13-3In each of the following cases, no shortage is allowed, and the lead time between placing and receiving an order is 35 days. Determine the optimal inventory policy and the associated cost per day.
(a) K = $120, h = $.04, D = 25 units per day
(b) K = $80, h = $.03, D = 35 units per day
(c) K = $100, h = $.02, D = 50 units per day
(d) K = $110, h = $.03, D = 25 units per day
13-4 McBurger orders ground meat at the start of each week to cover the week’s demand of 300 lb. The fixed cost per order is $20. It costs about $.03 per lb per day to refrigerate and store the meat.
(a) Determine the inventory cost per week of the present ordering policy.
(b) Determine the optimal inventory policy that McBurger should use, assuming zero lead time between the placement and receipt of an order.
13-13 Consider the hotel laundry service situation in Problem 13-8. The normal charge for washing a soiled towel is $.60, but the laundry service will charge only $.45 if the hotel delivers them in lots of at least 2600 towels. Should the hotel take advantage of the discount?
13-15 An item sells for $30 a unit, but a 10% discount is offered for lots of 200 units or more. A company uses this item at the rate of 20 units per day. The setup cost for ordering a lot is $50, and the holding cost per unit per day is $.30. The lead time is 15 days. Should the company take advantage of the discount?
13-18 The following data describe five inventory items:11
Item i Ki ($) Di (units per day) hi ($) ai (ft2)
1 35 22 0.35 1.0 2 28 34 0.15 0.8 3 30 14 0.28 1.1 4 25 21 0.30 0.5 5 20 26 0.42 1.2
Total available storage area = 22 ft2
Determine the optimal order quantities.
13-21 The following data describe four inventory items:
Item i Ki ($) Di (units per day) hi ($)
1 100 10 .1 2 50 20 .2 3 90 5 .2 4 20 10 .1
The company wishes to determine the economic order quantity for each of the four items such that the total number of orders per 365-day year is at most 150. Formulate the problem as a nonlinear program, and find the optimum solution.
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