The subject of this paper is a flow-shop based on a case study aimed at the optimisation of ordering production jobs in mechanical engineering, in order to minimize the overall processing time, the makespan. The production jobs are processed by machines, and each job is assigned to a certain machine for technological reasons. Before processing a job, the machine has to be adjusted; there is only one adjuster who adjusts all of the machines. This problem is treated as a hybrid two-stage flow-shop: the first stage of the job processing is represented by the machine adjustment for the respective job, and the second stage by the processing of the job itself on the adjusted machine. In other words, the job-processing consists of two tasks, where the first task is the machine adjustment for the job, and the second task is the job processing itself. A mathematical model is proposed, a heuristic method is formulated, and the NP hardness of the problem, called a "hybrid flow-shop with adjustment," is proved.
We deal with a logistic problem motivated by a case study from a company dealing with inland transportation of piece goods in regular cycles. The problem consists in transportation of goods among regional centres -- hubs of a network. Demands on transportation are contained in a matrix of flows of goods between pairs of hubs. The transport is performed by vehicles covering the shipping demands and the task is to design a cyclical route and to place a depot for each vehicle. The route depot can be placed in any hub of the route. Goods can be transferred from one route and vehicle to another route and vehicle. The aim is to minimize the total transportation cost. The task is classified as a new case of the pickup and delivery problem with split demand and transfers (SDPDPT). We propose a mathematical model and prove NP-hardness of the problem. We study demand reducibility. We also deal with skip pickup and delivery problem as a special case and show its complexity.