Resource allocation in multi-class dynamic PERT networks with finite capacity

In this paper, the resource allocation problem in multi-class dynamic PERT networks with finite capacity of concurrent projects (COnstant Number of Projects In Process (CONPIP)) is studied. The dynamic PERT network is modeled as a queuing network, where new projects from different classes (types) are generated according to independent Poisson processes with different rates over the time horizon. Each activity of a project is performed at a devoted service station with one server located in a node of the network, whereas activity durations for different classes in each service station are independent and exponentially distributed random variables with different service rates. Indeed, the projects from different classes may be different in their precedence networks and also the durations of the activities. For modeling the multi-class dynamic PERT . networks with CONPIP, we first consider every class separately and convert the queueing network of every class into a proper stochastic network. Then, by constructing a proper finite-state continuous-time Markov model, a system of differential equations is created to compute the project completion time distribution for any particular project. The problem is formulated as a multi-objective model with three objectives to optimally control the resources allocated to the service stations. Finally, we develop a simulated annealing (SA) algorithm to solve this multi-objective problem, using the goal attainment formulation.We also compare the SA results against the results of a discrete-time approximation of the original optimal control problem, to show the effectiveness of the proposed solution technique.N/

The dynamic lot-sizing problem with convex economic production costs and setups

In this work the uncapacitated dynamic lot-sizing problem is considered. Demands are deterministic and production costs consist of convex costs that arise from economic production functions plus set-up costs. We formulate the problem as a mixed integer, non-linear programming problem and obtain structural results which are used to construct a forward dynamic-programming algorithm that obtains the optimal solution in polynomial time. For positive setup costs, the generic approaches are found to be prohibitively time-consuming; therefore we focus on approximate solution methods. The forward DP algorithm is modified via the conjunctive use of three rules for solution generation. Additionally, we propose six heuristics. Two of these are single-stepSilver–Meal and EOQ heuristics for the classical lot-sizing problem. The third is a variant of the Wagner–Whitin algorithm. The remaining three heuristics are two-step hybrids that improve on the initial solutions of the first three by exploiting the structural properties of optimal production subplans. The proposed algorithms are evaluated by an extensive numerical study. The two-step Wagner–Whitin algorithm turns out to be the best heuristic

Heuristics for dynamic and stochastic routing in industrial shipping

Maritime transportation plays a central role in international trade, being responsible for the majority of long-distance shipments in terms of volume. One of the key aspects in the planning of maritime transportation systems is the routing of ships. While static and deterministic vehicle routing problems have been extensively studied in the last decades and can now be solved effectively with metaheuristics, many industrial applications are both dynamic and stochastic. In this spirit, this paper addresses a dynamic and stochastic maritime transportation problem arising in industrial shipping. Three heuristics adapted to this problem are considered and their performance in minimizing transportation costs is assessed. Extensive computational experiments show that the use of stochastic information within the proposed solution methods yields average cost savings of 2.5% on a set of realistic test instances

Developing lean and responsive supply chains : a robust model for alternative risk mitigation strategies in supply chain designs

This paper investigates how organization should design their supply chains (SCs) and use risk mitigation strategies to meet different performance objectives. To do this, we develop two mixed integer nonlinear (MINL) lean and responsive models for a four-tier SC to understand these four strategies: i) holding back-up emergency stocks at the DCs, ii) holding back-up emergency stock for transshipment to all DCs at a strategic DC (for risk pooling in the SC), iii) reserving excess capacity in the facilities, and iv) using other facilities in the SC’s network to back-up the primary facilities. A new method for designing the network is developed which works based on the definition of path to cover all possible disturbances. To solve the two proposed MINL models, a linear regression approximation is suggested to linearize the models; this technique works based on a piecewise linear transformation. The efficiency of the solution technique is tested for two prevalent distribution functions. We then explore how these models operate using empirical data from an automotive SC. This enables us to develop a more comprehensive risk mitigation framework than previous studies and show how it can be used to determine the optimal SC design and risk mitigation strategies given the uncertainties faced by practitioners and the performance objectives they wish to meet

Supply network capacity planning for semiconductor manufacturing with uncertain demand and correlation in demand considerations

A semiconductor supply network involves many expensive steps, which have to be executed to serve global markets. The complexity of global capacity planning combined with the large capital expenditures to increase factory capacity makes it important to incorporate optimization methodologies for cost reduction and long-term planning. The typical view of a semiconductor supply network consists of layers for wafer fab, sort, assembly, test and demand centers. We present a two-stage stochastic integer-programming formulation to model a semiconductor supply network. The model makes strategic capacity decisions, (i.e., build factories or outsource) while accounting for the uncertainties in demand for multiple products. We use the model not only to analyze how variability in demand affects the make/buy decisions but also to investigate how the correlation between demands of different products affects these strategic decisions. Finally, we demonstrate the value of incorporating demand uncertainty into a decision-making scheme

A bi˗objective hub location-allocation model considering congestion

In this paper, a new hub location-allocation model is developed considering congestion and production scheduling. This model assumes that manufacturing and distributing goods, including raw materials and semi-finished or finished goods, take place in hubs only (such as industrial township). The main objective of this study is to minimize the total costs and to minimize the sum of waiting times for processing goods in factories and warehouses. In order to solve the bi-objective model, goal attainment and LP metric techniques are combined to develop a more effective multi-objective technique. Due to the exponential complexity of the proposed approach as well as the nonlinearity of the mathematical model, a number of small and medium-sized problems are solved to demonstrate the effectiveness of the solution methodology

Dynamic lot sizing problem with continuous-time Markovian production cost

This paper develops a polynomial algorithm for obtaining dynamic economic lot sizes in a single product multiperiod production system with the objective of minimizing total production and inventory costs over T periods. It is assumed that production costs are linear, inventory costs are concave, setup costs are zero and backlogging is not permitted in all periods. Moreover, the unit production cost is a stochastic variable, which is evolved according to a continuous-time Markov process over the planning horizon. The model is formulated as a stochastic dynamic programming (DP) optimization with the state variable being unit production cost. Then, it is solved using the backward dynamic programming approach. To justify the application of the proposed model, two practical cases are presented.</p