A large electronics manufacturing firm that produces a single product is faced with rapid sales growth. Its planning group is developing an overall capacity-expansion strategy, that would balance the cost of building new capacity, the cost of operating the new and existing facilities, and the cost associated with unmet demand (that has to be subcontracted outside at a higher cost).

 The following model has been proposed to assist in defining an appropriate strategy for the firm.

Decision variables

 Yit                                      A binary integer variable that will be 1 if a facility exists at site i in period t, and 0 otherwise.

(I Y )it                                A binary integer variable that will be 1 if facility is constructed at site i in period                                               t, and 0 otherwise.

 Ait                                    Capacity (sq ft) at site i in period t.

 (I A)it                               The increase in capacity at site i in period t.

 (D A)it                              The decrease in capacity at site i in period t.

 Pit                                     Total units produced at site i in period t.

Ut                                      Total unmet demand (subcontracted) units in period t.

                                          Forecast parameters

Dt                                     Demand in units in period t.

 Cost parameters–Capacity

 sit                                      Cost of operating a facility at site i in period t.

 dit                                     Cost of building a facility at site i in period t.

ait                                      Cost of occupying 1 sq ft of fully equipped capacity at site i in period t.

bit                                     Cost of increasing capacity by 1 sq ft at site i in period t.

Cit                                    Cost of decreasing capacity by 1 sq ft at site i in period t.

 Cost parameters–Production

Ot                                      Cost of unmet demand (subcontracting + opportunity cost) for one unit in period                                             t.

 vit                                     Tax-adjusted variable cost (material + labor + taxes) of producing one unit at site                                             i in period t.

 Productivity parameters

 (pa)it                                Capacity needed (sq ft years) at site i in period t to produce one unit of the                                                       product.

Policy parameters

Fit, Fit                                 Maximum, minimum facility size at site i in period t (if the site exists).

Git                                       Maximum growth (sq ft) of site i in period t.

 Objective function

The model’s objective function is to minimize total cost:

Description of constraints

1. Demand constraint

 2. Productivity constraint

 3. Facility-balance constraint

4. Area-balance constraint

5. Facility-size limits

 6. Growth constraint

 7. Additional constraints

All variables nonnegative. Explain the choice of decision variables, objective function, and constraints. Make a detailed discussion of the model assumptions. Estimate the number of constraints, continuous variables, and integer variables in the model. Is it feasible to solve the model by standard branch-and-bound procedures?

TN Min sis Yit + dir(IY)it t=l i=l TN + air Air + bi(IA)i + sci(DA) t=1 i=l TN T + vPir + , t=l i=l t=l