A Simulation Study of Due-date Assignment Rules in a Dynamic Job Shop

This paper is a report of a simulation study that investigates a dynamic approach to scheduling jobs in a multi-machine job shop. The workload information of a job is used in different forms to evaluate the shop performance based on three measures: mean job lateness, percentage of tardy jobs and lateness variance. Different combinations of due-date assignment methods and sequencing rules are compared based on specific performance criteria. The results indicate that using the cumulative distribution function of workload information can yield a better performance than using a proportional function of workload information or ignoring shop congestion information. A few situations are identified in which workload information is not critical.     

Improving delivery reliability by a new due-date setting rule

We study the dynamic due-date setting problem where the objective is to improve delivery performance. Since the problem is NP-hard, we propose a simple, new, general, heuristic due-date setting procedure called the SL rule. For the classical M/M/1 queuing model, we analytically determine the optimum parameter for the proposed rule to achieve best due-date performance. We then show that the optimized SL rule outperforms the work-content-based TWK rule in terms of fraction tardy, mean tardiness, and mean earliness. Additional numerical and simulation analysis for a range of conditions, covering different shop workload levels and priority regimes, confirms that the proposed rule produces best due-date performance, compared to the work-content-based rule, under most of the conditions studied.     

Evaluating models for classifying customers in retail banking collections

When seeking to establish a repayment strategy with delinquent borrowers, it is useful to determine how they are likely to behave, so that an optimal use of resources can be made. We examine two behavioural classifications (‘settle immediately’ versus ‘not settle immediately’, and ‘make some repayment’ versus ‘make no repayment’) and apply a variety of rules for predicting into which class each customer is likely to belong. Since no such rule will yield perfect predictions, the way in which performance is evaluated is crucial in choosing a good rule, and hence subsequently in obtaining accurate predictions of likely future behaviour. We examine some popular standard performance evaluation criteria, showing that they have major weaknesses. We describe and illustrate the use of an alternative measure that overcomes these weaknesses.     

On a single-machine optimal constant due-date assignment and sequencing problem

This paper considers the problem of optimal constant due-date assignment and sequencing of jobs in a single-machine shop. We formulate the problem as a general constrained optimization problem and apply the Kuhn-Tucker conditions to find the optimal solution which is shown to be independent of the job sequence.     

Batch scheduling and common due-date assignment on a single machine

We consider the problem of scheduling n groups of jobs on a single machine where three types of decisions are combined: scheduling, batching and due-date assignment. Each group includes identical jobs and may be split into batches; jobs within each batch are processed jointly. A sequence independent machine set-up time is needed between each two consecutively scheduled batches of different groups. A due-date common to all jobs has to be assigned. A schedule specifies the size of each batch, i.e. the number of jobs it contains, and a processing order for the batches. The objective is to determine a value for the common due-date and a schedule so as to minimize the sum of the due date assignment penalty and the weighted number of tardy jobs. Several special cases of this problem are shown to be ordinary NP-hard. Some cases are solved in O(n log n) time. Two pseudopolynomial dynamic programming algorithms are presented for the general problem, as well as a fully polynomial approximation scheme.     

Minimizing weighted earliness–tardiness and due-date cost with unit processing-time jobs

The classical single-machine scheduling and due-date assignment problem of Panwalker et al. [Panwalker, S.S., Smith, M.L., Seidmann, A., 1982. Common due date assignment to minimize total penalty for the one machine scheduling problem. Operations Research 30(2) (1982) 391–399] is the following: All n jobs share a common due-date, which is to be determined. Jobs completed prior to or after the due-date are penalized according to a cost function which is linear and job-independent. The objective is to minimize the total earliness–tardiness and due-date cost. We study a generalized version of this problem in which: (i) the earliness and tardiness costs are allowed to be job dependent and asymmetric and (ii) jobs are processed on parallel identical machines. We focus on the case of unit processing-time jobs. The problem is shown to be solved in polynomial (O(n⁴)) time. Then we study the special case with no due-date cost (a classical problem known in the literature as TWET). We introduce an O(n³) solution for this case. Finally, we study the minmax version of the problem, (i.e., the objective is to minimize the largest cost incurred by any of the jobs), which is shown to be solved in polynomial time as well.     

Optimal due-date assignment problem with learning effect and resource-dependent processing times

In this paper, we consider a single-machine earliness-tardiness scheduling problem with due-date assignment, in which the processing time of a job is a function of its position in a sequence and its resource allocation. The due date assignment methods studied include the common due date, and the slack due date, which reflects equal waiting time allowance for the jobs. For each combination of due date assignment method and processing time function, we provide a polynomial-time algorithm to find the optimal job sequence, due date values, and resource allocations that minimize an integrated objective function, which includes earliness, tardiness, due date assignment, and total resource consumption costs.     

