A small engineering company makes two products for export, A and B. Both products go through a four-stage process: turning, grinding, polishing, finishing.

The two products are produced in batches of 100 items and the time taken, in hours, for each batch to go through each stage is shown in Table 11.5.

Profit contribution per batch of product A is £4 and for product B is £5.

year period, stock levels had been reduced by some

$115 million without affecting sales volumes or requiring a reduction in the size of the product line.

Raw material costs – through reduced fabric waste

– were also substantially reduced with annual cost savings estimated at $1 million.

EXERCISES 429 This application is based on the article: ‘Blue Bell Trims its Inventory’, JR Edwards, HM Wagner and WP Wood, Interfaces, 15 (1), 1985, pp 34
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52. Copyright is held by the Operations Research Society of America and the Institute of Management Sciences, 290 Westminster Street, Providence, Rhode Island 02093, USA.

(a) Formulate this problem in terms of determining the profit-maximising combination of the two products on a weekly basis.

(b) Solve the problem graphically.

(c) Confirm the solution using simultaneous equations.

(d) Identify the binding and non-binding constraints.

(e) Undertake sensitivity analysis on each of the binding constraints and evaluate the management information that this generates.

(f ) What is it worth to the company to have extra hours available in turning?