Ada Che

Multicyclic hoist scheduling with constant processing times

Proposes an exact algorithm for the multicyclic schedules of hoist moves in a printed circuit board (PCB) electroplating facility, where exactly r(r>1) parts enter and r parts leave the production line during each cycle, and the processing time at each production stage is a given constant. The multicyclic scheduling problem is transformed into enumeration of intervals for linear functions of decision variables. This enumeration is accomplished with a branch and bound procedure. At each node of the search tree, by solving a linear programming problem (LPP), either the corresponding partial solution is proved to be unable to lead to a feasible solution, or a lower bound is computed. Due to its particular structure, this LPP is equivalent to a cycle time evaluation problem in a bivalued graph which can be solved efficiently. The proposed algorithm is polynomial in the number of tanks for a fixed r, but exponential if r is arbitrary. Computational experience with both benchmark and randomly generated test instances is presented.

Cyclic hoist scheduling in large real-life electroplating lines

This paper addresses cyclic scheduling of a single hoist in large real-life electroplating lines, where a part visits some processing tanks more than once and multiple duplicate tanks are used at some production stages having long processing times. We present a formal analysis of the problem and propose an efficient branch-and-bound algorithm. The developed analytical properties allow us to considerably eliminate dominated or infeasible solutions in the branch-and-bound procedure. Computational results on benchmark and real-life instances show that the algorithm is very efficient in scheduling large electroplating lines.

A polynomial algorithm for 2-degree cyclic robot scheduling

Abstract This paper studies the 2-degree cyclic scheduling of identical parts in a no-wait robotic flow shop where exactly two parts enter and leave the production line in a cycle. The objective is to minimize the cycle time. We propose a polynomial algorithm to find an optimal 2-degree cyclic schedule of robot moves. The algorithm can be implemented in O( N 8 log N ) where N is the number of machines in the considered robotic cell. The proposed algorithm is also extended to problems where the two parts are not identical. Computational results is presented to test and evaluate the proposed algorithm.

Single-track multi-hoist scheduling problem: a collision-free resolution based on a branch-and-bound approach

An analytical mathematical model and a branch-and-bound algorithm for single-track cyclic multi-hoist scheduling problems are proposed. The objective is to minimize the cycle time for a given number of hoists. The collision-free single-track constraints are first formulated as disjunctive inequalities. It is then shown that this formulation is a very strict and necessary condition. To be a sufficient and necessary one, two additional properties, like collision-checking rules, must hold in optimal solutions. It is proved that a solution violating these two properties due to their relaxation is always dominated by a collision-free one. Therefore, these two properties are relaxed in the branch-and-bound algorithm. The computation of lower bounds in the branch-and-bound algorithm requires the solution of a specific linear programming problem, which can be solved by using a graph-based polynomial algorithm. Computational results with both benchmark and randomly generated test instances are presented.

The bullwhip effect on product orders and inventory: a perspective of demand forecasting techniques

Demand forecasting is one of the key causes of the bullwhip effect on product orders. Although this aspect of order oscillation is not ignored, the current study focuses on another critical aspect of oscillation: the bullwhip effect on inventory, i.e. the net inventory variance amplification. In particular, this paper studies a two-level supply chain in which the demand is price sensitive, while the price follows a first-order autoregressive pricing process. We derive the analytical expressions of the bullwhip effect on product orders and inventory using minimum mean-squared error, moving average and exponential smoothing forecasting techniques. We also propose the conditions under which the three forecasting techniques would be chosen by the retailer to minimise the sum of the bullwhip effect on product orders and inventory under different weightings. These observations are used to develop managerial insights regarding choosing an appropriate forecasting technique after considering certain distinct characteristics of the product.

A branch and bound algorithm for optimal cyclic scheduling in a robotic cell with processing time windows

A branch and bound algorithm is described for optimal cyclic scheduling in a robotic cell with processing time windows. The objective is to minimise the cycle time by determining the exact processing time on each machine which is limited within a time window. The problem is formulated as a set of prohibited intervals of the cycle time, which is usually applied in the robotic cyclic scheduling problem with fixed processing times. Since both bounds of these prohibited intervals are linear expressions of the processing times, we divide these prohibited intervals into a series of the subsets and transform the problem into enumerating the non-prohibited intervals of cycle time in each subset. This enumeration procedure is completed by an efficient branch and bound algorithm, which could find an optimal solution by enumerating partial non-prohibited intervals. Computational results on the benchmark instances and randomly generated test instances indicate that the algorithm is effective.

Multi-degree cyclic scheduling of a no-wait robotic cell with multiple robots

This paper addresses cyclic scheduling of a no-wait robotic cell with multiple robots. In contrast to many previous studies, we consider r-degree cyclic (r > 1) schedules, in which r identical parts with constant processing times enter and leave the cell in each cycle. We propose an algorithm to find the minimal number of robots for all feasible r-degree cycle times for a given r (r > 1). Consequently, the optimal r-degree cycle time for any given number of robots for this given r can be obtained with the algorithm. To develop the algorithm, we first show that if the entering times of r parts, relative to the start of a cycle, and the cycle time are fixed, minimizing the number of robots for the corresponding r-degree schedule can be transformed into an assignment problem. We then demonstrate that the cost matrix for the assignment problem changes only at some special values of the cycle time and the part entering times, and identify all special values for them. We solve our problem by enumerating all possible cost matrices for the assignment problem, which is subsequently accomplished by enumerating intervals for the cycle time and linear functions of the part entering times due to the identification of the special values. The algorithm developed is shown to be polynomial in the number of machines for a fixed r, but exponential if r is arbitrary.

Optimal cyclic scheduling of a hoist and multi-type parts with fixed processing times

This paper proposes an exact algorithm to solve a cyclic hoist scheduling problem in a printed circuit board (PCB) electroplating facility, where multi-type parts with fixed processing times are processed in the same time and the parts are not allowed to wait in the tanks or on the hoist. Finding an optimal schedule in such a production line is equivalent to finding two types of related sequences: part input sequence and hoist move sequence. We show that the entering times of the parts are the decision variables of the problem. We formulate our problem using the notion of prohibited intervals and solve it by enumerating the non-prohibited intervals of the decision variables. This enumeration is accomplished more efficiently with a dynamic branch and bound procedure, which utilises relaxed solutions to eliminate redundant non-prohibited intervals in the search process. The proposed algorithm is polynomial in the number of tanks if the number of part types is fixed, but exponential if it is arbitrary. Computational results on randomly generated test instances indicate that the algorithm is effective.

A polynomial algorithm for no-wait cyclic hoist scheduling in an extended electroplating line

This paper addresses cyclic hoist scheduling in a no-wait electroplating line where a part visits some processing tanks more than once and multiple duplicate tanks are used at some production stages. We prove that such an extended problem can be solved in polynomial time.

Multi-degree cyclic hoist scheduling with time window constraints

This paper deals with the multi-degree cyclic single-hoist scheduling problem with time window constraints, in which multiple identical parts enter and leave the system during each cycle. We propose an analytical mathematical model and a branch-and-bound algorithm so as to find a cyclic sequence of hoist moves that maximises the throughput. The branch-and-bound algorithm implicitly enumerates the sequence of hoist moves and requires the solution of a specific set of linear programming problems (LPPs). Computational results on benchmark instances and randomly generated test instances are presented.