A Generalized Model of Optimal Due-Date Assignment by Linear Programming

A linear-programming model to find the optimal ‘CON due-date’ is considered for n independent jobs to be processed on a single machine. The term ‘CON due-date’ stands for constant-allowance due-date, where each job receives exactly the same due-date. The measure of performance considered is a more generalized version of similar problems studied earlier. Duality theory is used to obtain an optimal solution. Some earlier studies are shown to be special cases of the model studied in this paper. Numerical examples are presented for better understanding.     

Estimating Job Flow-Times in a Job Shop for Contractually Negotiated Due-Dates

One of the most important aspects of job shop planning is the contract negotiation process. In this process the job shop vendor must negotiate a job due-date acceptable to both job shop and the customer. Failure to obtain reasonably accurate predictions of the job completion time can result in penalties and/or lost future sales for the job shop. As such, estimation of job flow-times is critical to successful job shop operation. This paper presents a network modelling approach to the difficult and complex task of estimating job flow-times not previously presented in the literature. The approach is demonstrated via a case example where the system model is developed as a Q-GERT network and simulation results are obtained.     

Minimizing the weighted number of tardy jobs with due date assignment and capacity-constrained deliveries for multiple customers in supply chains

In this paper, an integrated due date assignment and production and batch delivery scheduling problem for make-to-order production system and multiple customers is addressed. Consider a supply chain scheduling problem in which n orders (jobs) have to be scheduled on a single machine and delivered to K customers or to other machines for further processing in batches. A common due date is assigned to all the jobs of each customer and the number of jobs in delivery batches is constrained by the batch size. The objective is to minimize the sum of the total weighted number of tardy jobs, the total due date assignment costs and the total batch delivery costs. The problem is NP-hard. We formulate the problem as an Integer Programming (IP) model. Also, in this paper, a Heuristic Algorithm (HA) and a Branch and Bound (B&B) method for solving this problem are presented. Computational tests are used to demonstrate the efficiency of the developed methods.     

Optimal Assignment of Total-work-content Due-dates and Sequencing in a Single-machine Shop

This paper considers the problem of optimal assignment of total-work-content due-dates to n jobs and of sequencing them on a single machine to minimize an objective function depending on the assigned due-date multiple value and maximum tardiness penalty. It is shown that both the earliest due-date and shortest processing time orders yield an optimal sequence. A simple analytical solution method is presented to find the optimal due-dates. After the theoretical treatment an illustrative example is presented for discussion.     

Supply chain scheduling with receiving deadlines and non-linear penalty

We study the operations scheduling problem with delivery deadlines in a three-stage supply chain process consisting of (1) heterogeneous suppliers, (2) capacitated processing centres (PCs), and (3) a network of business customers. The suppliers make and ship semi-finished products to the PCs where products are finalized and packaged before they are shipped to customers. Each business customer has an order quantity to fulfil and a specified delivery date, and the customer network has a required service level so that if the total quantity delivered to the network falls below a given targeted fill rate, a non-linear penalty will apply. Since the PCs are capacitated and both shipping and production operations are non-instantaneous, not all the customer orders may be fulfilled on time. The optimization problem is therefore to select a subset of customers whose orders can be fulfilled on time and a subset of suppliers to ensure the supplies to minimize the total cost, which includes processing cost, shipping cost, cost of unfilled orders (if any), and a non-linear penalty if the target service level is not met. The general version of this problem is difficult because of its combinatorial nature. In this paper, we solve a special case of this problem when the number of PCs equals one, and develop a dynamic programming-based algorithm that identifies the optimal subset of customer orders to be fulfilled under each given utilization level of the PC capacity. We then construct a cost function of a recursive form, and prove that the resulting search algorithm always converges to the optimal solution within pseudo-polynomial time. Two numerical examples are presented to test the computational performance of the proposed algorithm.     

Job sequencing and due date assignment in a single machine shop with uncertain processing times

This paper considers due date assignment and sequencing for multiple jobs in a single machine shop. The processing time of each job is assumed to be uncertain and is characterized by a mean and a variance with no knowledge of the entire distribution. A heuristic procedure is developed to find job sequence and due date assignment to minimize a linear combination of three penalties: penalty on job earliness, penalty on job tardiness, and penalty associated with long due date assignment. Numerical experiments indicate that the performance of the procedure is stable and robust to job processing time distributions. In addition, the performance improves when the means and variances of job processing times are uncorrelated or negatively correlated or when the penalty of a long due date assignment is significant.     

