Product selection, machine time allocation, and scheduling decisions for manufacturing perishable products subject to a deadline

We are concerned about the following problem: a manufacturer owns a certain amount of perishable raw material which can be produced into different types of products. He must, however, finish the manufacturing process before a deadline (which represents, e.g., a fixed flight schedule). Due to the deadline constraint and the raw material limit, it is imperative for the manufacturer to determine three decisions: (i) the product types to be produced; (ii) the machine time to be allocated for each product type; and (iii) the sequence to process the products selected. We develop, in this paper, a model to formulate this problem. We show that (i) and (iii) can be determined by analytical rules, and (ii) can be computed by an efficient algorithm. The optimal policy with the three decisions for the problem is therefore completely constructed. We also show the relationships of our model to stochastic scheduling and stochastic knapsack, and discuss the contributions of our work to the two areas.

[1]  E. Steinberg,et al.  A Preference Order Dynamic Program for a Knapsack Problem with Stochastic Rewards , 1979 .

[2]  Christos Douligeris,et al.  Single Machine Scheduling and Selection to Minimize Total Flow Time with Minimum Number Tardy , 1993 .

[3]  Chris N. Potts,et al.  Scheduling with batching: A review , 2000, Eur. J. Oper. Res..

[4]  L L Lu,et al.  Optimal project selection: Stochastic knapsack with finite time horizon , 1999, J. Oper. Res. Soc..

[5]  John A. Buzacott,et al.  Stochastic models of manufacturing systems , 1993 .

[6]  Prabuddha De,et al.  Job selection and sequencing on a single machine in a random environment , 1993 .

[7]  Jatinder N. D. Gupta,et al.  Minimizing tardy jobs in a flowshop with common due date , 2000, Eur. J. Oper. Res..

[8]  Joseph Y.-T. Leung,et al.  Handbook of Scheduling: Algorithms, Models, and Performance Analysis , 2004 .

[9]  Xian Zhou,et al.  Stochastic Scheduling with Earliness and Tardiness Penalties , 2004, Handbook of Scheduling.

[10]  E. M. L. Beale,et al.  Nonlinear Programming: A Unified Approach. , 1970 .

[11]  Chris N. Potts,et al.  Integrating Scheduling with Batching and Lot-Sizing: A Review of Algorithms and Complexity , 1992 .

[12]  Anton J. Kleywegt,et al.  The Dynamic and Stochastic Knapsack Problem with Random Sized Items , 2001, Oper. Res..

[13]  Jerzy Kyparisis,et al.  Note-Project Selection and Sequencing to Maximize Net Present Value of the Total Return , 1992 .

[14]  Kenneth R. Baker,et al.  Scheduling Groups of Jobs on a Single Machine , 1995, Oper. Res..

[15]  Izak Duenyas,et al.  Optimal Admission Control and Sequencing in a Make-to-Stock/Make-to-Order Production System , 2000, Oper. Res..

[16]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[17]  Helman I. Stern,et al.  The selection and scheduling of textile orders with due dates , 1990 .

[18]  Bala Shetty,et al.  The nonlinear knapsack problem - algorithms and applications , 2002, Eur. J. Oper. Res..