** Case study background and problem formulations**

Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, PSG MATLAB Subroutines and PSG R.

**PROBLEM: problem_production_planning_FXCHG**

Minimize Linear + Fxchg_pos (minimizing total costs)

subject to

Linearmulti = Const (constraint on production demand)

Box constraints (bounds on positions)

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Fxchg_pos = Fixed Charge Positive

Box constraints = constraints on individual decision variables

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Data and solution in Run-File Environment. The same problem is solved with two different solvers: VAN and CARGRB (which needs GUROBI).

Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 2.66GHz (sec) | |||
---|---|---|---|---|---|---|---|

Dataset1 | Problem Statement | Data | Solution | 8 | 4 | 660 | <0.01 |

Dataset1 | Problem Statement | Data | Solution | 8 | 4 | 660 | <0.01 |

Data and solution in MATLAB Environment

Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|

Dataset1 | Matlab code | Data | Solution | 8 | 4 | 660 | 0.01 |

Data and solution in R Environment

Problem Datasets | # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.50GHz (sec) | |||
---|---|---|---|---|---|---|---|

Dataset1 | R code | Data | 8 | 4 | 660 | 0.01 |

**CASE STUDY SUMMARY**

This case study demonstrates an optimization setup and relevant graphs for a single item capacitated lot size model. For a finite time horizon T, there is demand for a single item in each production period. This demand must be satisfied by the production in that period or by inventory from previous periods, that is, no backlogging is allowed. The production level cannot exceed a certain capacity limit. Two kinds of costs are considered, production cost and holding cost. Production, if initiated in a certain period, requires initial setup cost. We are trying to find a feasible production plan that minimizes total costs.

**References**

• Chen, H-D., Hearn, D. W., Lee, C-Y. (1994): A new dynamic programming algorithm for the single item capacitated dynamic lot size model, *Journal of Global Optimization*, Vol.4, No. 3/April.

• Chen, H-D., Hearn, D. W., Lee, C-Y. (1994): A dynamic programming algorithm for dynamic lot size models with piecewise linear costs, *Journal of Global Optimization*, Vol.4, No. 4/June.

• Chen, H-D., Hearn, D. W., Lee, C-Y. (1995): Minimizing the error bound for the dynamic lot size model, *Operations Research Letters*, 17, 57-68.

• Atamturk, A., Munoz, J. C. (2004): A study of the lot-sizing polytope, Mathematical Programming 99, 443-465.