Order acceptance with weighted tardiness

A branch and price solution approach for order acceptance and capacity planning in make-to-order operations

“…The constraint sets (3-10) -(3-12) impose the non-negativity restrictions on the decision variables. In particular, the constraint sets (3)(4)(5)(6)(7)(8)(9)(10)(11) and (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) impose the binary restrictions on the decision variables Y and U.…”

“…We introduce a demand-to-capacity ratio (DC ratio) to control the load on the MTO shop-floor. The DC ratio is the ratio of the demand to the regular time capacity available in the MTO operation given by equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13), over the planning horizon with |T| time periods. If we know the total demand and the available resources, we can generate problem instances by computing the number of time periods required for a fixed DC ratio using Equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14).…”

“…In [6], Slotnick and Morton model a manufacturing facility that considers a pool of orders, and chooses for processing the subset that results in the highest profit. In addition to the problem characteristics in [13] they consider customer weight.…”

“…Production is concerned with limited capacity and it tries to maximize utilization and minimize the number of tardy deliveries. Given these conflicting goals of turnover and tardiness, order acceptance decisions are often made without involving production department or with incomplete information on the available capacity in production department [6]. Accepting too many orders, which is the objective of the sales department, leads to an over-loaded production system, in which lead times increase and orders are increasingly delivered late.…”

“…This may lead to lower profit margins or even negative profits. Tardy deliveries may also lead to higher penalty costs, and possibly lead to loss of customer goodwill [6,7].…”