when it is completed? and how might the schedule change if the scheduling objective changes? To answer these questions the problem is formulated as an integer linear program in which the large network analysis is used to enhance its efficiency. The integer program accommodates different audit objectives and many real life situations. It is solved using existing computer codes. The model is then applied to a real life audit scheduling case to generate optimal audit schedules to all auditors and audit tasks. Naturally, the model allows for conducting parametric analysis and the generation of revised optimal schedules as the audit environment changes.

Incentives and yield management in improving productivity of manufacturing facilities

Abstract Financial incentives are used to improve productivity and quality in manufacturing and service facilities. This improvement in productivity would normally release part of the facilitys productive capacity. Without stimulating additional demand to consume this released capacity, the facility would Be unable to tap the full benefits of the improvements in productivity. Hence, yield management is introduced in an attempt to entice more demand and increase revenues. In this paper, we develop a Non Linear Programming (NLP) model to jointly determine the optimum financial incentives and price discount levels for each rate class. The model aims at maximizing net revenues. It includes nonlinear relationships representing the impact of incentives on productivity and quality improvements as well as the effect of price discounts on customer demand in each market segment. The generic nature of our NLP model makes it applicable to all multi-product manufacturing facilities covering sales, production and delivery. The model is applied to determine the optimum incentive and price discount levels for perishable products in a multi-product ready-mix concrete plant. It is demonstrated that the model is useful in maximizing net revenues through productivity improvements and an increase in customer demand.

Determining the optimal sequences and the distributional properties of their completion times in stochastic flow shops

Abstract This paper deals with a stochastic flow shop problem consisting of M machines and N jobs. The processing time of job j on machine i is an independent random variable with a given probability distribution function. It is assumed that preemption is not allowed and the existence of unlimited intermediate storage between the machines. The objective here, as it is in most flow shop investigations, is to determine a permutation (sequence) of the N jobs with the minimum makespan, which is the completion time of the last job on the last machine. Calculating the minimum makespan in the stochastic flow shop, if compared with the deterministic case, is harder, on the one hand; and on the other, the problem involves issues not existent in the deterministic case. It is shown in this paper that the minimum makespan (MM) in the stochastic case is a random variable (r.v.) not always connected to a particular sequence. Different realizations of the r.v. may correspond to different sequences. Consequently, a new concept for the optimal sequence is introduced. The distributional properties of the MM and their relations to those of the makespan of any sequence are analyzed. A lower bound on the expected value of the makespan of any sequence is derived. A practical heuristic procedure for determining or approximating the optimal sequence is developed. It is practtical in the sense that it is less restrictive than what has been developed so far and easier to implement. Computational experience is also provided.