Tools › Operations Research › Optimization

Optimization

2 tools in the Operations Research area.

Linear Programming

Solves a small linear or integer program typed in plain algebra (an objective line, then one constraint per line) and reports what goes into the memo: the optimal solution and objective, the slack or surplus of every constraint and which ones bind, the shadow price of each right-hand side, the reduced cost of each variable, and the ranges of the objective coefficients and right-hand sides over which the present basis stays optimal. The simplex tableaus can be printed step by step for small problems, the dual problem is written out, two-variable problems are drawn, and integer or binary variables are handled by branch and bound on the LP relaxation.

4 worked examples reproduced, listed on the tool page.

Transportation and Assignment

Solves the transportation, transshipment and assignment problems of operations research the way the textbooks work them, step by step: the table is balanced with a dummy source or destination, the initial basic feasible solution is found by the northwest-corner rule, the least-cost method and Vogel's approximation method with each method's steps and cost, and the optimum is reached by the transportation simplex (MODI, the u–v method) with the u and v values, the reduced costs, the entering cell and the stepping-stone loop of every iteration, degeneracy handled with a zero allocation. The optimal shipping plan comes with its total cost, the shadow prices, a flag for alternative optima and the range of every cost coefficient over which the plan stays optimal. A transshipment network (sources, intermediate nodes, sinks and an arc list) is converted to the transportation form with a buffer, and an assignment matrix is solved by the Hungarian algorithm with the row and column reductions, the minimum line cover and the adjustment of every iteration. The default cases are the P&T Company example of Hillier and Lieberman (optimal cost 152,535) and the Machineco assignment of Winston (total 15).

4 worked examples reproduced, listed on the tool page.

Other Operations Research sections

Queueing and Simulation · Scheduling · Inventory and Supply Chain · Decision Analysis · Networks and Routing