We study a problem in which a set of n jobs has to be batched as well as scheduled for processing on a single machine. A constant machine set-up time is required before the first job of each batch is processed. A schedule specifies the sequence of batches, where each batch comprises a sequence of jobs. The batch delivery time is defined as the completion time of the last job in a batch. The ear...

We study a single machine scheduling problem with batch setup time and batch delivery cost. In this problem, n jobs have to be scheduled on a single machine and delivered to a customer. Each job has a due date, a processing time and a weight. To save delivery cost, several jobs can be delivered together as a batch including the late jobs. The completion (delivery) time of each job in the same b...

In e-commerce markets, on time delivery is of great importance to customer satisfaction. this paper, we present a Deep Reinforcement Learning (DRL) approach for deciding how and when orders should be batched picked in warehouse minimize the number tardy orders. particular, technique facilitates making decisions whether an order individually (pick-by-order) or batch with other (pick-by-batch), i...

In traditional scheduling problems, most literature assumes that the processing time of a job is fixed. However, there are many situations where the processing time of a job depends on the starting time or the position of the job in a sequence. In such situations, the actual processing time of a job may be more or less than its normal processing time if it is scheduled later. This phenomenon is...

Article history: Received June 25, 2015 Received in revised format: October 12, 2015 Accepted December 15, 2015 Available online December 17 2015 This paper analyzes a supply chain, which consists of a manufacturer, a retailer and several suppliers in which the retailer orders jobs to the manufacturer and the suppliers provide the requiring parts. The manufacturer schedules and processes the or...

This paper addresses the Tardy/Lost penalty minimization on a single machine. According to this penalty criterion, if the tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. Besides its application in real world problems, Tardy/Lost measure is a general form for popular objective functions like weighted tardiness, late work and tardiness with reje...