Due-date assignment on uniform machines

The classical weighted minsum scheduling and due-date assignment problem (with earliness, tardiness and due-date costs) was shown to be polynomially solvable on a single machine, more than two decades ago. Later, it was shown to have a polynomial time solution in the case of identical processing time jobs and parallel identical machines. We extend the latter setting to parallel uniform machines. We show that the two-machine case is solved in constant time. Furthermore, the problem remains polynomially solvable for a given (fixed) number of machines.     

New assignment algorithms for the multi-depot vehicle routing problem

This paper considers the design and analysis of algorithms for the multi-depot vehicle routing problem with time windows (MDVRPTW). Given the intrinsic difficulty of this problem class, approximation methods of the type ‘cluster first, route second’ (two-step approaches) seem to offer the most promise for practical size problems. After describing six heuristics for the cluster part (assignment of customers to depots) an initial computational study of their performance is conducted. Finding, as expected, that the heuristics with the best results (in terms of the routing results) are those with the largest computational efforts.     

New measures of proximity for the assignment algorithms in the MDVRPTW

This paper proposes new proximity measures for assignment algorithms for the Multi-Depot Vehicle Routing Problem with Time Windows (MDVRPTW). Given the intrinsic difficulty of this problem class, two-step approximation methods of the type ‘cluster first, route second’ seem to be the most promising for practical size problems. The focus is on the clustering phase, the assignment of customers to depots. Our approach is to extend the existing metrics with time windows. New measures that include time windows and distances are added to two assignment heuristics, that previously only used distance to evaluate proximity between customers and depots. A computational study of their performance is presented, which shows that the inclusion of time windows in the measures of proximity gives better results, in terms of routing, than only using the distance.     

Due dates in a manufacturing shop: An unweighted case

A dispatching rule is proposed for job shop operations where the performance criteria are due date related. The dispatching rule is constructed by combining the characteristics of the shortest process time rule and a dynamically determined earliest due date rule. The performance of the proposed rule is compared to currently well known rules across various shop environments using discrete simulation.This work was partially supported by: The National Science Foundation, Grant No. CDR-8300965; member companies of the Material Handling Research Center, the Georgia Institute of Technology and Texas A&M University.     

Due date assignment for multistage assembly systems

This paper is concerned with the study of the constant due-date assignment policy in a multistage assembly system. The multistage assembly system is modeled as an open queueing network. It is assumed that the product order arrives according to a Poisson process. In each service station, there is either one or infinite machine with exponentially distributed processing time. The transport times between every pair of service stations are independent random variables with generalized Erlang distributions. It is assumed that each product has a penalty cost that is some linear function of its due-date and its actual completion time. The due date is found by adding a constant to the time that the order arrives. This constant value is the constant lead time that a product might expect between time of placing the order and time of delivery. By applying the longest path analysis in queueing networks, we obtain the distribution function of manufacturing lead time. Then, the optimal constant lead time is computed by minimizing the expected aggregate cost per product. Finally, the results are verified by Monte Carlo simulation.     

Heuristic and stochastic methods in optimization

The shifting bottleneck (SB) heuristic is among the most successful approximation methods for solving the job shop problem. It is essentially a machine based decomposition procedure where a series of one machine sequencing problems (OMSPs) are solved. However, such a procedure has been reported to be highly ineffective for the flow shop problems. In particular, we show that for the 2-machine flow shop problem, the SB heuristic will deliver the optimal solution in only a small number of instances. We examine the reason behind the failure of the machine based decomposition method for the flow shop. An optimal machine based decomposition procedure is formulated for the 2-machine flow shop, the time complexity of which is worse than that of the celebrated Johnson’s rule. The contribution of the present study lies in showing that the same machine based decomposition procedures which are so successful in solving complex job shops can also be suitably modified to optimally solve the simpler flow shops.     

Optimization of setup times in the furniture industry

The aim of this paper is to develop a scheduling policy oriented towards minimizing setup times in the made-to-order furniture industry. The task is treated as a dynamic job shop scheduling problem, with the exception that customers?? orders collected over a?specified period of time are combined into a?production plan and released together. A?simulation of a production flow based on technological routes of real subassemblies was performed. The proposed method of calculating a setup time eliminates the need to determine machine setup time matrices. Among the tested priority rules the best performance was observed in the case of the hierarchical rule that combines similar setup, the earliest due date and the shortest processing time. This rule allowed the setup time per operation to be reduced by 58?% compared to a combination of the earliest due date with the shortest setup and processing time rule and by over 70?% compared to the single shortest processing time rule.