``` ! Perishable product inventory management; ! Our product has a finite shelf life, after which it goes to waste. We must order product in batches or cases. Not all demand need be satisfied, so that there may be lost sales; ! Keywords: Perishable inventory, Shelf life, Lot sizing, Lost sales; SETS: Period: EI, Waste, Order, Sales, Demand, Y; ENDSETS DATA: Life = 2; ! Shelf life = number periods in which product can be sold, before it is out-of-date; FCost = 200; ! Fixed cost of placing an order; SPrice = 75; ! Selling price per unit; PCost = 35; ! Purchase cost per unit; InCase = 12; ! Case size or batch size for ordering, assume >= 1; Demand = 33, 21, 63, 32, 13, 17, 53, 15; ENDDATA ! Order(t) = number cases ordered and arriving at beginning of period t, Y(t) = 1 if we place an order to arrive in period t, EI( t) = units in ending inventory in period t, Waste(t) = number units going to waste/perish in period t; ! Maximize revenues - ( cost/unit of purchase + fixed cost of purchases); MAX = @SUM( Period(t): SPrice*Sales(t) - PCost*InCase*Order(t) - FCost*Y(t)); ! For period 1, Initial inventory is 0; EI(1) + Waste(1) = InCase*Order(1) - Sales(1); Sales(1) <= Demand(1); Order(1) <= Y(1)* @SUM( Period(s) | s #LE# Life: Demand(s)); ! Subsequent periods; @FOR( Period( t) | t #GT# 1: EI(t) + Waste(t) = EI(t-1) + InCase*Order(t) - Sales(t); Sales(t) <= Demand(t); ! (Useful) Ending inventory can be no greater than demand over its shelf life. Any more goes to waste; EI(t) <= @SUM( Period(s) | t #LE# s #AND# s #LT# t+Life: Demand(t)); ! Where p = number periods of shelf life; ! Fixed cost forcing (this could be tighter); Order(t) <= Y(t)* @SUM( Period(s) | t #LE# s #AND# s #LT# t+Life: Demand(t)); ); @FOR( Period(t): @GIN( Order(t)); @BIN( Y(t)); ); ```