Janny Leung

The impact of forecasting model selection on the value of information sharing in a supply chain

Abstract This paper presents a study on the impact of forecasting model selection on the value of information sharing in a supply chain with one capacitated supplier and multiple retailers. Using a computer simulation model, this study examines demand forecasting and inventory replenishment decisions by the retailers, and production decisions by the supplier under different demand patterns and capacity tightness. Analyses of the simulation output indicate that the selection of the forecasting model significantly influences the performance of the supply chain and the value of information sharing. Furthermore, demand patterns faced by retailers and capacity tightness faced by the supplier also significantly influence the value of information sharing. The result also shows that substantial cost savings can be realized through information sharing and thus help to motivate trading partners to share information in the supply chain. The findings can also help supply chain managers select suitable forecasting models to improve supply chain performance.

Inventory lot-sizing with supplier selection

This paper presents a multi-period inventory lot-sizing scenario, where there are multiple products and multiple suppliers. We consider a situation where the demand of multiple discrete products is known over a planning horizon. Each of these products can be sourced from a set of approved suppliers, a supplier-dependent transaction cost applying for each period in which an order is placed on a supplier. A product-dependent holding cost per period applies for each product in the inventory that is carried across a period in the planning horizon. The decision maker needs to decide what products to order in what quantities with which suppliers in which periods. An enumerative search algorithm and a heuristic are presented to address the problem.

Devising a Cost Effective Schedule for a Baseball League

In this paper, we discuss the problem of devising a cost effective schedule for a baseball league. Sports scheduling is a notoriously difficult problem. A schedule must satisfy constraints on timing such as the number of games to be played between every pair of teams, the bounds on the number of consecutive home (or away) games for each team, that every pair of teams must have played each other in the first half of the season, and so on. Often, there are additional factors to be considered for a particular league, for example, the availability of venues on specific dates, home-game preferences of teams on specific dates, and balancing of schedules so that games between two teams are evenly-spaced throughout the season. In addition to finding a feasible schedule that meets all the timing restrictions, the problem addressed in this paper has the additional complexity of having the objective of minimizing travel costs. We discuss some structural properties of a schedule that meets the timing constraints and present two heuristics for finding a low-cost schedule. The methodology is used to develop an improved schedule for the Texas Baseball League.

Optimal Cyclic Multi-Hoist Scheduling: A Mixed Integer Programming Approach

In the manufacture of circuit boards, panels are immersed sequentially in a series of tanks, with upper and lower bounds on the processing time within each tank. The panels are mounted on carriers that are lowered into and raised from the tanks, and transported from tank to tank by programmable hoists. The sequence of hoist moves does not have to follow the sequence of processing stages for the circuit boards. By optimising the sequence of hoist moves, we can maximise the production throughput.We consider simple cyclic schedules, where the hoist move sequence repeats every cycle and one panel is completed per cycle. Phillips and Unger (1976) developed the first mixed integer programming model for finding the hoist move schedule to minimise the cycle time for lines with only one hoist. We discuss how their formulation can be tightened, and introduce new valid inequalities. We present the first mixed integer programming formulation for finding the minimum-time cycle for lines with multiple hoists and present valid inequalities for this problem. Some preliminary computational results are also presented.

Routing in Point-to-Point Delivery Systems: Formulations and Solution Heuristics

We develop an optimization-based approach for a point-to-point route planning problem that arises in many large scale delivery systems (for example, less-than-truckload freight, rail, mail and package delivery, communications). In these settings, a firm which must ship goods between many origin and destination pairs on a network needs to specify a route for each origin–destination pair so as to minimize transportation costs and/or transit times. Typically, the cost structure is very complicated. The approach discussed in this paper exploits the structure of the problem to decompose it into two smaller subproblems, each amenable to solution by a combination of optimization and heuristic techniques. One subproblem is an “assignment” problem with capacity constraints. The other subproblem is a mixed-integer multicommodity flow problem. We propose solution methods based on Lagrangian relaxation for each subproblem. Computational results with these methods and with a heuristic procedure for the multicommodity flow problem on a problem met in practice are encouraging and suggest that mathematical programming methods can be successfully applied to large-scale problems in delivery systems planning and other problems in logistical system design.

Optimal cyclic scheduling for printed circuit board production lines with multiple hoists and general processing sequence

We introduce a mixed-integer programming formulation for finding optimal cyclic schedules for printed circuit board lines with multiple hoists on a shared track, where the processing sequence may be different than the location sequence of the tanks. Computational results on some benchmark problems indicate that optimal cyclic schedules for problems of realistic size can be found in a reasonable time.

Min-up/min-down polytopes

In power generation and other production settings, technological constraints force restrictions on the number of time periods that a machine must stay up once activated, and stay down once deactivated. We characterize the polyhedral structure of a model representing these restrictions. We also describe a cutting-plane method for solving integer programs involving such min-up and min-down times for machines. Finally, we demonstrate how the polytope of our study generalizes the well-known cross polytope (i.e., generalized octahedron).

An efficient algorithm for multi-hoist cyclic scheduling with fixed processing times

We consider no-wait production processes, where identical products are processed sequentially on n machines and transported by programmable hoists. We present an O(n^5) algorithm that determines the minimum number of hoists required for all possible cycle-times; given the number of hoists, it also finds the minimum-time cyclic hoist-schedule.

Solving a manpower scheduling problem for airline catering using metaheuristics

We study a manpower scheduling problem with job time windows and job-skills compatibility constraints. This problem is motivated by airline catering operations, whereby airline meals and other supplies are delivered to aircrafts on the tarmac just before the flights take-off. Jobs (flights) must be serviced within a given time-window by a team consisting of a driver and loader. Each driver/loader has the skills to service some, but not all, of the airline/aircraft/configuration of the jobs. Given the jobs to be serviced and the roster of workers for each shift, the problem is to form teams and assign teams and start-times for the jobs, so as to service as many flights as possible. Only teams with the appropriate skills can be assigned to a flight. Workload balance among the teams is also a consideration. We present model formulations and investigate a tabu search heuristic and a simulated annealing heuristic approach to solve the problem. Computational experiments show that the tabu search approach outperforms the simulated annealing approach, and is capable of finding good solutions.

A Polytope for a Product of Real Linear Functions in 0/1 Variables

In the context of integer programming, we develop a polyhedral method for linearizing a product of a pair of real linear functions in 0/1 variables. As an example, by writing a pair of integer variables in binary expansion, we have a technique for linearizing their product. We give a complete linear description for the resulting polytope, and we provide an efficient algorithm for the separation problem. Along the way to establishing the complete description, we also give a complete description for an extended-variable formulation, and we point out a generalization.