Steef L. van de Velde

Scheduling a batching machine

textabstractWe study the problem of scheduling a chain-reentrant shop, in which each job goes for its processing first to a machine called the primary machine, then to a number of other machines in a fixed sequence, and finally back to the primary machine for its last operation. The problem is to schedule the jobs so as to minimize the makespan. This problem is unary NP-hard for a general number of machines. We focus in particular on the two-machine case that is also at least binary NP-hard. We prove some properties that identify a specific class of optimal schedules, and then use these properties in designing an approximation algorithm and a branch-and-bound type optimization algorithm. The approximation algorithm, of which we present three versions, has a worst-case performance guarantee of f32 along with an excellent empirical performance. The optimization algorithm solves large instances quickly. Finally, we identify a few well solvable special cases and present a pseudo-polynomial algorithm for the case in which the first and the last operations of any job (on the primary machine) are identical.

An Iterated Dynasearch Algorithm for the Single-Machine Total Weighted Tardiness Scheduling Problem

This paper introduces a new neighborhood search technique, called dynasearch, that uses dynamic programming to search an exponential size neighborhood in polynomial time. While traditional local search algorithms make a single move at each iteration, dynasearch allows a series of moves to be performed. The aim is for the lookahead capabilities of dynasearch to prevent the search from being attracted to poor local optima. We evaluate dynasearch by applying it to the problem of scheduling jobs on a single machine to minimize the total weighted tardiness of the jobs. Dynasearch is more effective than traditional first-improve or best-improve descent in our computational tests. Furthermore, this superiority is much greater for starting solutions close to previous local minima. Computational results also show that an iterated dynasearch algorithm in which descents are performed a few random moves away from previous local minima is superior to other known local search procedures for the total weighted tardiness scheduling problem.

Linking warehouse complexity to warehouse planning and control structure: An exploratory study of the use of warehouse management information systems

Warehousing is becoming more and more a critical activity in the supply chain to outperform competitors on customer service, lead times, and costs. However, if warehousing is to be a source of competitive advantage, then the implementation of a warehouse management information system (WMS) is a necessary condition to achieve efficiently the high performance of warehousing operations required in today’s marketplace. A major practical question is then whether a given warehouse should implement a standard or a tailor‐made WMS. A standard WMS offers many advantages; it is a proven solution, it is less costly, the implementation lead time is shorter, and the after‐sales service is better. On the other hand, a standard WMS remains largely making compromises between the way a warehouse wants to work and the way the system allows the warehouse to work. In certain environments, such compromises might seriously degrade warehouse performance, in which case it then seems better to implement a tailor‐made WMS. To answer the above question, we conducted an exploratory field study of warehouses with recently implemented WMSs to first understand the empirical reality and then build up a theory linking the constructs warehouse complexity and warehouse planning and control structure. Warehouse complexity refers to the number and variety of items to be handled, the degree of their interaction, and the number, nature, i.e. technologies used, and variety of processes, determined among others by the warehouse’s position in the logistic chain and the nature of its market. Warehouse planning and control structure refers to the management functions that plan, direct, coordinate and control the flow of goods through the warehouse, from the time of receiving to the time of shipping. It is strongly related to the WMS in use. We found that the number of orderlines to be processed per day and the number of stock‐keeping units are the two main observable aspects of warehouse complexity; that the more complex the warehouse is, the more tailor‐made the planning and control structure should be; that for simple warehouses a standardized planning and control structure suffices; and that the design of a new‐to‐build warehouse should be carried out in close concert with the design of the warehouse planning and control structure.

Scheduling deteriorating jobs to minimize makespan

We consider a single-machine problem of scheduling n independent jobs to minimize makespan, in which the processing time of job J j grows by W j with each time unit its start is delayed beyond a given common critical date d. This processing time is p if J j starts by d. We show that this problem is NP-hard, give a pseudopolynomial algorithm that runs in O(ndΣ j=1 n p j ) time and O(nd) space, and develop a branch-and-bound algorithm that solves instances with up to 100 jobs in a reasonable amount of time. We also introduce the case of bounded deterioration, where the processing time of a job grows no further if the job starts after a common maximum deterioration date D > d. For this case, we give two pseudopolynomial time algorithms: one runs in O(n 2 d(D - d) Σ j=1 n pj) time and O(nd(D - d)) space, the other runs in O(nd Σ j=1 n w j (Σ j=1 n pj) 2 ) time and O(nd Σ j=1 n w j Σ j=1 n pj) space.

Multi-product lot-sizing with a transportation capacity reservation contract

Abstract Although transportation costs can form more than 50% of the total logistics costs of a product, they are often neglected in lot-sizing research and modelling. Nonetheless, the body of research that does take transportation costs into account is gradually growing. The bulk of this type of research, however, assumes that freight rates decrease as shipping weights and/or volumes increase. Inspired by the situation with a large European manufacturing company, we study a multi-product lot-sizing model where, in any period, any portion of a reserved transportation capacity can be used in exchange for a guaranteed price. If the capacity is insufficient, then the shipper needs to contract additional transportation capacity on the spot market, where the prevailing price is higher. Accordingly, the freight rates are piece-wise linearly increasing in our model. We prove that the problem of determining transportation lot-sizes so as to meet warehouse demand with no backlogging allowed and to minimize total costs, that is, the sum of inventory carrying, ordering, and transportation costs, is NP -hard in the strong sense. Furthermore, we present a Lagrangean relaxation algorithm to compute lower and upper bounds, of which comprehensive computational experiments show the compelling performance in terms of quality and speed.

Combining Column Generation and Lagrangean Relaxation to Solve a Single-Machine Common Due Date Problem

Column generation has proved to be an effective technique for solving the linear programming relaxation ofhuge set covering or set partitioning problems, and column generation approaches have led to state-of-the-art so-called branch-and-price algorithms for various archetypical combinatorial optimization problems. We use a combination of column generation and Lagrangean relaxation to tackle a single-machine common due date problem, where Lagrangean relaxation is exploited for early termination of the column generation algorithm and for speeding up the pricing algorithm. We show that the Lagrangean lower bound dominates the lower bound that can be derived from the column generation algorithm when applied to the standard linear programming formulation, but we also show how the linear programming formulation can be adapted such that the corresponding lower bound is equal to the Lagrangean lower bound.Our comprehensive computational study shows that the combined algorithm is by far superior to two existing purely column generation algorithms: it solves instances with up to 125 jobs to optimality, while a purely column generation algorithm can solve instances with up to only 60 jobs.

Approximation algorithms for the parallel flow shop problem

textabstractWe consider the NP-hard problem of scheduling n jobs in m two-stage parallel flow shops so as to minimize the makespan. This problem decomposes into two subproblems: assigning the jobs to parallel flow shops; and scheduling the jobs assigned to the same flow shop by use of Johnsons rule. For m = 2, we present a 32-approximation algorithm, and for m = 3, we present a 127-approximation algorithm. Both these algorithms run in O(n log n) time. These are the first approximation algorithms with fixed worst-case performance guarantees for the parallel flow shop problem.

Lower bounds for minimizing total completion time in a two-machine flow shop

For the

The lot sizing and scheduling of sand casting operations

\mathcal{NP}